thermoelectric technical reference

Thermoelectric Technical Reference — Introduction to Thermoelectric Cooling

Ferrotec's Thermoelectric Technical Reference Guide is a comprehensive technical explanation of

thermoelectrics and thermoelectric technology.

1.0 Introduction to Thermoelectric Cooling

1.1 A thermoelectric (TE) cooler, sometimes called a thermoelectric module or Peltier cooler, is a

semiconductor-based electronic component that functions as a small heat pump. By applying a low

voltage DC power source to a TE module, heat will be moved through the module from one side to

the other. One module face, therefore, will be cooled while the opposite face simultaneously is

heated. It is important to note that this phenomenon may be reversed whereby a change in the

polarity (plus and minus) of the applied DC voltage will cause heat to be moved in the opposite

direction. Consequently, a thermoelectric module may be used for both heating and cooling thereby

making it highly suitable for precise temperature control applications.

1.1.1 To provide the new user with a general idea of a thermoelectric cooler's capabilities, it might

be helpful to offer this example. If a typical single-stage thermoelectric module was placed on a

heat sink that was maintained at room temperature and the module was then connected to a

suitable battery or other DC power source, the "cold" side of the module would cool down to

approximately -40°C. At this point, the module would be pumping almost no heat and would have

reached its maximum rated "DeltaT (DT)." If heat was gradually added to the module's cold side,

the cold side temperature would increase progressively until it eventually equaled the heat sink

temperature. At this point the TE cooler would have attained its maximum rated "heat pumping

capacity" (Qmax).

1.2 Both thermoelectric coolers and mechanical refrigerators are governed by the same

fundamental laws of thermodynamics and both refrigeration systems, although considerably

different in form, function in accordance with the same principles.

In a mechanical refrigeration unit, a compressor raises the pressure of a liquid and circulates the

refrigerant through the system. In the evaporator or "freezer" area the refrigerant boils and, in the

process of changing to a vapor, the refrigerant absorbs heat causing the freezer to become cold.

The heat absorbed in the freezer area is moved to the condenser where it is transferred to the

environment from the condensing refrigerant. In a thermoelectric cooling system, a doped

semiconductor material essentially takes the place of the liquid refrigerant, the condenser is

replaced by a finned heat sink, and the compressor is replaced by a DC power source. The

application of DC power to the thermoelectric module causes electrons to move through the

semiconductor material. At the cold end (or "freezer side") of the semiconductor material, heat is

absorbed by the electron movement, moved through the material, and expelled at the hot end.

Since the hot end of the material is physically attached to a heat sink, the heat is passed from the

material to the heat sink and then, in turn, transferred to the environment.

1.3 The physical principles upon which modern thermoelectric coolers are based actually date back

to the early 1800's, although commercial TE modules were not available until almost 1960. The first

important discovery relating to thermoelectricity occurred in 1821 when a German scientist, Thomas

Seebeck, found that an electric current would flow continuously in a closed circuit made up of two

dissimilar metals provided that the junctions of the metals were maintained at two different

temperatures. Seebeck did not actually comprehend the scientific basis for his discovery, however,

and falsely assumed that flowing heat produced the same effect as flowing electric current. In 1834,

a French watchmaker and part time physicist, Jean Peltier, while investigating the "Seebeck Effect,"

found that there was an opposite phenomenon whereby thermal energy could be absorbed at one

dissimilar metal junction and discharged at the other junction when an electric current flowed within

the closed circuit. Twenty years later, William Thomson (eventually known as Lord Kelvin) issued a

comprehensive explanation of the Seebeck and Peltier Effects and described their interrelationship.

At the time, however, these phenomena were still considered to be mere laboratory curiosities and

were without practical application.

In the 1930's Russian scientists began studying some of the earlier thermoelectric work in an effort

to construct power generators for use at remote locations throughout the country. This Russian

interest in thermoelectricity eventually caught the attention of the rest of the world and inspired the

development of practical thermoelectric modules. Today's thermoelectric coolers make use of

modern semiconductor technology whereby doped semiconductor material takes the place of

dissimilar metals used in early thermoelectric experiments.

1.4 The Seebeck, Peltier, and Thomson Effects, together with several other phenomena, form the

basis of functional thermoelectric modules. Without going into too much detail, we will examine

some of these fundamental thermoelectric effects.

1.4.1 SEEBECK EFFECT: To illustrate the Seebeck Effect let us look at a simple thermocouple

circuit as shown in Figure (1.1). The thermocouple conductors are two dissimilar metals denoted as

Material x and Material y.

In a typical temperature measurement application, thermocouple A is used as a "reference" and is

maintained at a relatively cool temperature of Tc. Thermocouple B is used to measure the

temperature of interest (Th) which, in this example, is higher than temperature Tc. With heat

applied to thermocouple B, a voltage will appear across terminals Tl and T2. This voltage (Vo),

known as the Seebeck emf, can be expressed as: Vo = axy x (Th - Tc)

where:

Vo is the output voltage in volts

axy is the differential Seebeck coefficient between the two materials, x and y, in volts/oK

Th and Tc are the hot and cold thermocouple temperatures, respectively, in oK

1.4.2 PELTIER EFFECT: If we modify our thermocouple circuit to obtain the configuration shown in

Figure (1.2), it will be possible to observe an opposite phenomenon known as the Peltier Effect.

If a voltage (Vin) is applied to terminals Tl and T2 an electrical current (I) will flow in the circuit. As

a result of the current flow, a slight cooling effect (Qc) will occur at thermocouple junction A where

heat is absorbed and a heating effect (Qh) will occur at junction B where heat is expelled. Note that

this effect may be reversed whereby a change in the direction of electric current flow will reverse

the direction of heat flow. The Peltier effect can be expressed mathematically as:

Qc or Qh=pxy x I

Where: pxy is the differential Peltier coefficient between the two materials, x and y, in volts I is the

electric current flow in amperes Qc, Qh is the rate of cooling and heating, respectively, in watts

Joule heating, having a magnitude of I x R (where R is the electrical resistance), also occurs in the

conductors as a result of current flow. This Joule heating effect acts in opposition to the Peltier

effect and causes a net reduction of the available cooling.

1.4.3 THOMSON EFFECT: When an electric current is passed through a conductor having a

temperature gradient over its length, heat will be either absorbed by or expelled from the

conductor. Whether heat is absorbed or expelled depends upon the direction of both the electric

current and temperature gradient. This phenomenon, known as the Thomson Effect, is of interest in

respect to the principles involved but plays a negligible role in the operation of practical

thermoelectric modules. For this reason, it is ignored.

Thermoelectric Technical Reference — Basic Principles of Thermoelectric Materials



2.0 Basic Principles of Thermoelectric Modules & Materials

2.1 THERMOELECTRIC MATERIALS: The thermoelectric semiconductor material most often used

in today's TE coolers is an alloy of Bismuth Telluride that has been suitably doped to provide

individual blocks or elements having distinct "N" and "P" characteristics. Thermoelectric materials

most often are fabricated by either directional crystallization from a melt or pressed powder

metallurgy. Each manufacturing method has its own particular advantage, but directionally grown

materials are most common. In addition to Bismuth Telluride (Bi2Te3), there are other

thermoelectric materials including Lead Telluride (PbTe), Silicon Germanium (SiGe), and Bismuth-

Antimony (Bi-Sb) alloys that may be used in specific situations. Figure (2.1) illustrates the relative

performance or Figure-of-Merit of various materials over a range of temperatures. It can be seen

from this graph that the performance of Bismuth Telluride peaks within a temperature range that is

best suited for most cooling applications.

APPROXIMATE FIGURE-OF-MERIT(Z)FOR VARIOUS TE MATERIALS

Figure (2.1) Performance of Thermoelectric Materials at Various Temperatures

2.1.1 BISMUTH TELLURIDE MATERIAL: Crystalline Bismuth Telluride material has several

characteristics that merit discussion. Due to the crystal structure, Bi2Te3 is highly anisotropic in

nature. This results in the material's electrical resistivity being approximately four times greater

parallel to the axis of crystal growth (C-axis) than in the perpendicular orientation. In addition,

thermal conductivity is about two times greater parallel to the C-axis than in the perpendicular

direction. Since the anisotropic behavior of resistivity is greater than that of thermal conductivity,

the maximum performance or Figure-of-Merit occurs in the parallel orientation. Because of this

anisotropy, thermoelectric elements must be assembled into a cooling module so that the crystal

growth axis is parallel to the length or height of each element and, therefore, perpendicular to the

ceramic substrates.

There is one other interesting characteristic of Bismuth Telluride that also is related to the material's

crystal structure. Bi2Te3 crystals are made up of hexagonal layers of similar atoms.

While layers of Bismuth and Tellurium are held together by strong covalent bonds, weak van der

Waals bonds link the adjoining [Te¹] layers. As a result, crystalline Bismuth Telluride cleaves readily

along these [Te¹][Te¹] layers, with the behavior being very similar to that of Mica sheets.

Fortunately, the cleavage planes generally run parallel to the C-axis and the material is quite strong

when assembled into a thermoelectric cooling module.

2.1.2 Bismuth Telluride material, when produced by directional crystallization from a melt, typically

is fabricated in ingot or boule form and then sliced into wafers of various thicknesses. After the

wafer's surfaces have been properly prepared, the wafer is then diced into blocks that may be

assembled into thermoelectric cooling modules. The blocks of Bismuth Telluride material, which

usually are called elements or dice, also may be manufactured by a pressed powder metallurgy

process.

2.2 THERMOELECTRIC COOLING MODULES: A practical thermoelectric cooler consists of two or

more elements of semiconductor material that are connected electrically in series and thermally in

parallel. These thermoelectric elements and their electrical interconnects typically are mounted

between two ceramic substrates. The substrates serve to hold the overall structure together

mechanically and to insulate the individual elements electrically from one another and from external

mounting surfaces. After integrating the various component parts into a module, thermoelectric

modules ranging in size from approximately 2.5-50 mm (0.1 to 2.0 inches) square and 2.5-5mm

(0.1 to 0.2 inches) in height may be constructed.

Figure (2.2) Schematic Diagram of a Typical Thermoelectric Cooler

2.2.1 Both N-type and P-type Bismuth Telluride thermoelectric materials are used in a

thermoelectric cooler. This arrangement causes heat to move through the cooler in one direction

only while the electrical current moves back and forth alternately between the top and bottom

substrates through each N and P element. N-type material is doped so that it will have an excess of

electrons (more electrons than needed to complete a perfect molecular lattice structure) and P-type

material is doped so that it will have a deficiency of electrons (fewer electrons than are necessary to

complete a perfect lattice structure). The extra electrons in the N material and the "holes" resulting

from the deficiency of electrons in the P material are the carriers which move the heat energy

through the thermoelectric material. Figure (2.2) shows a typical thermoelectric cooler with heat

being moved as a result of an applied electrical current (I). Most thermoelectric cooling modules are

fabricated with an equal number of N-type and P-type elements where one N and P element pair

form a thermoelectric "couple." The module illustrated in Figure (2.2) has two pairs of N and P

elements and is termed a "two-couple module".

Heat flux (heat actively pumped through the thermoelectric module) is proportional to the

magnitude of the applied DC electric current. By varying the input current from zero to maximum, it

is possible to adjust and control the heat flow and temperature.

Thermoelectric Technical Reference — Applications of Thermoelectric Coolers



3.0 Applications for Thermoelectric Coolers

3.1 Applications for thermoelectric modules cover a wide spectrum of product areas. These include

equipment used by military, medical, industrial, consumer, scientific/laboratory, and

telecommunications organizations. Uses range from simple food and beverage coolers for an

afternoon picnic to extremely sophisticated temperature control systems in missiles and space

vehicles.

Unlike a simple heat sink, a thermoelectric cooler permits lowering the temperature of an object

below ambient as well as stabilizing the temperature of objects which are subject to widely varying

ambient conditions. A thermoelectric cooler is an active cooling module whereas a heat sink

provides only passive cooling.

Thermoelectric coolers generally may be considered for applications that require heat removal

ranging from milliwatts up to several thousand watts. Most single-stage TE coolers, including both

high and low current modules, are capable of pumping a maximum of 3 to 6 watts per square

centimeter (20 to 40 watts per square inch) of module surface area. Multiple modules mounted

thermally in parallel may be used to increase total heat pump performance. Large thermoelectric

systems in the kilowatt range have been built in the past for specialized applications such as cooling

within submarines and railroad cars. Systems of this magnitude are now proving quite valuable in

applications such as semiconductor manufacturing lines.

3.2 Typical applications for thermoelectric modules include:

Avionics

Black Box Cooling

Calorimeters

CCD (Charged Couple Devices)

CID (Charge Induced Devices)

Cold Chambers

Cold Plates

Compact Heat Exchangers

Constant Temperature Baths

Dehumidifiers

Dew Point Hygrometers

Electronics Package Cooling

Electrophoresis Cell Coolers

Environmental Analyzers

Heat Density Measurement

Ice Point References

Immersion Coolers

Integrated Circuit Cooling

Inertial Guidance Systems

Infrared Calibration Sources and Black Body References

Infrared Detectors

Infrared Seeking Missiles

Laser Collimators

Laser Diode Coolers

Long Lasting Cooling Devices

Low Noise Amplifiers

Microprocessor Cooling

Microtome Stage Coolers

NEMA Enclosures

Night Vision Equipment

Osmometers

Parametric Amplifiers

Photomultiplier Tube Housing

Power Generators (small)

Precision Device Cooling (Lasers and Microprocessors)

Refrigerators and on-board refrigeration systems (Aircraft, Automobile, Boat, Hotel, Insulin,

Portable/Picnic, Pharmaceutical, RV)

Restaurant Portion Dispenser

Self-Scanned Arrays Systems

Semiconductor Wafer Probes

Stir Coolers

Thermal Viewers and Weapons Sights

Thermal Cycling Devices (DNA and Blood Analyzers)

Thermostat Calibrating Baths

Tissue Preparation and Storage

Vidicon Tube Coolers

Wafer Thermal Characterization

Water and Beverage Coolers

Wet Process Temperature Controller

Wine Cabinets Thermoelectric Technical Reference — Advantages of Thermoelectric Cooling



4.0 Advantages of Thermoelectric Cooling

4.1 The use of thermoelectric modules often provides solutions, and in some cases the ONLY

solution, to many difficult thermal management problems where a low to moderate amount of heat

must be handled. While no one cooling method is ideal in all respects and the use of thermoelectric

modules will not be suitable for every application, TE coolers will often provide substantial

advantages over alternative technologies. Some of the more significant features of thermoelectric

modules include:

No Moving Parts: A TE module works electrically without any moving parts so they are virtually

maintenance free.

Small Size and Weight: The overall thermoelectric cooling system is much smaller and lighter

than a comparable mechanical system. In addition, a variety of standard and special sizes and

configurations are available to meet strict application requirements.

Ability to Cool Below Ambient: Unlike a conventional heat sink whose temperature necessarily

must rise above ambient, a TE cooler attached to that same heat sink has the ability to reduce the

temperature below the ambient value.

Ability to Heat and Cool With the Same module: Thermoelectric coolers will either heat or cool

depending upon the polarity of the applied DC power. This feature eliminates the necessity of

providing separate heating and cooling functions within a given system.

Precise Temperature Control: With an appropriate closed-loop temperature control circuit, TE

coolers can control temperatures to better than +/- 0.1°C.

High Reliability: Thermoelectric modules exhibit very high reliability due to their solid state

construction. Although reliability is somewhat application dependent, the life of typical TE coolers is

greater than 200,000 hours.

Electrically "Quiet" Operation: Unlike a mechanical refrigeration system, TE modules generate

virtually no electrical noise and can be used in conjunction with sensitive electronic sensors. They

are also acoustically silent.

Operation in any Orientation: TEs can be used in any orientation and in zero gravity

environments. Thus they are popular in many aerospace applications.

Convenient Power Supply: TE modules operate directly from a DC power source. Modules having

a wide range of input voltages and currents are available. Pulse Width Modulation (PWM) may be

used in many applications

Spot Cooling: With a TE cooler it is possible to cool one specific component or area only, thereby

often making it unnecessary to cool an entire package or enclosure.

Ability to Generate Electrical Power: When used "in reverse" by applying a temperature

differential across the faces of a TE cooler, it is possible to generate a small amount of DC power.

Environmentally Friendly: Conventional refrigeration systems can not be fabricated without using

chlorofluorocarbons or other chemicals that may be harmful to the environment. Thermoelectric

devices do not use or generate gases of any kind.

Thermoelectric Technical Reference — Heat Sink Considerations



5.0 Heat Sink Considerations

5.1 Rather than being a heat absorber that consumes heat by magic, a thermoelectric cooler is a

heat pump which moves heat from one location to another. When electric power is applied to a TE

module, one face becomes cold while the other is heated. In accordance with the laws of

thermodynamics, heat from the (warmer) area being cooled will pass from the cold face to the hot

face. To complete the thermal system, the hot face of the TE cooler must be attached to a suitable

heat sink that is capable of dissipating both the heat pumped by the module and Joule heat created

as a result of supplying electrical power to the module.

A heat sink is an integral part of a thermoelectric cooling system and its importance to total system

performance must be emphasized. Since all operational characteristics of TE devices are related to

heat sink temperature, heat sink selection and design should be considered carefully.

A perfect heat sink would be capable of absorbing an unlimited quantity of heat without exhibiting

any increase in temperature. Since this is not possible in practice, the designer must select a heat

sink that will have an acceptable temperature rise while handling the total heat flow from the TE

device(s). The definition of an acceptable increase in heat sink temperature necessarily is

dependent upon the specific application, but because a TE module's heat pumping capability

decreases with increasing temperature differential, it is highly desirable to minimize this value. A

heat sink temperature rise of 5 to 15°C above ambient (or cooling fluid) is typical for many

thermoelectric applications.

Several types of heat sinks are available including natural convection, forced convection, and liquid-

cooled. Natural convection heat sinks may prove satisfactory for very low power applications

especially when using small TE devices operating at 2 amperes or less. For the majority of

applications, however, natural convection heat sinks will be unable to remove the required amount

of heat from the system, and forced convection or liquid-cooled heat sinks will be needed.

Heat sink performance usually is specified in terms of thermal resistance (Q):

Qs=

Ts - Ta

____________

Q

where:

Qs = Thermal Resistance in Degrees C per Watt

Ts = Heat Sink Temperature in Degrees C

Ta =Ambient or Coolant Temperature in Degrees C

Q = Heat Input to Heat Sink in Watts

5.2 Each thermoelectric cooling application will have a unique heat sink requirement and frequently

there will be various mechanical constraints that may complicate the overall design. Because each

case is different, it is virtually impossible to suggest one heat sink configuration suitable for most

situations. We have several off the shelf heat sinks and liquid heat exchangers appropriate for many

applications but encourage you to contact our engineering department.

Note that when combining thermoelectric cooling modules and heat sinks into a total thermal

system, it normally is NOT necessary to take into account heat loss or temperature rise at the

module to heat sink junctions. Module performance data presented herein already includes such

losses based on the use of thermal grease at both hot and cold interfaces. When using commercially

available heat sinks for thermoelectric cooler applications, it is important to be aware that some off-

the-shelf units do not have adequate surface flatness. A flatness of 1mm/m (0.001 in/in) or better

is recommended for satisfactory thermal performance and it may be necessary to perform an

additional lapping, flycutting, or grinding operation to meet this flatness specification.

5.2.1 NATURAL CONVECTION HEAT SINKS: Natural convection heat sinks normally are useful

only for low power applications where very little heat is involved. Although it is difficult to

generalize, most natural convection heat sinks have a thermal resistance (Qs) greater than

0.5°C/watt and often exceeding 10°C/watt. A natural convection heat sink should be positioned so

that (a) the long dimension of the fins is in the direction of normal air flow, vertical operation

improves natural convection and (b) there are no significant physical obstructions to impede air

flow. It also is important to consider that other heat generating components located near the heat

sink may increase the ambient air temperature, thereby affecting overall performance.

5.2.2 FORCED CONVECTION HEAT SINKS: Probably the most common heat-sinking

method used with thermoelectric coolers is forced convection. When compared to natural convection

heat sinks, substantially better performance can be realized. The thermal resistance of quality

forced convection systems typically falls within a range of 0.02 to 0.5°C/watt. Many standard heat

sink extrusions are available that, when coupled with a suitable fan, may be used to form the basis

of a complete cooling assembly. Cooling air may be supplied from a fan or blower and may either be

passed totally through the length of the heat sink or may be directed at the center of the fins and

pass out both open ends. This second air flow pattern, illustrated in Figure (5.l), generally provides

the best performance since the air blown into the face of the heat sink creates greater turbulence

resulting in improved heat transfer. For optimum performance, the housing of an axial fan should be

mounted a distance of 8-20mm (0.31-0.75") from the fins. Other configurations may be considered

depending on the application.

Figure (5.1) Forced Convection Heat Sink System Showing Preferred Air Flow

The thermal resistance of heat sink extrusions often is specified at an air flow rate stated in terms of

velocity whereas the output of most fans is given in terms of volume. The conversion from volume

to velocity is:

Velocity = Volume / Cross-sectional Area of Air Passage

or: Linear Feet per Minute = Cubic Feet per Minute / Area in Square Feet

or: Linear Meters per Minute = Cubic Meters per Minute / Area in Square Meters

5.2.3 LIQUID COOLED HEAT SINKS: Liquid cooled heat sinks provide the highest thermal

performance per unit volume and, when optimally designed, can exhibit a very low thermal

resistance. Although there are many exceptions, the thermal resistance of liquid cooled heat sinks

typically falls between 0.01 and 0.1°C/watt. Simple liquid heat sinks can be constructed by

soldering copper tubing onto a flat copper plate or by drilling holes in a metal block through which

water may pass. With greater complexity (and greater thermal performance), an elaborate

serpentine water channel may be milled in a copper or aluminum block that later is sealed-off with a

cover plate. We offer several liquid-type heat sinks that may be used advantageously in

thermoelectric systems. With other commercial heat sinks, always check the surface flatness prior

to installation. While liquid cooling may be considered undesirable and/or unsatisfactory for many

applications, it may be the only viable approach in specific situations.

Thermoelectric Technical Reference — Installation of Thermoelectric Modules



6.0 Installation of Thermoelectric Modules

This section of the technical reference guide explaines the techniques that can used to install or

mount a thermoelectric module or peltier cooler including:

» Clamping

» Bonding with Epoxy

» Soldering

» Mounting Pads and other Material

http://www.ferrotec.com/technology/thermoelectric/thermalRef06/




6.1 Important Installation Considerations

Techniques used to install thermoelectric modules in a cooling system are extremely important.

Failure to observe certain basic principles may result in unsatisfactory performance or reliability.

Some of the factors to be considered in system design and module installation include the following:

Thermoelectric modules have high mechanical strength in the compression mode but shear

strength is relatively low. As a result, a TE cooler should not be designed into a system

where it serves as a significant supporting member of the mechanical structure.

All interfaces between system components must be flat, parallel, and clean to minimize

thermal resistance. High conductivity thermal interface material is often used to ensure

good contact between surfaces.

The "hot" and "cold" sides of standard thermoelectric modules may be identified by the

position of the wire leads. Wires are attached to the hot side of the module, which is the

module face that is in contact with the heat sink. For modules having insulated wire leads,

when the red and black leads are connected to the respective positive and negative

terminals of a DC power supply, heat will be pumped from the module's cold side, through

the module, and into the heat sink. Note that for TE modules having bare wire leads, the

positive connection is on the right side and the negative connection is on the left when the

leads are facing toward the viewer and the substrate with the leads attached presented on

the bottom.

When cooling below ambient, the object being cooled should be insulated as much as

possible to minimize heat loss to the ambient air. To reduce convective losses, fans should

not be positioned so that air is blowing directly at the cooled object. Conductive losses also

may be minimized by limiting direct contact between the cooled object and external

structural members.

When cooling below the dew point, moisture or frost will tend to form on exposed cooled

surfaces. To prevent moisture from entering a TE module and severely reducing its thermal

performance, an effective moisture seal should be installed. This seal should be formed

between the heat sink and cooled object in the area surrounding the TE module(s). Flexible

foam insulating tape or sheet material and/or silicone rubber RTV are relatively easy to

install and make an effective moisture seal. Several methods for mounting thermoelectric

modules are available and the specific product application often dictates the method to be

used. Possible mounting techniques are outlined in the following paragraphs.

6.1.1 HEIGHT TOLERANCE: Most thermoelectric cooling modules are available with two height

tolerance values, +/-0.3mm (+/-0.010") and +/-0.03mm (0.001"). When only one module is used

in a thermoelectric subassembly, a +/-0.3mm tolerance module generally is preferable since it

provides a slight cost advantage over a comparable tight-tolerance module. For applications where

more than one module is to be mounted between the heat sink and cooled object, however, it is

necessary to closely match the thickness of all modules in the group to ensure good heat transfer.

For this reason, +/-0.03mm (+/-0.001") tolerance modules should be used in all multiple-module

configurations.

6.2 Clamping

The most common mounting method involves clamping the thermoelectric module(s) between a

heat sink and flat surface of the article to be cooled. This approach, as illustrated in Figure (6.1),

usually is recommended for most applications and may be applied as follows:


a) Machine or grind flat the mounting surfaces between which the TE module(s) will be located. To

achieve optimum thermal performance mounting surfaces should be flat to within 1mm/m (0.001

in/in).

b) If several TE modules are mounted between a given pair of mounting surfaces, all modules

within the group must be matched in height/thickness so that the overall thickness variation does

not exceed 0.06mm (0.002"). Module P/N with a "B" ending should be specified.

c) Mounting screws should be arranged in a

symmetrical pattern relative to the module(s) so as

to provide uniform pressure on the module(s)

when the assembly is clamped together. To

minimize heat loss through the mounting screws, it

is desirable to use the smallest size screw that is

practical for the mechanical system. For most

applications, M3 or M3.5 (4-40 or 6-32) stainless

steel screws will prove satisfactory. Alternately,

nonmetallic fasteners can be used, e.g., nylon.

Smaller screws may be used in conjunction with

very small mechanical assemblies. Belleville

spring washers or split lock-washers should be

used under the head of each screw to maintain

even pressure during the normal thermal

expansion or contraction of system components.

d) Clean the module(s) and mounting surfaces to ensure that all burrs, dirt, etc., have been

removed.

e) Coat the "hot" side of the module(s) with a thin layer (typically 0.02mm / 0.001" or less

thickness) of thermally conductive grease and place the module, hot side down, on the heat sink in

the desired location. Gently push down on the module and apply a back and forth turning motion to

squeeze out excess thermal grease. Continue the combined downward pressure and turning motion

until a slight resistance is detected. Ferrotec America recommends and stocks American Oil and

Supply (AOS) type 400 product code 52032.

f) Coat the "cold" side of the module(s) with thermal grease as specified in step (e) above. Position

and place the object to be cooled in contact with the cold side of the module(s). Squeeze out the

excess thermal grease as previously described.

g) Bolt the heat sink and cooled object together using the stainless steel screws and spring

washers. It is important to apply uniform pressure across the mounting surfaces so that good

parallelism is maintained. If significantly uneven pressure is applied, thermal performance may be

reduced, or worse, the TE module(s) may be damaged. To ensure that pressure is applied

uniformly, first tighten all mounting screws finger tight starting with the center screw (if any). Using

a torque screwdriver, gradually tighten each screw by moving from screw to screw in a crosswise

pattern and increase torque in small increments. Continue the tightening procedure until the proper

torque value is reached. Typical mounting pressure ranges from 25 - 100 psi depending on the

application. If a torque screwdriver is not available, the correct torque value may be approximated

by using the following procedure:

In a crosswise pattern, tighten the screws until they are "snug" but not actually tight. In the same

crosswise pattern, tighten each screw approximately one quarter turn until the spring action of the

washer can be felt.

h) A small additional amount of thermal grease normally is squeezed out soon after the assembly is

first clamped together. In order to insure that the proper screw torque is maintained, wait a

minimum of one hour and recheck the torque by repeating step (g) above.

i) CAUTION: Over-tightening of the clamping screws may result in bending or bowing of either the

heat sink or cold object surface especially if these components are constructed of relatively thin

material. Such bowing will, at best, reduce thermal performance and in severe cases may cause

physical damage to system components. Bowing may be minimized by positioning the clamping

screws close to the thermoelectric module(s) and by using moderately thick materials. However, if

hot and/or cold surfaces are constructed of aluminum which is less than 6mm (0.25") thick or

copper which is less than 3.3mm (0.13") thick, it may be necessary to apply screw torque of a lower

value than specified in step (g) above.

Figure (6.1)

TE Module Installation Using the Clamping Method The proper bolt torque for TE module assemblies

can be determined by the following relationship:

T=((Sa x A)/N) x K x d

Where:

T= torque on each bolt

Sa= cycling 25-50 psi, static 50-75 psi.

A= total surface area of module(s)

N= number of bolts used in assembly

K= torque coefficient (use K=0.2 for steel, K=0.15 for nylon)

d= nominal bolt diameter

For steel fasteners, we typically recommend either:

6-32 d=.138 in (.350 cm)

4-40 d=.112 in (.284 cm)

The following recommended torque is calculated for nine 9500/065/018 modules held by four 4-40

steel fasteners:

T=((75 lbs/in.2 x (.44" x .48") x 9)/4)x 0.2 x .112 in. = 0.8 in-lbs.

6.3 BONDING WITH EPOXY

A second module mounting method that is useful for certain applications involves bonding the

module(s) to one or both mounting surfaces using a special high thermal-conductivity epoxy

adhesive. Since the coefficients of expansion of the module's ceramics, heat sink and cooled object

vary, we do not recommend bonding with epoxy for larger modules. Please consult your applications

engineer for guidance. Note: Unless suitable procedures are used to prevent outgassing, epoxy

bonding is not recommended if the TE cooling system is to be used in a vacuum. For module

mounting with epoxy:

a) Machine or grind flat the mounting surfaces between which the TE module(s) will be located.

Although surface flatness is less critical when using epoxy, it is always desirable for mounting

surfaces to be as flat as possible.

b) Clean and degrease the module(s) and mounting surfaces to insure that all burrs, oil, dirt, etc.,

have been removed. Follow the epoxy manufacturer's recommendations regarding proper surface

preparation.

c) Coat the hot side of the module with a thin layer of the thermally conductive epoxy and place the

module, hot side down, on the heat sink in the desired location. Gently push down on the module

and apply a back and forth turning motion to squeeze out excess epoxy. Continue the combined

downward pressure and turning motion until a slight resistance is detected.

d) Weight or clamp the module in position until the epoxy has properly cured. Consult the epoxy

manufacturer's data sheet for specific curing information. If an oven cure is specified, be sure that

the maximum operating temperature of the TE module is not exceeded during the heating

procedure. Note that most TE cooling modules manufactured by Ferrotec have maximum operating

temperatures of 200°C for the 95-Series.

6.4 SOLDERING

Thermoelectric modules that have metallized external faces may be soldered into an assembly

provided that reasonable care is taken to prevent module overheating. Soldering to a rigid

structural member of an assembly should be performed on one side of the module only (normally

the hot side) in order to avoid excessive mechanical stress on the module. Note that with a

module's hot side soldered to a rigid body, however, a component or small electronic circuit may be

soldered to the module's cold side provided that the component or circuit is not rigidly coupled to

the external structure. Good temperature control must be maintained within the soldering system in

order to prevent damage to the TE module due to overheating. Our thermoelectric modules are

rated for continuous operation at relatively high temperatures (150 or 200°C) so they are suitable

in most applications where soldering is desirable. Naturally these relative temperatures should not

be exceeded in the process. Since the coefficients of expansion of the module ceramics, heat sink

and cooled object vary, we do not recommend soldering modules larger than 15 x 15 millimeters.

Soldering should not be considered in any thermal cycling application. For module mounting with

solder, the following steps should be observed:

a) Machine or grind flat the mounting surface on which the module(s) will be located. Although

surface flatness is not highly critical with the soldering method, it is always desirable for mounting

surfaces to be as flat as possible. Obviously, the heat sink surface must be a solderable material

such as copper or copper plated material.

b) Clean and degrease the heat sink surface and remove any heavy oxidation. Make sure that there

are no burrs, chips, or other foreign material in the module mounting area.

c) Pre tin the heat sink surface in the module mounting area with the appropriate solder. The

selected solder must have a melting point that is less than or equal to the rated maximum operating

temperature of the TE device being installed. When tinning the heat sink with solder, the heat sink's

temperature should be just high enough so that the solder will melt but in no case should the

temperature be raised more than the maximum value specified for the TE device.

d) Apply soldering flux to the TE module's hot side and place the module on the pre tinned area of

the heat sink. Allow the module to "float" in the solder pool and apply a back and forth turning

motion on the module to facilitate solder tinning of the module surface. A tendency for the module

to drag on the solder surface rather than to float is an indication that there is an insufficient amount

of solder. In this event, remove the module and add more solder to the heat sink.

e) After several seconds the module surface should be tinned satisfactorily. Clamp or weight the

module in the desired position, remove the heat sink from the heat source, and allow the assembly

to cool. When sufficiently cooled, degrease the assembly to remove flux residue.

6.5 Mounting Pads And Other Material

There are a wide variety of products available designed to replace thermally conductive grease as

an interface material. Perhaps the most common are silicon-based mounting pads. Originally for use

in mounting semiconductor devices, these pads often exhibit excessive thermal resistance in

thermoelectric applications. Since the pads allow for rapid production and eliminate cleanup time,

they are popular in less demanding applications. Leading manufacturers in this area include The

Bergquist Company and the Chomerics Division of Parker Hannifin Corporation.

Thermoelectric Technical Reference — Power Supply Requirements



7.0 Power Supply Requirements

7.1 Thermoelectric coolers operate directly from DC power suitable power sources can range from

batteries to simple unregulated "brute force" DC power supplies to extremely sophisticated closed-

loop temperature control systems. A thermoelectric cooling module is a low-impedance

semiconductor device that presents a resistive load to its power source. Due to the nature of the

Bismuth Telluride material, modules exhibit a positive resistance temperature coefficient of

approximately 0.5 percent per degree C based on average module temperature. For many

noncritical applications, a lightly filtered conventional battery charger may provide adequate power

for a TE cooler provided that the AC ripple is not excessive. Simple temperature control may be

obtained through the use of a standard thermostat or by means of a variable-output DC power

supply used to adjust the input power level to the TE device. In applications where the thermal load

is reasonably constant, a manually adjustable DC power supply often will provide temperature

control on the order of +/- 1°C over a period of several hours or more. Where precise temperature

control is required, a closed-loop (feedback) system generally is used whereby the input current

level or duty cycle of the thermoelectric device is automatically controlled. With such a system,

temperature control to +/- 0.1°C may be readily achieved and much tighter control is not unusual.

7.2 Power supply ripple filtering normally is of less importance for thermoelectric devices than for

typical electronic applications. However we recommend limiting power supply ripple to a maximum

of 10 percent with a preferred value being < 5%.

7.2.1 Multistage cooling and low-level signal detection are two applications which may require lower

values of power supply ripple. In the case of multistage thermoelectric devices, achieving a large

temperature differential is the typical goal, and a ripple component of less than two percent may be

necessary to maximize module performance. In situations where very low level signals must be

detected and/or measured, even though the TE module itself is electrically quiet, the presence of an

AC ripple signal within the module and wire leads may be unsatisfactory. The acceptable level of

power supply ripple for such applications will have to be determined on a case-by-case basis.

7.3 Figure (7.1) illustrates a simple power supply capable of driving a 71-couple, 6-ampere module.

This circuit features a bridge rectifier configuration and capacitive-input filter. With suitable

component changes, a full-wave-center-tap rectifier could be used and/or a filter choke added

ahead of the capacitor. A switching power supply, having a size and weight advantage over a

comparable linear unit, also is appropriate for powering thermoelectric devices.

Figure (7.1)

Simple Power Supply to Drive a 71-Couple, 6-Ampere TE Module

7.4 A typical analog closed-loop temperature controller is illustrated in Figure (7.2). This system is

capable of closely controlling and maintaining the temperature of an object and will automatically

correct for temperature variations by means of the feedback loop. Many variations of this system

are possible including adaptation to digital and/or computer control.

Figure (7.2)

Block Diagram of a Typical Closed-Loop Temperature Controller

Thermoelectric Technical Reference — Thermal System Design Considerations



8.0 Thermal System Design Considerations

8.1 The first step in the design of a thermoelectric cooling system involves making an analysis of

the system's overall thermal characteristics. This analysis, which may be quite simple for some

applications or highly complex in other cases, must never be neglected if a satisfactory and efficient

design is to be realized. Some of the more important factors to be considered are discussed in the

following paragraphs. Although we have made certain simplifications that may horrify the pure

thermodynamicist, the results obtained have been found to satisfy all but those few applications

that approach state-of-the-art limits.

Please note that design information contained in this manual is presented for the purpose of

assisting those engineers and scientists who wish either to estimate cooling requirements or to

actually develop their own cooling systems. For the many individuals who prefer not to become

involved in the details of the thermoelectric design process, however, we encourage you to contact

us for assistance. Ferrotec America is committed to providing strong customer technical support and

our engineering staff is available to assist in complex thermoelectric-related design activities.

8.2 ACTIVE HEAT LOAD: The active heat load is the actual heat generated by the component,

"black box" or system to be cooled. For most applications, the active load will be equal to the

electrical power input to the article being cooled (Watts = Volts x Amps) but in other situations the

load may be more difficult to determine. Since the total electrical input power generally represents

the worst case active heat load, we recommend that you use this value for design purposes.

8.3 PASSIVE HEAT LOAD: The passive heat load (sometimes called heat leak or parasitic heat

load) is that heat energy which is lost or gained by the article being cooled due to conduction,

convection, and/or radiation. Passive heat losses may occur through any heat-conductive path

including air, insulation, and electrical wiring. In applications where there is no active heat

generation, the passive heat leak will represent the entire heat load on the thermoelectric cooler.

Determination of the total heat leak within a cooling system is a relatively complicated issue but a

reasonable estimate of these losses often can be made by means of some basic heat transfer

calculations. If there is any uncertainty about heat losses in a given design, we highly recommend

that you contact our engineering staff for assistance and suggestions.

8.4 HEAT TRANSFER EQUATIONS: Several fundamental heat transfer equations are presented to

assist the engineer in evaluating some of the thermal aspects of a design or system.

8.4.1 HEAT CONDUCTION THROUGH A SOLID MATERIAL: The relationship that describes the

transfer of heat through a solid material was suggested by J.B. Fourier in the early 1800's. Thermal

conduction is dependent upon the geometry and thermal conductivity of a given material plus the

existing temperature gradient through the material. Although thermal conductivity varies with

temperature, the actual variation is quite small and can be neglected for our purposes.

Mathematically, heat transfer by conduction may be expressed as:

Q=(K)(DT)(A)

x

Symbol Definition English

Units Metric Units

Q Heat Conducted Through the

Material BTU/hour watts

K Thermal conductivity of the material BTU/hour-

ftoF

watts/meter-oC

A Cross-sectional area of the material square feet square

meters

x Thickness of length of the materials feet meters

DT Temperature difference between

cold and hot sides of the material Degrees F Degrees C

8.4.2 HEAT TRANSFER FROM AN EXPOSED SURFACE TO AMBIENT BY CONVECTION: Heat

leak to or from an uninsulated metal surface can constitute a significant heat load in a thermal

system. Isaac Newton proposed the relationship describing the transfer of heat when a cooled (or

heated) surface is exposed directly to the ambient air. To account for the degree of thermal

coupling between the surface and surrounding air, a numerical value (h), called the Heat Transfer

Coefficient, must be incorporated into the equation. Heat lost or gained in this manner may be

expressed mathematically as: Q=(h)(A)(DT)


Units Metric Units

Q Heat transferred to or from ambient BTU/hour watts

h

Heat transfer coefficient.

For still air use a value of:

For turbulent air use a value of:

BTU/hour-

ft2-oF

4 to 5

15 to 20

watts/meter2-

oC

23 to 28

85 to 113

A Area of the exposed surface square feet square

meters

DT Temperature difference between

the exposed surface and ambient Degrees F Degrees C

8.4.3 HEAT TRANSFER THROUGH THE WALLS OF AN INSULATED ENCLOSURE: Heat leak to

or from an insulated container combines an element of thermal conduction through the insulating

material with an element of convection loss at the external insulation surfaces. Heat lost from (or

gained by) an insulated enclosure may be expressed mathematically as:

Q = (A)(DT)

x + 1

K h


Units Metric Units

Q Heat conducted through the

enclosure BTU/hour watts

K Thermal conductivity of the

insulation

BTU/hour-

ftoF

watts/meter-oC

A External surface area of the

enclosure square feet

square

meters

x Thickness of the insulation feet meters

DT

Temperature difference between

the inside and outside of the

enclosure

Degrees F Degrees C

h

Heat transfer coefficient

For still air use a value of:

For turbulent air use a value of:

BTU/hour-

ft2-oF

4 to 5

15 to 20

watts/meter2-

oC

23 to 28

85 to 113

8.4.4 TIME NEEDED TO CHANGE THE TEMPERATURE OF AN OBJECT: Determination of the

time required to thermoelectrically cool or heat a given object is a moderately complicated matter.

For good accuracy, it would be necessary to make a detailed analysis of the entire thermal system

including all component parts and interfaces. By using the simplified method presented here,

however, it is possible to make a reasonable estimate of a system's thermal transient response.

(m)(Cp)(DT) t =

Q


Units

Metric

Units

t Time period for temperature

change hours seconds

m Weight of material pounds grams

Cp Specific heat of the material BTU/pound-oF calgram-

oC

DT Temperature change of the

material Degrees F Degrees C

Q Heat transferred to or from material BTU/hour cal/second

Note (1): 1 Watt = 0.239 calories/second

Note (2):Thermoelectric modules pump heat at a rate that is proportional to the temperature

difference (DT) across the module. In order to approximate actual module performance, the

average heat removal rate should be used when determining the transient behavior of a thermal

system. The average heat removal rate is:

Q = 0.5 (Qc at DTmin + Qc at DTmax)

Where: Qc at DTmin is the amount of heat a thermoelectric module is pumping at the initial object

temperature when DC power is first applied to the module. The DT is zero at this time and the heat

pumping rate is at the highest point.

Qc at DTmax is the amount of heat a thermoelectric module is pumping when the object has cooled to

the desired temperature. The DT is higher at this time and the heat pumping rate is lower.

8.4.5 HEAT TRANSFER FROM A BODY BY RADIATION: Most thermoelectric cooling applications

involve relatively moderate temperatures and small surface areas where radiation heat losses

usually are negligible. Probably the only situation where thermal radiation may be of concern is that

of a multistage cooler operating at a very low temperature and close to its lower limit. For such

applications, it sometimes is possible to attach a small radiation shield to one of the lower module

stages. By fabricating this shield so that it surrounds the upper stage and cooled object, thermal

radiation losses may be reduced substantially.

As an indication of the magnitude of heat leak due to thermal radiation, consider the following. A

perfect black-body having a surface area of 1.0 cm2 and operating at -100°C (173K) will receive

approximately 43 milliwatts of heat from its 30°C (303K) surroundings. Be aware that the accurate

determination of radiation loss is a highly complicated issue and a suitable heat transfer textbook

should be consulted for detailed information. A very simplified estimation of such losses may be

made, however, by using the equation given below.

QR=(s)(A) (e) (Th4 – Tc

4)

Symbol Definition English Units Metric Units

QR Radiation heat loss BTU/hour watts

s Stefan-Boltzmann constant

1.714 x 10-9

BTU/hour-ft2-

oR

4

5.67 x 10-8

watts/meter2-

K4

A Area of the exposed surface square feet square meters

e Emissivity of exposed surfaces -- --

Th Absolute temperature of warmer

surface Degrees R Degrees K

Tc Absolute temperature of colder

surface Degrees R Degrees K

8.4.6 R-VALUE OF INSULATION: The R-value of an insulating material is a measure of the

insulation's overall effectiveness or resistance to heat flow. R-value is not a scientific term, per se,

but the expression is used extensively within the building construction industry in the United States.

The relationship between R-value, insulation thickness, and thermal conductivity may be expressed

by the equation:

x R =

12K

where:

x = Thickness of the insulation in inches

k = Thermal conductivity of the insulation in BTU/hr-ft-°F

Note: Insulation R-value normally is based on insulation thickness in inches. Since thermal

conductivity values in Appendix B are expressed in feet, the k value in the equation's denominator

has been multiplied by 12.

8.5 THERMAL INSULATION CONSIDERATIONS: In order to maximize thermal performance and

minimize condensation, all cooled objects should be properly insulated. Insulation type and

thickness often is governed by the application and it may not be possible to achieve the optimum

insulation arrangement in all cases. Every effort should be made, however, to prevent ambient air

from blowing directly on the cooled object and/or thermoelectric device.

Figures (8.1) and (8.2) illustrate the relationship between the heat leak from an insulated surface

and the insulation thickness. It can be seen that even a small amount of insulation will provide a

significant reduction in heat loss but, beyond a certain point, greater thicknesses give little benefit.

The two heat leak graphs show heat loss in watts per square unit of surface area for a one degree

temperature difference (DT) through the insulation. Total heat leak (Qtot) in watts for other surface

areas (SA) or DT's may be calculated by the expression:

Qtot = Qleak x SA x DT

Figure (8.1)

Heat Leak from an Insulated Surface in Metric Units

Figure (8.2)

Heat Leak from an Insulated Surface in English Units

Thermoelectric Technical Reference — Thermoelectric Module Selection



9.0 Thermoelectric Module Selection

9.1 Selection of the proper TE Cooler for a specific application requires an evaluation of the total

system in which the cooler will be used. For most applications it should be possible to use one of the

standard module configurations while in certain cases a special design may be needed to meet

stringent electrical, mechanical, or other requirements. Although we encourage the use of a

standard device whenever possible, Ferrotec America specializes in the development and

manufacture of custom TE modules and we will be pleased to quote on unique devices that will

exactly meet your requirements.

The overall cooling system is dynamic in nature and system performance is a function of several

interrelated parameters. As a result, it usually is necessary to make a series of iterative calculations

to "zero-in" on the correct operating parameters. If there is any uncertainty about which TE device

would be most suitable for a particular application, we highly recommend that you contact our

engineering staff for assistance.

Before starting the actual TE module selection process, the designer should be prepared to answer

the following questions:

1. At what temperature must the cooled object be maintained?

2. How much heat must be removed from the cooled object?

3. Is thermal response time important? If yes, how quickly must the cooled object change

temperature after DC power has been applied?

4. What is the expected ambient temperature? Will the ambient temperature change

significantly during system operation?

5. What is the extraneous heat input (heat leak) to the object as a result of conduction,

convection, and/or radiation?

6. How much space is available for the module and heat sink?

7. What power is available?

8. Does the temperature of the cooled object have to be controlled? If yes, to what precision?

9. What is the expected approximate temperature of the heat sink during operation? Is it

possible that the heat sink temperature will change significantly due to ambient

fluctuations, etc.?

Each application obviously will have its own set of requirements that likely will vary in level of

importance. Based upon any critical requirements that can not be altered, the designer's job will be

to select compatible components and operating parameters that ultimately will form an efficient and

reliable cooling system. A design example is presented in section 9.5 to illustrate the concepts

involved in the typical engineering process.

9.2 USE OF TE MODULE PERFORMANCE GRAPHS: Before beginning any thermoelectric design

activity it is necessary to have an understanding of basic module performance characteristics.

Performance data is presented graphically and is referenced to a specific heat sink base

temperature. Most performance graphs are standardized at a heat sink temperature (Th) of +50°C

and the resultant data is usable over a range of approximately 40°C to 60°C with only a slight error.

Upon request, we can supply module performance graphs referenced to any temperature within a

range of -80°C to +200°C.

9.3 To demonstrate the use of these performance curves let us present a simple example. Suppose

we have a small electronic "black box" that is dissipating 15 watts of heat. For the electronic unit to

function properly its temperature may not exceed 20°C. The room ambient temperature often rises

well above the 20°C level thereby dictating the use of a thermoelectric cooler to reduce the unit's

temperature. For the purpose of this example we will neglect the heat sink (we cannot do this in

practice) other than to state that its temperature can be maintained at 50°C under worst-case

conditions. We will investigate the use of a 71-couple, 6-ampere module to provide the required

cooling.

9.3.1 GRAPH: Qc vs. I This graph, shown in Figure (9.1), relates a module's heat pumping

capacity (Qc) and temperature difference (DT) as a function of input current (I). In this example,

established operating parameters for the TE module include Th = 50°C, Tc = 20°C, and Qc = 15

watts. The required DT = Th-Tc = 30°C.

It is necessary first to determine whether a single 71-couple, 6-ampere module is capable of

providing sufficient heat removal to meet application requirements. We locate the DT=30 line and

find that the maximum Qc value occurs at point A and with an input current of 6 amperes. By

extending a line from point A to the left y-axis, we can see that the module is capable of pumping

approximately 18 watts while maintaining a Tc of 20°C. Since this Qc is slightly higher than

necessary, we follow the DT=30 line downward until we reach a position (point B) that corresponds

to a Qc of 15 watts. Point B is the operating point that satisfies our thermal requirements. By

extending a line downward from point B to the x-axis, we find that the proper input current is 4.0

amperes.

Figure (9.1)

Heat Pumping Capacity Related to Temperature Differential as a Function of Input Current for a 71-

Couple, 6-Ampere Module

9.3.2 GRAPH: Vin vs. I This graph, shown in Figure (9.2), relates a module's input voltage (Vin)

and temperature difference (DT) as a function of input current (I). In this example, parameters for

the TE module include Th = 50°C, DT = 30°C, and I = 4.0 amperes. We locate the DT=30 line and,

at the 4.0 ampere intersection, mark point C. By extending a line from point C to the left y-axis, we

can see that the required module input voltage (Vin) is approximately 6.7 volts.

Figure (9.2)

Input Voltage Related to Temperature Differential as a

Function of Input Current for a 7I-Couple, 6-Ampere Module

9.3.3 GRAPH:COP vs. I This graph, shown in Figure (9.3), relates a module's coefficient of

performance (COP) and temperature differential (DT) as a function of input current (I). In this

example, parameters for the TE module include Th = 50°C, DT = 30°C, and I = 4.0 amperes.

We locate the DT=30 line and, at the 4.0 ampere intersection, mark point D. By extending a line

from point D to the left y-axis, we can see that the module's coefficient of performance is

approximately 0.58.

Figure (9.3)

Coefficient of Performance Related to Temperature Differential as a

Function of Input Current for a 71-Couple, 6-Ampere Module

Note that COP is a measure of a module's efficiency and it is always desirable to maximize COP

whenever possible. COP may be calculated by:

9.4 An additional graph of Vin vs. Th, of the type shown in Figure (9.4), relates a module's input

voltage (Vin) and input current (I) as a function of module hot side temperature (Th). Due to the

Seebeck effect, input voltage at a given value of I and Th is lowest when DT=O and highest when

DT is at its maximum point. Consequently, the graph of Vin vs. Th usually is presented for a DT=30

condition in order to provide the average value of Vin.

Figure (9.4)

Input Voltage Related to Input Current as a Function of

Hot Side Temperature for a 71-Couple, 6-Ampere Module

9.5 DESIGN EXAMPLE: To illustrate the typical design process let us present an example of a TE

cooler application involving the temperature stabilization of a laser diode. The diode, along with

related electronics, is to be mounted in a DIP Kovar housing and must be maintained at a

temperature of 25°C. With the housing mounted on the system circuit board, tests show that the

housing has a thermal resistance of 6°C/watt. The laser electronics dissipate a total of 0.5 watts

and the design maximum ambient temperature is 35°C.

It is necessary to select a TE cooling module that not only will have sufficient cooling capacity to

maintain the proper temperature, but also will meet the dimensional requirements imposed by the

housing. An 18-couple, 1.2 ampere TE cooler is chosen initially because it does have compatible

dimensions and also appears to have appropriate performance characteristics. Performance graphs

for this module will be used to derive relevant parameters for making mathematical calculations. To

begin the design process we must first evaluate the heat sink and make an estimate of the worst-

case module hot side temperature (Th). For the TE cooler chosen, the maximum input power (Pin)

can be determined from Figure (9.5) at point A.

Max. Module Input Power (Pin) = 1.2 amps x 2.4 volts = 2.9 watts

Max. Heat Input to the Housing = 2.9 watts + 0.5 watts = 3.4 watts

Housing Temperature Rise = 3.4 watts x 6°C/watt = 20.4°C

Max. Housing Temperature (T,) = 35°C ambient + 20.4°C rise = 55.4°C Since the hot side

temperature (Th) of 55.4°C is reasonably close to the available Tin = 50°C performance

graphs, these graphs may be used to determine thermal performance with very little error.

Figure (9.5)

Vin vs. I Graph for an 18-Couple, I.2 Ampere Module

Now that we have established the worst-case Th value it is possible to assess module performance.

Module Temperature Differential (DT) = Th - Tc = 55.4 - 25 = 30°C

Figure (9.6)

Qc vs. I Graph for an 18-Couple, 1.2 Ampere Module

From Figure (9.6) it can be seen that the maximum heat pumping rate (Qc) for DT=30 occurs at

point B and is approximately 0.9 watts. Since a Qc of only 0.5 watts is needed, we can follow the

DT=30 line down until it intersects the 0.5 watt line marked as point C. By extending a line

downward from point C to the x-axis, we can see that an input current (I) of approximately 0.55

amperes will provide the required cooling performance. Referring back to the Vin vs. I graph in

Figure (9.5), a current of 0.55 amperes, marked as point D, requires a voltage (Vin) of about 1.2

volts. We now have to repeat our analysis because the required input power is considerably lower

than the value used for our initial calculation. The new power and temperature values will be:

Max. Module Input Power (Pin) = 0.55 amps x 1.2 volts = 0.66 watts

Max. Heat Input to the Housing = 0.66 watts + 0.50 watts = 1.16 watts

Housing Temperature Rise = 1.16 watts x 6°C/watt = 7°C

Max. Housing Temperature (Th) = 35°C ambient + 7°C rise = 42°C

Module Temperature Differential (DT) = Th-Tc = 42°C-25°C = 17°C

It can be seen that because we now have another new value for Th it will be necessary to continue

repeating the steps outlined above until a stable condition is obtained. Note that calculations usually

are repeated until the difference in the Th values from successive calculations is quite small (often

less that 0.1°C for good accuracy). There is no reason to present the repetitive calculations here but

we can conclude that the selected 18-couple TE module will function very well in this application.

This analysis clearly shows the importance of the heat sink in any thermoelectric cooling application.

9.6 USE OF MULTIPLE MODULES: Relatively large thermoelectric cooling applications may require

the use of several individual modules in order to obtain the required rate of heat removal. For such

applications, TE modules normally are mounted thermally in parallel and connected electrically in

series. An electrical series-parallel connection arrangement may also be used advantageously in

certain instances. Because heat sink performance becomes increasingly important as power levels

rise, be sure that the selected heat sink is adequate for the application.

Thermoelectric Technical Reference — Mathematical Modeling of TEC Modules



11.0 Mathematical Modeling of thermoelectric Cooling Modules

11.1 INTRODUCTION: The operation of thermoelectric cooling devices may be described

mathematically and device performance can readily be modeled on a personal computer. Since the

semiconductor material used in module fabrication has several temperature-dependent properties,

temperature effects on module operation must be considered if a realistic model is to be developed.

We have not attempted to provide a highly detailed description of computer modeling techniques,

but rather to present the basic algebraic expressions needed to simulate thermoelectric module

performance.

Ferrotec America has performed a comprehensive analysis of many thermoelectric cooling modules

over a wide temperature range. This study has resulted in the development of mathematical models

that may be used to reliably predict module performance under typical operating conditions. Data

presented herein is based on module operation in a normal air atmosphere with thermally

conductive grease (heat sink compound) used at both hot and cold module interfaces. These

conditions are applicable to the majority of thermoelectric cooling applications. It should be noted

that for modules having metabolized external surfaces, slight performance improvement may be

observed if the modules are mounted with solder as opposed to thermal grease. In addition, when

modules are operated in a vacuum, a small to moderate performance increase may be seen,

especially in the case of multi-stage devices.

11.2 TEMPERATURE-DEPENDENT MATERIAL PROPERTIES: There are a number of parameters

associated with thermoelectric materials and modules that normally would have to be considered in

a mathematical model. However, since actual module test data was used to derive several

important coefficients, certain factors may be neglected thereby simplifying the modeling process.

Elements that must be incorporated into the model include the module's effective Seebeck

coefficient (SM), Electrical Resistance (RM), and Thermal Conductance (KM).

The values of SM, RM, and KM can be expressed mathematically by polynomial equations. The

specified equation coefficients, applicable over a range of -100°C to +150°C, were derived from an

industry-standard 71-couple, 6-ampere module. Other module configurations easily can be modeled

by applying a simple correction factor as described in paragraph 11.2.4. Note that when using the

various equations, temperature values must be stated in degrees Kelvin.

An alternative method for estimating temperature-dependent module properties, which may be

useful under certain circumstances, involves the use of tabulated module data. Values representing

average SM, RM, and KM characteristics for selected modules over a wide temperature range will be

found in Appendix A at the end of this manual. Although somewhat less accurate than using

calculated values, this method provides a relatively simple approach to predicting module

performance.

11.2.1 SEEBECK COEFFICIENT: When a temperature differential is maintained across a

thermoelectric device, a voltage can be detected at the input terminals. The magnitude of the

resultant voltage, called the Seebeck emf, is proportional to the magnitude of the temperature

difference. The Seebeck coefficient, as a function of temperature, can be expressed as a third order

polynomial:

SM = s1 + s2T = s3T2 + s4T

3

Where: SM is the Seebeck coefficient of the module in volts/°K

T is the average module temperature in °K

Coefficients for a 71-cpl, 6-amp module

s1 = 1.33450 x 10-2

s2 = -5.37574 x 10-5

s3 = 7.42731 x 10-7

s4 = -1.27141 x 10-9

The above polynomial expression represent the Seebeck coefficient when the temperature

difference across the module is zero (DT = Th - Tc = 0). When DT>0, the Seebeck coefficient must

be evaluated at both temperatures Th and Tc using the expressions:

s2T2 s3T

3 s4T

4

+ _____

+ ______

+ ______

SMTh or SMTc = s1T

2 3 4

SM = (SMTh - SMTc) / DT

Where: SMTh is the module's Seebeck coefficient at the hot side temperature Th

SMTc is the module's Seebeck coefficient at the cold side temperature Tc

11.2.2 MODULE RESISTANCE: The electrical resistance of a thermoelectric module, as a function

of temperature, can be expressed as third order polynomials for the two conditions (a) and (b):

(a) when DT = 0: RM = r1 + r2T + r3T2 + r4T

3

r2T2 r3T

3 r4T4

(b) when DT > 0: RMTh or RMTC = r1T + ____

+ ____

+ ____

2 3 4

RM = (RMTh - RMTc) / DT

Where:

RM is the module's resistance in ohms

RMTh is the module's resistance at the hot side temperature Th

RMTc is the module's resistance at the cold side temperature Tc


Coefficients for a 71-cpl, 6-amp module

r1 = 2.08317

r2 = -1.98763 x 10-2

r3 = 8.53832 x 10-5

r4 = -9.03143 x 10-8

11.2.3 MODULE THERMAL CONDUCTANCE: The thermal conductance of a thermoelectric

module, as a function of temperature, can be expressed as third order polynomials for the two

conditions (a) and (b):

(a) when DT = 0: KM = k1 + k2T + k3T2 + k4T

3

k2T2 k3T

3 k4T

4

(b) when DT > 0: KMTh or KMTc = k1T + ____

+ ____

+ ____

2 3 4

KMTh - KMTc

KM = ___________

DT

Where:

K is the module's thermal conductance in watts/°K

KMTh is the thermal conductance at the hot side temperature Th

KMTc is the thermal conductance at the cold side temperature Tc


coefficients for a 71-cpl, 6-amp module

k1 = 4.76218 x 10-1

k2 = -3.89821 x 10-6

k3 = -8.64864 x 10-6

k4 = 2.20869 x 10-8

11.2.4 PARAMETER CONVERSIONS FOR OTHER MODULE CONFIGURATIONS: The SM, RM,

and KM parameters shown are calculated for a 71-couple, 6-ampere thermoelectric module. If a

new or different module configuration is to be modeled, it is necessary to apply a conversion factor

to each of these parameters, as follows:

Nnew

Snew = SM x _____

71

6 Nnew

Rnew = RM x _____ x _____

Inew 71

Inew Nnew

Knew = KM x _____ x _____

6 71

Where:

Snew is the Seebeck coefficient for the new module

Rnew is the electrical resistance of the new module

Knew is the thermal conductance of the new module

Nnew is the number of couples in the new module

Inew is the optimum or maximum current of the new module

11.3 CALCULATION OF THERMOELECTRIC MODULE PERFORMANCE: There are five variable

parameters applicable to a thermoelectric module that affect its operation. These parameters

include:

I - the input current to the module expressed in amperes

Vin - the input voltage to the module expressed in volts

Th - the hot side temperature of the module expressed in °K

Tc - the cold side temperature of the module expressed in °K

Qc - the heat input to (or heat pumped by) the module expressed in watts

In order to calculate module performance it is necessary to set at least three of these variables to

specific values. Two common calculation schemes involve either (a) fixing the values of Th, I, and

Qc or, (b) fixing the values of Th, I and Tc. For the computer-oriented individual, a relatively

straightforward calculation routine can be developed to incrementally step through a series of fixed

values to produce an output of module performance over a range of operating conditions.

11.4 SINGLE-STAGE MODULE CALCULATIONS: These equations mathematically describe the

performance of a single-stage thermoelectric module as illustrated in Figure (11-l). When entering

numerical data, do not forget that temperature values must be expressed in degrees Kelvin (°K).

Calculations of the various parameters should be performed in the order shown.

Figure (11-1)

a) The temperature difference (DT) across the module in °K or °C is:

DT = Th - Tc

b) Heat pumped (Qc) by the module in watts is:

Qc = (SM x Tc x I) - (0.5 x I2 x RM) - (KM x DT)

c) The input voltage (Vin) to the module in volts is:

Vin = (SM x DT) + (I x RM)

d) The electrical input power (Pin) to the module in watts is:

Pin = Vin x I

e) The heat rejected by the module (Qh) in watts is:

Qh = Pin + Qc

f) The coefficient of performance (COP) as a refrigerator is:

COP = Qc / Pin

11.5 HEATING MODE OPERATION: Thermoelectric modules may be operated in the heating

mode by reversing the polarity of the applied DC power. When used in this manner, the TE module

functions as a "heat pump" and heating efficiencies in excess of 100 percent may be realized under

certain conditions. A rapid increase in temperature occurs when heating a small-mass object, and

care must be taken to avoid overheating either the module or object. In the heating mode,

illustrated in Figure (11-2), the heat sink and object effectively are in opposite positions whereby

the object is now at temperature (Th) and the heat sink is at temperature (Tc).

Figure (11-2) a) Heat flow to the object (Qh) is given by the expression:

Qh = (SM x Th x I) + (0.5 x I2 x RM) - (KM x (Th - Tc))

b) The coefficient of performance as a heater (COPH) is:

COPH = Qh / Pin

11.5.1 Heating mode performance of a standard 71-Couple, 6-Ampere module is presented

graphically in Figures (11-3) and (11-4). These graphs illustrate module performance at a heat sink

temperature of 25°C.

Figure (11-3)

Heat Output at Various Hot-Side Object Temperatures

Figure (11-4)

Coefficient of Performance in the Heating Mode

11.6 OTHER THERMOELECTRIC DEVICE ATTRIBUTES: There are many other properties of

thermoelectric devices that can be described mathematically. Several characteristics that might be

of interest for specific situations follow. Remember that temperature values must be expressed in

°K.

a) The maximum heat pumping capacity (Qmax) in watts of a thermoelectric module is given by the

following expression. Note that DT =0 at the maximum Qc condition and, therefore, Tc = Th.

SM2 x TC

2

__________ Qmax =

2 x RM

b) The maximum temperature differential (DTmax) in °K may be expressed as shown below. To

obtain an accurate DTmax value, however, it will be necessary to perform an iterative series of

calculations comparing Tc to DTmax at a fixed value of Th.

SM2 x TC

2

__________ DTmax =

2 x RM x KM

c) The Figure-of-Merit (Z) is a measure of the overall performance of a thermoelectric device or

material. Z always is higher for raw thermoelectric semiconductor material than for an actual

module functioning within a thermal system. Since an operating module is affected by interface,

conductive, convective, and other losses, the effective Figure-of-Merit is less than that of the raw

material. The Figure-of-Merit may be expressed:

For Raw Material For a TE Module

Z =

a2

__________

p x k

Z =

SM2

__________

RM x KM

where:

a is the Seebeck coefficient of the material in v/°K

p is the electrical resistivity of the material in ohm-cm

k is the thermal conductivity of the material in w/cm-°K

d) The optimum current (Iopt) in amperes required to produce the maximum heat removal rate

(Qmax) is:

For Raw Material For a TE Module

Iopt =

a x Tc x a ___________

p x l

a x Tc = _________

R

SM x Tc

Iopt = _____________

RM

where:

a is the cross-sectional area of an individual thermoelectric element in centimeters.

l is the length (height) of an individual thermoelectric element in centimeters

R is the resistance of an individual thermoelectric element in ohms.

11.7 MODELING OF COMPLETE THERMOELECTRIC COOLING SYSTEMS: Information

presented in the foregoing paragraphs describes the mathematical modeling of thermoelectric

modules as opposed to complete thermal systems. By incorporating the module calculations into a

more sophisticated system model, it is possible to accurately simulate the overall thermal

performance. Two heat leak sources that must not be overlooked in a complete thermal model

include (a) heat conduction between the cooled object and heat sink, and, (b) heat conduction

through clamping screws, if any, that physically connect the heat sink and cooled object.

Heat conduction between the heat sink and object generally involves the transfer of heat through

the air gap surrounding the module mounting area. The actual heat leak value can be calculated

using the equation in paragraph 8.4.1 where area (A) is the "open" surface area not covered by the

thermoelectric modules, distance (x) is the width of the air gap, and thermal conductivity (K) is the

value for air.

Heat conduction through the clamping screws also can be calculated by means of the same

equation. In this case, area (A) is the cross-sectional area of all mounting screws calculated from

the screw's pitch diameter and (K) is the thermal conductivity of the screw material.

Thermoelectric Technical Reference — Modeling of Cascade Thermoelectric Modules



12.0 Description & Modeling of Cascade Thermoelectric Modules

12.1 A standard single-stage thermoelectric cooling module is capable of achieving a maximum no-

load temperature differential (DTmax) of approximately 72°C. It is possible to obtain DTs of up to

130°C by mechanically stacking modules on top of one another whereby the cold side of one

module becomes the hot side of another module mounted above. This stacking arrangement is

called a Cascade or Multi-Stage module configuration. Cascade modules usually, but not always,

have a pyramid shape thereby the higher stages are physically smaller than those below.

Regardless of the physical shape, however, lower stages must always have greater heat pumping

capacity than the higher stages. although cascade configurations of up to six and seven stages have

been constructed, practical cascade devices usually have from two to four stages.

The principal factor that limits cascade module performance is related to the temperature

dependent properties of the thermoelectric semiconductor materials. The performance of Bismuth

Telluride alloys used in most thermoelectric coolers generally peaks near 70°C and performance

falls-off appreciably at lower temperatures. Consequently, cascade modules exhibit a condition of

diminishing returns where, as successive stages are added, the increase in DT becomes smaller.

Figure (12-1)

Performance Graph of a Typical Cascade Module

12.2 MODELING OF CASCADE MODULES: Modeling of cascaded or multi-stage thermoelectric

coolers is somewhat more complicated than for single-stage devices. With multi-stage coolers, the

temperature between each stage is critically important and module performance cannot be

established until each interstage temperature value is known. With a two-stage cooler only one

interstage temperature must be determined but, as more stages are added, the thermal analysis

becomes increasingly complex. Manually calculating multi-stage module performance is extremely

laborious, yet with a computer, the required calculations can be performed with little effort.

The most common method for computer-modeling cascade modules involves carrying out an

iterative series of performance calculations beginning with assumed interstage temperature values.

Using this technique, the performance of each stage is repeatedly calculated until the difference

between successive interstage temperature calculations becomes very small (typically 0.1°C or

less). When this point is reached, each of the relevant module performance parameters can be

ascertained. Note that the temperature-dependent value of SM, RM, and KM must be converted as

explained in paragraph 11.2.4 to reflect the number of couples in each stage together with their

optimum TE element currents. The following paragraphs describe the calculations needed to model

two and three-stage cascaded thermoelectric modules. Four and greater-stage modules may be

modeled in a similar manner by expanding the three-stage calculation routines to include terms for

each additional stage. Calculations of the various parameters should be performed in the order

shown.

12.2.1 TWO-STAGE MODULE CALCULATIONS: A typical two-stage thermoelectric module is

illustrated in Figure (12-2). The following new terms will be used in the module performance

calculations:

TM12 is the interstage temperature between stages 1 and 2 in °K

SM1 is the Seebeck coefficient of the 1st stage in volts/°K

SM2 is the Seebeck coefficient of the 2nd stage in volts/°K

RM1 is the resistance of the 1st stage in ohms

RM2 is the resistance of the 2nd stage in ohms

KM1 is the thermal conductance of the 1st stage in watts/°K

KM2 is the thermal conductance of the 2nd stage in watts/°K

Figure (12-2) a) The interstage temperature (TM12) in °K is:

TM12 =

(0.5 x I2) x (RM2 + RM1) + (KM1 x Th) + (KM2 x Tc)

________________________________________________________________I x (SM1 - SM2) +

KM1 + KM2

b) Heat pumped (Qc) by the module in watts is:

Qc = (SM2 x Tc x I) - (0.5 x I2 x RM2) - (KM2 x (TM12 -Tc))

c) The input voltage (Vin) to the module in volts is:

Vin = (SM2 x (TM12 -Tc) + (I x RM2) + (SM1 x (Th - TM12)) + (I x RM1)

d) The electrical input power (Pin) to the module in watts is:

Pin = Vin x I

e) The heat rejected by the module (Qh) in watts is:

Qh = (SM1 x Th x I) + (0.5 x I2 x RM1) - (KM1 x (Th - TM12)

or

Qh = Qc - Pin

f) The coefficient of performance (COP) as a refrigerator is:

COP = Qc / Pin

12.2.2 THREE-STAGE MODULE CALCULATIONS: A typical three-stage module is illustrated in

Figure (12-3). The following new terms will be used in the module performance calculations:

TM23 is the interstage temperature between stages 2 and 3 in °K

SM3 is the Seebeck coefficient of the 3rd stage in volts/°K

RM3 is the resistance of the 3rd stage in ohms

KM3 is the thermal conductance of the 3rd stage in watts/°K

Figure (12-3) a) The lower interstage temperature (TM12) in

oK is:

TM12 =

(0.5 x I2 x (RM1 + RM2)) + (KM1 x Th) + (KM2 x TM23)

___________________________________________

I x (SM1 - SM2) + KM1 + KM2

b) The upper interstage temperature (TM23) in oK is:

TM23=

(0.5 x I2 x (RM2 + RM3)) + (KM2 x TM12) + (KM3 x Tc)

___________________________________________

I x (SM2 - SM3) + KM2 + KM3

c) Heat pumped by the module (Qc) in watts is:

Qc = (SM3 x Tc x I) - (0.5 x I2 x RM3) - (KM3 x (TM23 - Tc))

d) The input voltage (Vin) to the module in volts is:

Vin = (SM1 x (Th - TM12)) + (I x RM1) + (SM2 x (TM12 - TM23)) +

(I x RM2) + (SM3 x (TM23 - Tc)) + (I x RM3)

e) The input power (Pin) to the module in watts is: Pin = Vin x I

f) The heat rejected by the module (Qh) in watts is: Qh = Qc + Pin

g) The coefficient of performance (COP) as a refrigerator is: COP = Qc / Pin

Thermoelectric Technical Reference — Power Generation



13.0 Power Generation

13.1 Bismuth Telluride-based thermoelectric modules are designed primarily for cooling or

combined cooling and heating applications where electrical power creates a temperature difference

across the module. By using the modules "in reverse," however, whereby a temperature differential

is applied across the faces of the module, it is possible to generate electrical power. Although power

output and generation efficiency are very low, useful power often may be obtained where a source

of heat is available.

13.2 A thermoelectric module used for power generation has certain similarities to a conventional

thermocouple. Let us look at a single thermoelectric couple with an applied temperature difference

as shown in Figure (13.1)

Figure (13-1)

Single Thermoelectric Couple where Th > Tc

With no load (RL not connected), the open circuit voltage as measured between points a and b is:

V = S x DT

where:

V is the output voltage from the couple (generator) in volts

S is the average Seebeck coefficient in volts/°K

DT is the temperature difference across the couple in °K where DT = Th-Tc

When a load is connected to the thermoelectric couple the output voltage (V) drops as a result of

internal generator resistance. The current through the load is:

I =

S x DT ____________________

RC + RL

where :

I is the generator output current in amperes

Rc is the average internal resistance of the thermoelectric couple in ohms

RL is the load resistance in ohms

The total heat input to the couple (Qh) is:

Qh = (S x Th x I) - (0.5 x I2 x Rc) + (Kc x DT)

where:

Qh is the heat input in watts

Kc is the thermal conductance of the couple in watts/°K

Th is the hot side of the couple in °K

The efficiency of the generator (Eg) is:

V x I

Eg = —————

Qh

We have thus far discussed an individual thermoelectric couple, but since a complete module

consists of a number of couples, it is necessary to rewrite our equation for an actual module, as

follows:

Vo = SM x DT = I x (RM + RL)

where:

Vo is the generators output in volts

SM is the module’s average Seebeck coefficient in volts/°K

RM is the module’s average resistance in ohms

It must be remembered that module Seebeck coefficient, resistance and thermal conductance

properties are temperature dependent and their values must be calculated as described in Section

11, paragraphs 11.2 through 11.2.4. As an alternative to these calculations, however, generator

performance may be reasonably approximated through the use of the data shown in Appendix A. In

either case, the values of SM, RM, and KM must be selected at the average module temperature

Tavg where:

Th + Tc

Tavg = ————

2

The power output (Po) from the module in watts is:

Po = RL x

It is possible, but unlikely, that the precise conditions will exist within a given generator application

whereby one module will provide the exact output power desired. As a result, most thermoelectric

generators contain a number of individual modules which may be electrically connected in either

series, parallel, or series/parallel arrangement. A typical generator configuration is illustrated in

Figure (13.2). This generator has a NT total number of modules with NS number of modules

connected in series and NP number of modules connected in parallel. The total number of modules

in the system is:

NT = NS x NP

Figure (13-2)

Typical Thermoelectric Generator with a Series-Parallel Arrangement of Modules

The current (I) in amperes passing through the load resistance RL is:

NS x SM x DT

I = ________________

NS x RM

_________

+ RL

NP

The output voltage (Vo) from the generator in volts is:

The Output Power (PO) from the generator in watts is:

Po = Vo x I =

NT x (SMx DT)2

___________

4 x RM

The total heat input (Qh) to the generator in watts is:

The efficiency (Eg) of the generator is:

Po

Eg = ————— x 100%

Qh

Maximum efficiency occurs when the internal resistance of the generator (RGEN) equals the load

resistance (RL). The generator resistance is:

NS x RM

RGEN = —————

NP

13.3 DESIGN EXAMPLE: To illustrate the typical design process let us analyze a requirement for a

12-volt, 1.5 ampere thermoelectric power generator. The generator is needed to power telemetry

electronics at a remotely located oil pipeline where the hot, continuously flowing oil produces a

130°C pipe casing temperature. Flowing water (having a temperature of 10°C) also is available at

the remote site, and it has been determined that an efficient water-cooled heat sink can maintain

the TE generator cold-side at a temperature of +30°C. We will use Appendix A to obtain the values

of SM, RM and KM for our calculations.

To begin the design process we will review the system parameters and make some preliminary

calculations.

Given:

Th = + 130°C = 403.2K

Tc = + 30°C = 303.2K

Vo = 12 volts

I = 1.5 amperes

therefore:

Tav = (Th+Tc)/2 = (403.2+303.2)/2 = 353.2K

RL = Vo/I = 12 / 1.5 = 8.0 ohms

Po = Vo x I = 12 x 1.5 = 18 watts

DT = Th-Tc = 403.2 - 303.2 = 100K

It is usually desirable to select a relatively "high power" thermoelectric module for generator

applications in order to minimize the total system cost. For this reason we will choose a 127 couple,

6-ampere module to be used in our design.

From Appendix A for our selected 127-couple, 6 ampere module, the following values are obtained

at Tav = 353.2K:

SM = 0.05544 volts/K

RM = 3.0994 ohms

KM = 0.6632 watts/K

The required power for the load has been calculated as 18 watts. It is now necessary to determine

the minimum number of modules needed to meet this load requirement. The maximum output

power from one module is:

(SM x DT)2 (0.05544 x 100)

2

Pmax= ————— = ——————— = 2.479 watts

4 x RM 4 x 3.0994

The minimum number of modules needed is:

NTmin =

Po

——

Pmax

18

= ——— =

2.479 7.3 » 8

Because maximum generator efficiency occurs when RGEN = RL, it is desirable for most applications

to select the series/parallel module configuration that will best approximate this resistance balance.

One possible exception to the equalizing RGEN with RL is in the situation where a relatively low

current (in the milliampere range) and moderate voltage is required. In this case, the connection of

all modules electrically in series may give the best results. Be aware, however that the maximum

output voltage from the generator will be obtained from a straight series-connected group of

modules only when the resistance of the load is significantly higher than the internal resistance of

the generator.

As a starting point in the evaluation of any thermoelectric power generator, it is often helpful to first

examine the straight series-connected configuration. The resistance of a series string of eight

modules is:

RGEN =

NS x RM

————— =

NP

8 x 3.0994

—————

1

= 24.8 ohms

It can be seen that the 24.8 ohm generator resistance is considerably higher than the 8.0 ohm load

resistance, thereby indicating that a straight series module connection probably is not the best

arrangement. For the all series condition where NS = 8 and NP = 1, the output voltage is:

With a group of eight modules, the next most logical connection configuration is two parallel strings

of four modules, i.e., NS = 4 and NP = 2. Generator resistance for this configuration is thus:

RGEN =

NS x RM

———— =

NP

4 x 3.0994

————

2

= 6.2 ohms

While 6.2 ohm RGEN value does not exactly match the 8.0 ohm load resistance, this value normally

would be considered as being within the satisfactory range. In any event, this is the closest

resistance match that can be obtained with the selected module type. The voltage for this

arrangement (12.49 volts) is calculated as follows:

We can now see that Vo is quite close to the desired value and it is apparent that we have obtained

the optimum series/parallel configuration. If "fine tuning" of Vo is required, it will be necessary to

accomplish this either by some form of electronic voltage regulation or by externally altering the

applied temperature differential (DT). In certain instances it will be found that the output voltage is

significantly out of range despite trying all possible series/parallel combinations. In this event it may

be necessary to use an alternate thermoelectric module having a different current rating and/or

number of couples.

It is now possible to complete our design analysis by determining power levels and efficiency. Since

we have established Vo, output power (Po) can be simply calculated:

(Vo)2 (12.49)

2

Po = ——— = ——— = 19.5 watts

RL 8.0

The total heat input (Qh) to the generator is:

The generator efficiency (Eg) is:

Eg =

Po

——

Qh

x 100% =

19.5

———

657.5

x 100% = 2.97%

The heat transferred to the cold-side heat sink (Qc) is :

Qc = Qh - Po = 657.7 - 19.5 = 638.2 watts

The maximum allowable thermal resistance (Qs) of the cold-side heat sink is :

(Qs)=

Trise

————— =

Qc

30°C - 10°C

—————— =

638.2

0.031 °C/watt

For any thermoelectric generator design it is always desirable to maximize the applied temperature

differential in order to minimize the total number of modules in the system. This situation can be

clearly seen in Figure (13.3). Module requirements for a typical 12-volt, 1-ampere power generator

are plotted at several fixed values of Th based on the use of 127-couple 6-ampere TE modules.

From this graph, it is evident that a very large number of modules is needed when the cold side

temperature (Tc) is high and the temperature differential, therefore, is small. Performance of the

cold-side heat sink is of the utmost importance and its thermal resistance must be extremely low.

In many cases, cold-side heat sink design will prove to be the most challenging engineering

problem.

Figure (13-3)

The Total Number of 127 Couple, 6 Amp Modules Required for a 12-volt, 1 Ampere Thermoelectric

Power Generator

13.4 USE OF THERMOELECTRIC MODULES IN A CALORIMETER: A lesser, yet viable,

application for thermoelectric modules operating in the power generation mode is in the

construction of calorimeters. The conventional calorimeter uses common thermocouples for heat

measurement based solely on the Seebeck effect. Through the use of a multi-couple thermoelectric

cooling module, it is possible to fabricate a calorimeter having a sensitivity (output voltage per unit

of heat flux density) as much as 10 to 200 times the sensitivity of a standard copper-constantine

thermocouple. When used in a calorimeter application, the thermoelectric module is often referred

to as a thermopile. The open-circuit output voltage (V) of a single thermoelectric couple, as

described in paragraph 13.2 and illustrated in Figure (13.1), is:

V = S x DT

where:

V is the output voltage from the couple in volts

S is the average Seebeck coefficient in volts/°K

DT is the temperature difference across the couple in °K where DT=Th-Tc

For an actual TE module having a number of couples and a Seebeck coefficient of SM, the output

voltage (Vo) is:

Vo = SM x DT

The heat flow through the TE or "thermopile" is:

Q = KM x DT =

KM x Vo

—————

SM

where:

Q is the heat flow in watts

KM is the thermal conductance of the module in watts/°K

The total cross-sectional area (AM) of all elements in the module is:

AM = A x N

where:

AM = total area of all module elements in cm2

A = cross-sectional area of one element in cm2

N = total number of elements in the module

The heat flux density (q) in watts/cm2 is:

q =

KM x DT

————— =

AM

KM x Vo

—————

SM x AM

Most standard thermoelectric cooling modules may be used in a calorimeter application but

improved sensitivity may be realized by modifying the length-to-area (L/A) aspect ration of the TE

elements. A relatively large L/A ratio resulting in a tall and "skinny" element will produce the best

calorimeter sensitivity. To illustrate this situation let us consider the following:

The sensitivity of a module as a calorimeter (Sc) is:

Sc =

Vo

—————

q

SM x AM

= —————

KM

It has been seen that sensitivity (Sc) is directly proportional to the Seebeck coefficient (SM) and

total cross-sectional element area (AM) and inversely proportional to the thermal conductance (KM).

By rewriting the above equation in respect to thermal conductivity (k) instead of thermal

conductance (KM) we have:

Sc=

SM x AM

—————

k x N x A/L

Since N x A = AM, the expression can be restated as:

Sc =

SM x L

—————

k

From this equation, it is evident that calorimeter sensitivity is directly related to the length (L)

dimension of an element and it is desirable, therefore, to select a thermoelectric module having the

largest possible element aspect ratio. Be aware that there are practical limits on element geometry

due to the fragility of crystalline Bismuth telluride material. Working within these limits, however, it

is possible to fabricate custom modules that are particularly suited for calorimeter use.

Thermoelectric Technical Reference — Averaged Module Material Parameters at Various Temperatures

For all tables:

SM = Module Seebeck coefficient in volts/K (or volts/degreeC)

RM = Module resistance in ohms

KM = Module thermal conductable in watts/K (or watts/degreeC)

NOTE: The data on the following tables reflects effective module parameters of Ferrotec

manufactured TEs, in normal ambient air using thermal grease at both the hot and cold module

interfaces. Raw Bismuth Telluride semiconductor material not in module form has substantially

different values for these parameters. We do not recommend using this data for the analysis of

other manufacturer's modules.

31-Couple Modules

9-Ampere Module 15-Ampere Module Temperature

SM RM KM RM KM

°C °K V/K ohms w/K ohms w/K

-100 173.2 0.00859 0.2130 0.2103 0.1278 0.3504

-90 183.2 0.00898 0.2186 0.2086 0.1312 0.3477

-80 193.2 0.00938 0.2263 0.2056 0.1358 0.3427

-70 203.2 0.00978 0.2360 0.2018 0.1416 0.3364

-60 213.2 0.01017 0.2474 0.1976 0.1484 0.3293

-50 223.2 0.01056 0.2604 0.1933 0.1562 0.3221

-40 233.2 0.01094 0.2748 0.1892 0.1649 0.3153

-30 243.2 0.01130 0.2906 0.1857 0.1743 0.3096

-20 253.2 0.01165 0.3075 0.1831 0.1845 0.3052

-10 263.2 0.01198 0.3253 0.1816 0.1952 0.3027

0 273.2 0.01229 0.3440 0.1815 0.2064 0.3024

10 283.2 0.01257 0.3634 0.1828 0.2180 0.3047

20 293.2 0.01282 0.3833 0.1858 0.2300 0.3096

30 303.2 0.01304 0.4035 0.1905 0.2421 0.3176

40 313.2 0.01323 0.4239 0.1971 0.2544 0.3286

50 323.2 0.01337 0.4444 0.2057 0.2666 0.3428

60 333.2 0.01347 0.4647 0.2162 0.2788 0.3602

70 343.2 0.01353 0.4848 0.2286 0.2909 0.3809

80 353.2 0.01353 0.5044 0.2428 0.3026 0.4047

90 363.2 0.01349 0.5234 0.2589 0.3140 0.4316

100 373.2 0.01338 0.5417 0.2768 0.3250 0.4613

110 383.2 0.01322 0.5590 0.2961 0.3354 0.4936

120 393.2 0.01300 0.5753 0.3169 0.3452 0.5282

130 403.2 0.01271 0.5904 0.3389 0.3542 0.5649

140 413.2 0.01235 0.6041 0.3619 0.3624 0.6032

150 423.2 0.01192 0.6162 0.3856 0.3697 0.6426

71-Couple Modules


SM RM KM RM KM


-100 173.2 0.01968 1.0980 0.2140 0.7318 0.3210

-90 183.2 0.02058 1.1270 0.2123 0.7511 0.3185

-80 193.2 0.02148 1.1663 0.2093 0.7775 0.3140

-70 203.2 0.02239 1.2159 0.2054 0.8106 0.3082

-60 213.2 0.02329 1.2746 0.2011 0.8498 0.3017

-50 223.2 0.02418 1.3417 0.1967 0.8945 0.2951

-40 233.2 0.02505 1.4162 0.1926 0.9441 0.2889

-30 243.2 0.02588 1.4974 0.1891 0.9983 0.2836

-20 253.2 0.02668 1.5844 0.1864 1.0563 0.2796

-10 263.2 0.02744 1.6766 0.1849 1.1177 0.2773

0 273.2 0.02814 1.7729 0.1847 1.1819 0.2771

10 283.2 0.02879 1.8727 0.1861 1.2485 0.2791

20 293.2 0.02937 1.9751 0.1891 1.3167 0.2837

30 303.2 0.02987 2.0793 0.1939 1.3862 0.2909

40 313.2 0.03029 2.1845 0.2007 1.4564 0.3010

50 323.2 0.03062 2.2899 0.2094 1.5266 0.3140

60 333.2 0.03085 2.3947 0.2200 1.5965 0.3300

70 343.2 0.03098 2.4980 0.2326 1.6654 0.3490

80 353.2 0.03100 2.5991 0.2472 1.7327 0.3708

90 363.2 0.03089 2.6971 0.2636 1.7981 0.3954

100 373.2 0.03066 2.7913 0.2817 1.8608 0.4226

110 383.2 0.03029 2.8807 0.3015 1.9205 0.4522

120 393.2 0.02977 2.9647 0.3226 1.9765 0.4839

130 403.2 0.02911 3.0423 0.3450 2.0282 0.5175

140 413.2 0.02828 3.1129 0.3684 2.0753 0.5526

150 423.2 0.02729 3.1755 0.3925 2.1170 0.5887

127-Couple Modules


SM RM KM RM KM


-100 173.2 0.03520 1.9634 0.3828 1.3089 0.5742

-90 183.2 0.03680 2.0152 0.3798 1.3435 0.5697

-80 193.2 0.03843 2.0862 0.3744 1.3908 0.5616

-70 203.2 0.04005 2.1749 0.3675 1.4500 0.5512

-60 213.2 0.04166 2.2800 0.3597 1.5200 0.5396

-50 223.2 0.04325 0.3999 0.3519 1.6000 0.5278

-40 233.2 0.04480 2.5332 0.3445 1.6888 0.5168

-30 243.2 0.04630 2.6784 0.3382 1.7856 0.5073

-20 253.2 0.04773 2.8341 0.3335 1.8894 0.5002

-10 263.2 0.04908 2.9989 0.3307 1.9993 0.4961

0 273.2 0.05034 3.1713 0.3304 2.1142 0.4956

10 283.2 0.05150 3.3498 0.3328 2.2332 0.4992

20 293.2 0.05253 3.5329 0.3383 2.3553 0.5074

30 303.2 0.05343 3.7193 0.3469 2.4796 0.5204

40 313.2 0.05418 3.9075 0.3590 2.6050 0.5384

50 323.2 0.05477 4.0961 0.3745 2.7307 0.5617

60 333.2 0.05519 4.2835 0.3936 2.8556 0.5903

70 343.2 0.05542 4.4683 0.4161 2.9789 0.6242

80 353.2 0.05544 4.6491 0.4422 3.0994 0.6632

90 363.2 0.05525 4.8244 0.4715 3.2163 0.7072

100 373.2 0.05483 4.9928 0.5039 3.3285 0.7559

110 383.2 0.05417 5.1528 0.5392 3.4352 0.8088

120 393.2 0.05325 5.3030 0.5771 3.5354 0.8656

130 403.2 0.05206 5.4419 0.6171 3.6280 0.9257

140 413.2 0.05059 5.5681 0.6589 3.7121 0.9884

150 423.2 0.04882 5.6801 0.7021 3.7867 1.0531

Thermoelectric Technical Reference — Glossary



13.0 Glossary of Thermoelectric and Thermal Terms

AMBIENT TEMPERATURE: Temperature of the air or environment surrounding a thermoelectric

cooling system; sometimes called room temperature.

ASPECT RATIO: The numerical ratio of the length (height) to cross-sectional area of a

thermoelectric element. An element’s L/A aspect ratio is inversely proportional to its optimum

current.

BISMUTH-ANTIMONY: A thermoelectric semiconductor material that exhibits optimum

performance characteristics at relatively low temperatures.

BISMUTH TELLURIDE: A thermoelectric semiconductor material that exhibits optimum

performance in a "room temperature" range. An alloy of bismuth telluride most often is used for

thermoelectric cooling applications.

BTU: British Thermal Unit: The amount of thermal energy required to raise one pound of water

by one degree Celsius at a standard temperature of 15°C.

CALORIMETER: A scientific apparatus used to measure the evolution or absorption of heat.

Thermoelectric modules, when used in a calorimeter, may exhibit much higher sensitivity than

conventional thermopiles.

CASCADE MODULE (MULTI-STAGE MODULE): A thermoelectric module configuration whereby

one module is stacked on top of another so as to be thermally in series. This arrangement makes it

possible to reach lower temperatures than can be achieved with a single-stage module.

CFM: Cubic Feet per Minute: The volgenerallyumetric flow rate of a gas, typically air, expressed in

the English system of units. For thermoelectric applications, this refers to the amount of air passing

through the fins of a forced convection heat sink.

CLOSED-LOOP TEMPERATURE CONTROLLER: A temperature controlling device having some

type of temperature sensor (thermocouple, thermistor, RTD, etc.) that will transmit or "feed back"

temperature data to the controller. Based on the returned information, the controller will

automatically adjust its output to maintain the desired temperature.

COEFFICIENT OF PERFORMANCE (COP): A measure of the efficiency of a thermoelectric module,

device or system. Mathematically, COP is the total heat transferred through the thermoelectric

device divided by the electric input power. COP sometimes is stated as COPR (Coefficient of

Performance as a Refrigerator) or as COPH (Coefficient of Performance as a Heater).

COLD SIDE OF A THERMOELECTRIC MODULE: The side of a module that normally is placed in

contact with the object being cooled. When the positive and negative module leads are connected to

the respective positive and negative terminals of a DC power source, heat will be absorbed by the

module's cold side. Typically, the leads of a TE module are attached to the hot side.

CONDUCTION(THERMAL): The transfer of heat within a material caused by a temperature

difference through the material. The actual material may be either a solid, liquid or gas (or a

combination) where heat will flow by means of direct contact from a high temperature region to a

lower temperature region.

CONVECTION (THERMAL): The transfer of heat by means of air (gas) movement over a surface.

Convection actually is a combined heat transfer process that involves elements of conduction,

mixing action, and energy storage.

COUPLE: A pair of thermoelectric elements consisting of one N-type and one P-type connected

electrically in series and thermally in parallel. Because the input voltage to a single couple is quite

low, a number of couples normally are joined together to form a "module."

DEGREES KELVIN: Absolute temperature scale where absolute zero (0K) represents the point

where all molecular kinetic energy of a mass is zero. When calculating the temperature dependent

properties of semiconductor materials, temperature values must be expressed in degrees Kelvin. On

the Celsius scale, 0°C equals 273.15K; in respect to quantity, one Kelvin degree equals one Celsius

degree. Note that the (°) symbol normally is not used when denoting degrees Kelvin.

DELTA-T: The temperature difference between the cold and hot sides of a thermoelectric module.

Delta T may also be expressed as "DT" or "DT."

DENSITY: The mass of a material per unit volume; often expressed as pounds per cubic foot or

grams per cubic centimeter.

DICE: A general term for blocks of the thermoelectric semiconductor material or "elements"

prepared for use in a thermoelectric module.

DIE: An individual block of thermoelectric semiconductor material used in the fabrication of a

module. A die may also be called an "element," "leg," or "thermoelement."

EFFICIENCY: For thermoelectric coolers, mathematical efficiency is the heat pumped by a module

divided by the electrical input power; for thermoelectric generators, efficiency is the electrical

output power from the module divided by the heat input. To convert to percent, multiply by 100.

See definition of Coefficient of Performance.

ELEMENT: An individual block of thermoelectric semiconductor material. See definition of DIE.

EMISSIVITY: The ratio of the energy emitted by a given object to the energy emitted by a black-

body at the same temperature. Emissivity is dependent upon an object’s material and surface finish.

ENERGY: Energy is the physical quantity which, in the context of thermoelectrics, generally is used

to express a unit of heat or electricity. Energy may be stated in British Thermal Units (BTU) or watt-

hours. It is important to note the difference between energy and power. Power is the rate at which

energy is being used, and power may be stated in BTU/hour or watts. The relationship between

power and energy is Power = Energy / Time.

FIGURE-OF-MERIT (Z): A measure of the overall performance of a thermoelectric device or

material. Material having the highest figure-of-merit also has the highest thermoelectric

performance.

FORCED CONVECTION HEAT SINK: A heat sink that incorporates a fan or blower to actively

move air over the heat sink’s fins. Greatly improved cooling performance may be realized with a

forced convection system when compared to a natural convection heat sink.

HEAT LEAK: The amount of energy gained or lost by an object being thermoelectrically controlled

due to heat transfer to or from external media. Heat transfer may occur due to conduction,

convection, and/or radiation.

HEAT LOAD: The quantity of heat presented to a thermoelectric device that must be absorbed by

the device’s cold side. The term heat load, when used by itself, tends to be somewhat ambiguous

and it is preferable to be more specific. Terms such as active heat load, passive heat load or total

heat load are more descriptive and less uncertain as to meaning.

HEAT OF FUSION: More correctly called Latent Heat of Vaporization. The amount of heat energy

required to change a given mass of a substance from a liquid to a gas without changing the

temperature of the substance. To change water into stream, for example, requires a heat input of

about 971 BTU/pound or 540 calories/gram.

HEAT PUMP: A general term describing a thermoelectric cooling device, often being used as a

synonym for a thermoelectric module. In somewhat less common usage, the term heat pump has

been applied to a thermoelectric device operating in the heating mode.

HEAT PUMPING CAPACITY: The amount of heat that a thermoelectric device is capable of

pumping at a given set of operating parameters. Frequently, this term will be used interchangeably

with the expression maximum heat pumping capacity. The two terms are not strictly synonymous,

however, because maximum heat pumping capacity specifically defines the maximum amount of

heat that a module will pump at the maximum rated input current and at a zero temperature

differential.

HEAT SINK: A body that is in contact with a hotter object and that expedites the removal of heat

from the object. Heat sinks typically are intermediate stages in the heat removal process whereby

heat flows into a heat sink and then is transferred to an external medium. Common heat sinks

include natural (free) convection, forced convection and fluid cooled.

HEAT TRANSFER COEFFICIENT: A numerical value that describes the degree of coupling that

exists between an object and a cooling or heating fluid. The heat transfer coefficient actually is an

extremely complex value that encompasses many physical factors.

HEIGHT TOLERANCE (MODULE): The maximum variation in height or thickness of a thermoelectric

module referenced to its nominal specified dimension. Most Ferrotec modules are available in two

tolerance ranges of +/-0.03mm (+/-0.001") and +/-0.3mm (+/-0.01"). When more than one

module will be installed between a given pair of mounting surfaces, the maximum height variation

of all modules should not exceed 0.06mm (0.002").

HOT SIDE OF A THERMOELECTRIC MODULE: The face of a thermoelectric module that usually is

placed in contact with the heat sink. When the positive and negative module leads are connected to

the respective positive and negative terminals of a DC power source, heat will be rejected by the

module’s hot side. Normally, the wire leads are attached to the hot side ceramic substrate.

INTERSTAGE TEMPERATURE: The temperature between specific stages or levels of a multi-stage

or cascade module.

JOULE HEATING: Heat produced by the passage of an electrical current through a conductor or

material due to the internal resistance.

KINEMATIC VISCOSITY: The ratio of a fluid’s viscosity to its density; typically units are

centimeters squared per second and feet squared per second.

LATENT HEAT: Thermal energy required to cause a change of state of a substance such as

changing water into ice or water into steam.

LEAD TELLURIDE: A thermoelectric semiconductor that exhibits its optimum performance within a

temperature range of 250-450°C. Lead telluride is used most often for thermoelectric power

generation applications.

LIQUID COOLING: A heat sink method involving the use of water or other fluids to carry away

unwanted heat. When comparing alternative heat-sinking methods, liquid cooled heat sinks

normally provide the highest thermal performance per unit volume.

MASS FLOW RATE: The weight of a fluid flowing per unit of time past a given cross-sectional area.

Typical units include pounds per hour-square foot and grams per second-square centimeter.

MAXIMUM TEMPERATURE DIFFERENTIAL (MAXIMUM DT): The largest difference that can be

obtained between the hot and cold faces of a thermoelectric module when heat applied to the cold

face is effectively zero. DTmax or Dmax is one of the significant thermoelectric module/device

specifications.

MAXIMUM HEAT PUMPING CAPACITY (MAXIMUM Qc): The maximum quantity of heat that can

be absorbed at the cold face of a thermoelectric module when the temperature differential between

the cold and hot module faces is zero and when the module is being operated at its rated optimum

current. Qmax is one of the significant thermoelectric module/device specifications.

MODULE: A thermoelectric cooling component or device fabricated with multiple thermoelectric

couples that are connected thermally in parallel and electrically in series.

MULTI-STAGE MODULE (CASCADE MODULE): A thermoelectric module configuration whereby one

module is mechanically stacked on top of another so as to be thermally in series. This arrangement

makes it possible to reach lower temperatures than can be achieved with a single-stage module.

NATURAL CONVECTION HEAT SINK: A heat sink from which heat is transferred to the

surrounding air by means of natural air currents within the environment. No external fan, blower or

other appliance is used to facilitate air movement around the heat sink.

N-TYPE MATERIAL: Semiconductor material that is doped so as to have an excess of electrons.

OPTIMUM CURRENT: The specific level of electrical current that will produce the greatest heat

absorption by the cold side of a thermoelectric module. At the optimum current, a thermoelectric

module will be capable of pumping the maximum quantity of heat; maximum temperature

differential (DTmax) typically occurs at a somewhat lower current level.

PELTIER EFFECT: The phenomenon whereby the passage of an electrical current through a

junction consisting of two dissimilar metals results in a cooling effect; when the direction of current

flow is reversed heating will occur.

PHASE CHANGE: The change of a substance from a liquid to solid, liquid to gas, etc. A phase

change occurs, for example, when water freezes and turns into ice. See Heat of Fusion and Heat of

Vaporization.

POWER SUPPLY: Any source of DC electrical power that may be used to operate a thermoelectric

device.

P-TYPE MATERIAL: Semiconductor material that is doped so as to have a deficiency of electrons.

RADIATION (THERMAL): The transfer of heat energy by electromagnetic waves as a result of a

temperature difference between two bodies. In thermoelectric cooling applications, radiation losses

are quite small and usually have to be considered only for multi-stage coolers operating near a

DTmax condition.

RESISTIVITY (ELECTRICAL): Resistivity is a bulk or inherent property of a material that is

unrelated to the physical dimensions of the material. Electrical resistance, on the other hand, is an

absolute value dependent upon the cross-sectional area (A) and Length (L) of the material. The

relationship between Resistivity (r) and Resistance (R) is: r = (A/L) (R)

SEEBECK EFFECT: The phenomenon whereby an electrical current will flow in a closed circuit made

up of two dissimilar metals when the junctions of the metals are maintained at two different

temperatures. A common thermocouple used for temperature measurement utilizes this principle.

SI: An abbreviation for System International, the international standard metric system of units.

SILICON-GERMANIUM: A high temperature thermoelectric semiconductor material that exhibits

its optimum performance within a temperature range of 500-1000°C. Silicon-Germanium material

most often is used for special thermoelectric power generation applications that utilize a

radioisotope/nuclear heat source

SINGLE-STAGE MODULE: The most common type of thermoelectric cooling module using a single

layer of thermoelectric couples connected electrically in series and thermally in parallel. Single-stage

modules will produce a maximum temperature differential of approximately 70°C under a no-load

condition.

SPECIFIC GRAVITY: The ratio of the mass of any material to the mass of an equal volume of

water at a temperature of 4°C.

SPECIFIC HEAT: The amount of thermal energy required to raise the temperature of a given

substance by one degree compared to the energy required to raise the temperature of an equal

mass of water by one degree. The specific heat of water is 1.000.

SUBSTRATE: A plate or sheet of thermally conductive and electrically insulated material on which a

thermoelectric module is fabricated. A typical module has two individual substrates each having a

metalized pattern to conduct electric current. Thermoelectric elements are sandwiched between the

two substrates to form a completed module. Most substrates used in thermoelectric coolers are

made of alumina ceramic although berylia ceramic and other materials may be used in special

circumstances.

THERMAL COEFFICIENT OF EXPANSION: A measure of the dimensional change of a material

due to a change in temperature. Common measurement units include centimeter per centimeter per

degree Celsius and inch per inch per degree Fahrenheit.

THERMAL CONDUCTANCE: The amount of heat a given object will transmit per unit of

temperature. Thermal conductance is independent of the physical dimensions, i.e., cross-sectional

area and length of the object. Typical units include watts per degree Celsius and BTU per hour per

degree Fahrenheit.

THERMAL CONDUCTIVITY: The amount of heat a material will transmit per unit of temperature

based on the material’s cross-sectional area and thickness.

THERMAL GREASE: A grease-like material used to enhance heat transfer between two surfaces by

filling in the microscopic voids caused by surface roughness. Most thermal greases, also known as

Transistor Heat Sink Compound or Thermal Joint Compound, are made from silicone grease loaded

with zinc oxide. Non-silicone based compounds are also available which in most cases are superior

but more expensive than silicone-based alternatives.

THERMAL RESISTANCE (HEAT SINK): A measure of a heat sink’s performance based on the

temperature rise per unit of applied heat. The best heat sinks have the lowest thermal resistance.

THERMOELECTRIC DEVICE: A general and broad name for any thermoelectric apparatus. The

term Thermoelectric Device has recently been modified to exclude thermoelectric modules in favor

of thermoelectric assemblies.

THERMOELECTRIC GENERATOR: A device that directly converts energy into electrical energy

based on the Seebeck Effect. Bismuth telluride-based thermoelectric generators have very low

efficiencies (generally not exceeding two or three percent) but may provide useful electrical power

in certain applications.

THERMOELECTRIC HEAT PUMP: Another name for a thermoelectric module or thermoelectric

cooler. The term Heat Pump has been used by some specifically to denote the use of a

thermoelectric module in the heating mode, but this usage is uncommon.

THERMOELEMENT: Another name for a thermoelectric element or die.

THERMOPILE: When a thermoelectric module is used in a calorimeter application it is frequently

called a thermopile. Some have used the word thermopile as a synonym for thermoelectric module

regardless of application, but such use is unusual.

THOMSON EFFECT: The phenomena whereby a reversible evolution or absorption of heat occurs at

opposite ends of a conductor having a thermal gradient when an electrical current passes through

the conductor.

VISCOSITY: A fluid property related to the interaction between fluid molecules that determines the

fluids resistance to sheering forces and flow.

thermoelectric technical reference

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