Title: Optimal Design of Thermoelectric Generators for Low Grade Heat Recovery

Developed by Dr. HoSung Lee on 12/15/2014

Low-grade waste heat conversion to electricity has drawn much attention toward reduction of

production cost (Matsuura, Rowe et al. 1992, Rowe 1995, Ebrahimi, Jones et al. 2014). Organic

Rankine cycle has been recently proved as a feasible solution with about 7% thermal efficiency

and initial cost of about $2/watt for a high temperature of 116 °C and low temperature of 25 °C

(Imran, Park et al. 2014, Matsuda 2014, Minea 2014). Thermoelectric generators is thought to be

an alternative solution. The barriers for thermoelectric generators are the low conversion

efficiency of about 3% and high initial cost of about $20/watt (Rowe 2012, Ebrahimi, Jones et al.

2014). However, recent development of optimal design on thermoelectric generators indicates

that significant improvement in both performance and cost could be achieved (Lee 2010, Lee

2013, Attar, Lee et al. 2014, Weera 2014). Together particularly with a small operating cost due

to no moving parts, thermoelectric generators would be a good and reliable candidate for low-

grade waste heat recovery with the present optimal design.

We consider low grade heat recovery from Steam Assisted Gravity Drainage (SAGD) oil sands

production. It is understood that the oil-water mixtures at about 200 °C be drawn to the ground

surface from a deep underground oil reservoir while injecting steam to the mixtures including

sands in the reservoir. The oil-water mixtures once at the surface are then cooled down to 80 °C

probably for separation of oil and water. After the completeness of cooling process, the hot water

at 80 °C is separated from the mixtures. It is conventionally difficult to recover the low grade

heat of the separated water and they are wasted. We herein focus on optimal design to recover

the waste heat using thermoelectric generators between the hot water at 80 °C and room-

temperature water at 25 °C. In addition, there is a possibility to recover the cooling energy of the

mixtures from 200 °C to 80 °C using also thermoelectric generators if the cooling process allows

applying thermoelectric generators for the oil-water mixtures. This possibility is briefly

discussed later.

Design of thermoelectric generator modules for various systems has been challenging:

manufacturers provide empirical performance curves for their products based on the ideal

(standard) condition which uses the constant high and low junction temperatures that assume no

thermal resistances between the junction surfaces and medium-fluids. This is indeed unrealistic.

Optimization with the ideal condition are often used erroneously in system design. Two

additional problems are confronted, which are firstly that the material properties are not known

(the manufacturers do not usually provide the properties due to their proprietary information) and

secondly that the thermal electrical contact resistances between the thermoelectric elements and

the conductors are not known and even difficult to handle in design. System designers may have

great difficulties to select suitable modules for their system among many commercial

thermoelectric modules available. A typical thick and long thermoelectric generator (TEG)

module is shown in Figure 1, which is very similar over those of other manufacturers, indicating

that no correct optimization is currently implemented (compared to the present optimal design).

Intuitive long element length for intention to decrease the thermal conductivity also provokes a

joule heating concurrently consuming the generated electricity turning into heat, so it is not clear

whether the long element length in Figure 1 is beneficial or not until the optimization for a

specific system is taken into account.

Figure 1. A commercial thermoelectric module

We considered a realistic case (Lee, 2013) taking a fluid flow with a heat sink on each side of the

hot and cold junctions, so that there exist two thermal resistances between the two junctions and

the hot and cold fluids, forming a unit cell (similar to a TEG module). Then, we defined five

independent dimensionless numbers, not conflicting one another, one of which called Nk which

includes the most important combined geometric information such as number of thermocouples,

dimensions of element (cross-sectional area and length), and thermal conductivity. The next

important dimensionless number is called Rr which is the ratio of external electrical resistance to

internal electrical resistance. The third dimensionless number is called Nh, the ratio of the hot

convection to the cold convection. The fourth is the ratio of the hot fluid temperature to the cold

fluid temperature. The fifth is called the dimensionless figure of merit ZT (which represent the

quality of a material, the higher the better). In the following calculations, ZT = 1.4 at 80 °C is

used throughout, of which the material is bismuth telluride nanocomposites and practically

feasible for the mass production (Poudel, Hao et al. 2008) although the currently available bulk

bismuth telluride alloy in the market is at approximately ZT = 1. We were able to optimize the

combined dimensionless number Nk along with other dimensionless numbers for a given

condition of the hot and cold water temperatures and the material properties, which is shown in

Figure 2 (a) and (b). The figures show dramatic thermal dynamics of power and efficiency as

functions of Rr and Nk. At an optimal Rr = 1.6 (note that the ideal condition with constant

junction temperatures gives an impractical value of Rr = 1), With decreasing Nk from the

maximum power output, the power output decreases in Figure 2 (a) while the efficiency

increases in Figure 2 (b). The optimal point can be compensated to have a high enough power

and also a reasonable efficiency, which is solely a different aspect of design compared with the

Rankin cycle. If the resource of hot water is abundant and free, the power output may be more

important than the conversion efficiency.

(a) (b)

Figure 2 (a) Power output (W) and (b) conversion efficiency (%) with respect to Rr and Nk.

These figures used hot water temperature of 80 °C and low water temperature of 25 °C, ZT =

1.4, Nh = 10 and base area 5 cm x 5 cm. The water velocity of 0.5 m/s in both channels is used.

One of important findings in this study (under publication) is that as mentioned earlier the

performance of TEG module is a function of element length, as shown in Figure 3, which is

qualitatively in excellent agreement with the analysis of the contact resistances since both are

thermal resistances anyway. This indicates that the present thermal resistances between the

junctions and fluids through the heat sinks have a potential to effectively take into account the

intractable contact resistances between the junctions and electrical conductors. This greatly

simplifies the analysis of the present optimal design. Figure 3 shows that the optimal element

length is near 0.5 mm which contrasts with the commercial TEG module in Figure 1

(approximately 5 mm). This result indicates that the thermoelectric material (initial cost) could

be significantly reduced with an even much higher power output. The 5-mm length commercial

TEG module in Figure 1 actually claims a power output of about 1 watt at this temperature,

which is approximately in agreement with this figure.

Figure 3. Power output and efficiency vs. element length. These figures used hot water

temperature of 80 °C and low water temperature of 25 °C, ZT = 1.4, Nh = 10 and base area 5 cm

x 5 cm.

This optimization of element length of 0.5 mm in Figure 3 is attained along with other optimal

dimensionless parameters, mainly Rr, Nk and Nh. It is practically very difficult to achieve the

optimization by a trial and error method without correct information of optimal Rr, definition of

Nk, and system (fluid and heat sink) conditions. It is noted that the reduction of element length

from 5 mm to 0.5 mm results in a fivefold increase in the power output from 1 watts to 5 watts

with an acceptable decrease in the conversion efficiency from 3.2% to 2.5%. In fact, the similar

phenomenon was surprisingly observed in the work of Matsuura and Rowe (Matsuura, 1992),

where they thought that the increase of power output with decreasing the element length

attributes solely to the contact resistances. However, the present study shows the thermal

resistances virtually includes many features such as the fluids convection, the heat sinks and the

contact resistances. Now, we can estimate the material cost per watt. According to the CRC

Handbook (Rowe 2012), the cost per watt for typical TEG modules is about $20/watt, which

might be estimated to be $20 per 1 watts-commercial modules in this case. If we divide $20 by

the present work of 5 watts instead of 1 watts, we may have $4/watt. Considering the reduction

of element length from 5 mm to 0.5 mm would even reduce the material cost further probably to

about $2/watt, which may be competitive to the cost $2/watt of the Rankine cycle. This

calculation is very rough because the hot water temperature of 80 °C used for the present work

does not match the hot water temperature of 116 °C used for the organic Rankine cycle. We just

try to illustrate the effectiveness of our optimal design compared to the bench mark values. If the

initial cost is competitive, TEG would be obviously a better choice when considering the

negligible operating cost.

The effects of ZT on performance are calculated using the present optimization method in Figure

4. The performance of TEG module can be improved with increasing ZT. ZT = 3 is expected in

the near future based on the trend and development of material research-currently ZT = 2.4 with

quantumdots superlattice material (Venkatasubramanian, Silvola et al. 2001, Dresselhaus, Chen

et al. 2007) using nanotechnology, which may produce about 10 watts per the base area of 5 cm

x 5 cm with 4.5 % efficiency as shown in Figure 4.

Figure 4. Optimal power output and efficiency vs. the dimensionless figure of merit. This figure

used hot water temperature of 80 °C and low water temperature of 25 °C, Nh = 10 and base area

5 cm x 5 cm.

One of advantages using TEG for waste heat recovery is that there is no limit for the temperature

difference between hot and cold water temperatures (although there may be a limit due to an

economic reason between gain and cost) while the Rankine cycle may have a limited range for

heat source water temperature for instance between 80 °C and 60 °C. It is then understood that

the hot water at 80 °C enters an evaporator and leaves at 60 °C in the Rankine cycle, where the

waste heat below 60 °C is not used for recovery. The thermal efficiency for the Rankine cycle is

calculated based on the power output generated by a turbine over the heat (input) absorbed in the

evaporator, actually this calculation is brought from the work of Matsuda (Matsuda 2014). The

optimal power output for TEG is calculated as a function of hot fluid temperature, which is

shown in Figure 5, showing clearly that there will be a waste heat recovery (additional gain)

from the heat source water below 60 °C. On the other hand, there appears a progressive power

output decreasing approximately from 6 watts to 3 watts as hot water passing through the

channel of TEG modules from 80°C to 60°C. If we presume that the gain from the recovery

below 60°C is the same as the loss from the power output decreasing from 80°C to 60°C, our

simple calculation of power output at 80°C would be a good approximation. Now we try to

estimate how many modules or arrays are required for a power output of 1000 kW if the power

output of 5 watts per base area of 25 cm^2 is used. Suppose that an array consists of 500

modules which has 1.25 m^2 in the surface area. A total number of modules is obtained by

dividing 1000 kW by 5 W, which is 200,000 modules. Dividing 200,000 by 500 leads to total

400 arrays, which is shown in the first column of Table 1. The first column uses nanocomposite

material of bismuth telluride alloy which has ZT = 1.4 developed by a MIT group (Poudel, 2008)

being considered to exhibit the mass production in the near future. However, the similar

calculations with currently available commercial bulk material of ZT = 1 are performed, which

are shown in the second column of Table 1. All the three payback values in Table 1 are less than

5 years, which indicates that all are beneficial and feasible.

Figure 5 Optimal power output as a function of hot fluid temperatures. This figure used low

water temperature of 25 °C, Nh = 10 and base area 5 cm x 5 cm.

Table 1. Summary for three specific waste heat recovery cases.

Performance of TEG Heat Recovery Units

(Performance for maximum power output)

Waste heat sources Hot Water 80 °C

Cold Water 25 °C

Hot Water 80 °C

Cold Water 25 °C

Hot oil and water

mixture 200 °C

Cold water 25 °C

Thermoelectric material

used

Bismuth telluride

nanocomposites

ZT = 1.4 at 80 °C

(Poudel, Hao et al. 2008)

Bismuth telluride

Bulk

ZT = 1.0 at 80 °C

(Poudel, Hao et al.

2008)

Bismuth telluride

nanocomposites

ZT = 1.1 at 200 °C

(Poudel, Hao et al.

2008)

Optimal calculations for one module

Power output (W)

per module base area 25

cm^2

~ 5 W (6.5 W) ~ 3.5 W (4.8 W) ~ 35 W

Total heat delivered (W)

~ 200 W ~ 194 W ~700 W

Conversion efficiency

(%)

~ 2.5 % (1.7 %) ~ 1.8 % (1.3 %) ~ 5 %

Ideal efficiency* /Carnot

efficiency (%)

3.4 % / 15.5 % 2.5 % / 15.5 % 6.6 % / 31 %

Estimate cost $ per

watt**

~ $2/W ~ $3/W < $1/W

Element length (mm) 0.5 mm 0.6 mm 0.3 mm

Calculations for 1000 kW power output

Total # of modules

(= 1000 kW / module

power output)

200,000 286,000 28,000

Volume of total arrays

(= Volume of array × #

of array)

10 m^3 15 m^3 1.5 m^3

Power density

(= 1000 kW / volume of

total arrays)

100 kW/m^3 70 kW/m^3 700 kW/m^3

Total hot water flow rate

(kg/s) based on water

velocity (m/s) in channel

~ 230 kg/s

0.5 m/s

~ 230 kg/s

0.5 m/s

~ 215 kg/s

0.5 m/s

Power generation (kW)

1000 kW 1000 kW 1,000 kW

Total waste heat (kW)

40,000 kW 56,000 kW 20,000 kW

Pump power (kW) for

hot & cold water flows

80 kW 80 kW 80 kW

Power generation

efficiency (%)

(1,000kW-80kW) /

40,000kW = 2.3 %

(1,000kW-80kW) /

56,000 kW = 1.6 %

(1,000kW-80kW) /

20,000 kW = 4.6 %

Payback (years) with

electricity price $0.1/kW

and operating time at

7000 hours/year

~ 3 years

=(1000kW*$2/W) /

[(1000kW-80kW)

×7000hr×$0.1/kWh]

~ 4.5 years

=(1000kW*$3/W) /

[(1000kW-80kW)

×7000hr×$0.1/kWh]

< 1.5 years

=(1000kW*$1/W) /

[(1000kW-80kW)

×7000hr×$0.1/kWh]

*Ideal efficiency assumes constant hot and cold junction temperatures which deems unrealistic.

**Prices were estimated with commercial product values.

As mentioned earlier, there is a potential to recover the additional cooling energy of the oil-water

mixtures from 200 °C to 80 °C once at the ground surface using also thermoelectric generators if

the cooling process allows applying thermoelectric generators for the mixtures. As for the hot

water at 80 °C, this case is similarly calculated, which is shown in the third column of Table 1.

The power density of 700 kW/m^3 is large compared to 100 kW/m^3 of the hot water at 80 °C

because of the higher temperature. Although the present calculations exhibit crudity at this time,

they give a good picture of the systematic idea. For instance, what would be the core space

occupancy, initial cost, and operating cost for a waste heat recovery of 1 MW of the cooling

down process of oil-water mixtures in SAGD? The answer is approximately 1.5 m^3, at most 1

million dollars ($1/W x 1000kW), and a negligible operating cost as shown in Table 1. It is good

to note that the TEG devices are very reliable and robust being used for two decades without

problems in Mars (Minnich, 2009).

It is seen in Table 1 that the three different cases yield different element lengths, which means

that the geometry of the TEG module are custom designed for the specific systems. In fact the

number of thermoelectric elements and the element’s cross-sectional areas of the module also

show different values although they are not shown in Table 1. This is indeed one of the most

challenging parts of optimal design, which would not be achieved without the solid mathematical

definitions of the present optimal design method. To my knowledge, this custom design of TEG

module with the optimal geometry (number of thermoelements, element length and cross-

sectional area) for a particular system has not been found in the literature.

As mentioned before, the unit cell includes the hot and cold fluid convections, heat sinks, contact

resistances, and thermoelectric module. Each unit cell in an array through a channel exhibits

thermal isolation, but connected through a heat balance (energy in and out) across the unit cell,

which implies that the junction temperatures of the unit cells along each channel reveal a step-

change rather than a continuous change. This allows mathematically the optimization tractable.

The adequacy of the thermal isolation is well verified (Attar, 2014). Therefore, the concept of the

unit cell in the present work is realistic. Likewise, we are able to optimize the geometry (number

of thermo-element, cross-sectional area and length) of each unit cell from the entry to the exit in

the channel for a specific system like this low grade heat recovery at 80 °C or 200 °C.

There is still a remaining question from the earlier discussion how to determine the material

properties such as the Seebeck coefficient, the electrical conductivity, and the thermal

conductivity for the optimal design. This question is fundamental and also formidable even for

manufacturers because the intrinsic material properties (provided by the material developer) will

be changed depending on manufacturability due mainly to the contact resistances and does not

usually show an agreement with the measurements of the performance (Huang, Weng et al.

2010). Therefore, we have developed a technique to determine the material properties using three

maximum parameters of Tmax, Imax, and Qmax either from manufacturer’s specification or

direct measurements (Ahiska and Ahiska 2010, Weera 2014). We first formulated theoretically

the maximum parameters and expressed the three material properties in terms of the three

maximum parameters (Lee, Attar et al. 2014). When the material properties are determined by

using the measured maximum parameters, the material properties become meaningful and

realistic including all uncertainties such as the contact resistances, Thomson effect, degradation

of materials, etc., which are called the effective material properties. One of my graduate students

conducted experiments as shown in Figure 6 to verify the adequacy of the effective material

properties developed. He compared the predictions using the effective material properties with

the measurements and also the manufacture’s data, showing all in good agreement, which is

shown in Figures 7 (a) and (b). This result justifies that the effective material properties are good

for the optimal design. It is important to note that the dimensionless figure of merit ZT using the

effective material properties exhibits a little less than the intrinsic ZT, which result from all the

uncertainties or losses imposed on the ZT.

Figure 6. Experimantal setup

Figure 7 (a) Measured power output vs. hot side temperature for thermoelectric generator HZ-2,

(b) measured cooling power vs. current for thermoelectric cooler RC12-04

References

Ahiska, R. and K. Ahiska (2010). "New method for investigation of parameters of real

thermoelectric modules." Energy Conversion and Management 51(2): 338-345.

Attar, A., et al. (2014). "Optimal Design of Automotive Thermoelectric Air Conditioner

(TEAC)." Journal of Electronic Materials.

Dresselhaus, M. S., et al. (2007). "New Directions for Low-Dimensional Thermoelectric

Materials." Advanced Materials 19(8): 1043-1053.

Ebrahimi, K., et al. (2014). "A review of data center cooling technology, operating conditions

and the corresponding low-grade waste heat recovery opportunities." Renewable and Sustainable

Energy Reviews 31: 622-638.

Huang, H.-S., et al. (2010). "Thermoelecrtic water-cooling device applied to electronic

equipment." International Communications in Heat Transfer 37: 140-146.

Imran, M., et al. (2014). "Thermo-economic optimization of refrigerative organic Rankine cycle

for waste heat recovery applications." Energy Conversion and Management 87: 107-118.

Lee, H. (2010). Thermal Design; Heat Sink, Thermoelectrics, Heat Pipes, Compact Heat

Exchangers, and Solar Cells. Hoboken, New Jersey, John Wiley & Sons.

Lee, H. (2013). "Optimal design of thermoelectric devices with dimensional analysis." Applied

Energy 106: 79-88.

Lee, H., et al. (2014). "Performance Prediction of Commercial Thermoelectric Cooler Modules

Using the Effective Material

Properties." Submitted to Journal of Electronic Materials.

Matsuda, K. (2014). "Low heat power generation system." Applied Thermal Engineering 70(2):

1056-1061.

Matsuura, K., et al. (1992). Design optimization for a large scale low temperature thermoelectric

generator. Proceedings of the International Conference on Thermoelectrics. 11th: 10-16.

Minea, V. (2014). "Power generation with ORC machines using low-grade waste heat or

renewable energy." Applied Thermal Engineering 69: 143-154.

Poudel, B., et al. (2008). "High-thermoelectric performance of nanostructured bismuth antimony

telluride bulk alloys." Science 320(5876): 634-638.

Rowe, D. M. (1995). CRC handbook of thermoelectrics. Boca Raton London New York, CRC

Press.

Rowe, D. M. (2012). Modules, systems and application in thermoelectrics. Roca Raton, CRC

Press, Taylor & Francis.

Venkatasubramanian, R., et al. (2001). "Thin film thermoelectric devices with high room

temperature figure of merit." Nature 413: 597-602.

Weera, s. (2014). Analytical performance evaluation of thermoelectric modules using effective

material properties. Kalamazoo, Michigan, Western Michigan University. Master of Science in

the Department of Mechanical and Aerospace Engineering: 143.

Weera, S. L. L. (2014). Analytical performance evaluation of thermoelectric modules using

effective material properties. Mechanical and Aerospace Engineering. Kalamazoo, Michigan,

Western Michigan University. Master of Science.

Evaluation Criteria

1. Proposed Technical Approach

2. Supporting Data - (Provide data to support your upgrade or conversion process; for

conceptual approaches provide scientific rationale, where possible provide diagrams,

performance predictions, measured data and cost data. Cost data may be in $/kW. Provide

payback period.)

3. Technical Readiness – (Describe the readiness of this idea to be executed in the field and

the investment required.)

The present optimal design method with the currently available bulk material in the

market (the second column of Table 1) shows a readiness of this idea providing a

reasonable payback of less than 5 years for 1000 kW power output using low grade heat

of water at 80 °C and a power density of 70 kW/m^3. This allows to install the TEG units

anywhere in a convenient place with a minimum space occupancy.

4. Plan for Execution – (Provide the tasks, time and cost estimates to take this idea to the

field.)

The structure of TEG units with the current bulk material of ZT = 1 (column one in Table

1) is relatively simple compared to an organic Rankine cycle; an array has 500 modules

(unit cells), each array unit having a thickness of 2 cm leading to a volume of 1.1 m x 1.1

m x 2 cm. There will be 572 array units leading to total volume of about 15 m^3 for 1000

kW. The present realistic optimal design method allows prompt calculations entering

experimental verifications using a readily available two-flow-loop apparatus at WMU.

Once the design is completed, the computer simulations will be performed to confirm the

performance in the system. Meanwhile, a 32-TEG-module prototype unit is constructed

and tested in my lab and compared with the computer model. Once the experimental

results with the computer simulations are satisfactory. We finalize the design of an array

unit and then start to construct/test a real prototype consisting of 500 modules array.

After confirmation of the test results, we may order 572 array units which may be divided

by a number of groups of arrays (called banks) for practical reasoning. It is anticipated to

take five years in total for the above mentioned tasks. We believe some collaboration will

be necessary for these tasks: potential companies are Marlow and Fraunhofer IPM for

thermoelectric modules or elements fabrication, GenTherm for the array (or bank) units,

and a company for piping and pumping design and installation. The payback for 1000

kW power output assuming electricity $0.1/kW may be estimated considering the TEG

materials of about three million dollars (as shown in Table 1), the construction of array

units, the piping and installation, and the pumping cost, which may lead to approximately

the payback of 7 years (this is a very rough estimation which may change significantly).

5. Energy efficiency Calculations – (Provide calculations to demonstrate that the energy

input is less than the highest value or electricity produced, using one of the two equations

below. Provide the usable heat temperature level that can be achieved and the waste heat

temperatures.)

Power generation E = (HVH – EC)/Q

Where:

E = Efficiency

HVH = High value in GJ (electricity produced)

EC = Energy consumed in GJ

Q = Total waste heat available in GJ

Table 1. Summary for three specific waste heat recovery cases.

Performance of TEG Heat Recovery Units

(Performance for maximum power output)

Waste heat sources Hot Water 80 °C

Cold Water 25 °C

Hot Water 80 °C

Cold Water 25 °C

Hot oil and water

mixture 200 °C

Cold water 25 °C

Thermoelectric material

used

Bismuth telluride

nanocomposites

ZT = 1.4 at 80 °C

(Poudel, Hao et al. 2008)

Bismuth telluride

Bulk

ZT = 1.0 at 80 °C

(Poudel, Hao et al.

2008)

Bismuth telluride

nanocomposites

ZT = 1.1 at 200 °C

(Poudel, Hao et al.

2008)

Optimal calculations for one module

Power output (W)

per module base area 25

cm^2

~ 5 W (6.5 W) ~ 3.5 W (4.8 W) ~ 35 W

Total heat delivered (W)

~ 200 W ~ 194 W ~700 W

Conversion efficiency

(%)

~ 2.5 % (1.7 %) ~ 1.8 % (1.3 %) ~ 5 %

Ideal efficiency* /Carnot

efficiency (%)

3.4 % / 15.5 % 2.5 % / 15.5 % 6.6 % / 31 %

Estimate cost $ per

watt**

~ $2/W ~ $3/W < $1/W

Element length (mm)

0.5 mm 0.6 mm 0.3 mm

Calculations for 1000 kW power output

Total # of modules

(= 1000 kW / module

power output)

200,000 286,000 28,000

Volume of total arrays

(= Volume of array × #

of array)

10 m^3 15 m^3 1.5 m^3

Power density

(= 1000 kW / volume of

total arrays)

101 kW/m^3 71 kW/m^3 700 kW/m^3

Total hot water flow rate

(kg/s) based on water

velocity (m/s) in channel

~ 230 kg/s

0.5 m/s

~ 230 kg/s

0.5 m/s

~ 215 kg/s

0.5 m/s

Power generation (kW)

1000 kW 1000 kW 1,000 kW

Total waste heat (kW)

40,000 kW 56,000 kW 20,000 kW

Pump power (kW) for

hot & cold water flows

80 kW 80 kW 80 kW

Power generation

efficiency (%)

(1,000kW-80kW) /

40,000kW = 2.3 %

(1,000kW-80kW) /

56,000 kW = 1.6 %

(1,000kW-80kW) /

20,000 kW = 4.6 %

Payback (years) with

electricity price $0.1/kW

and operating time at

7000 hours/year

~ 3 years

=(1000kW*$2/W) /

[(1000kW-80kW)

×7000hr×$0.1/kWh]

~ 4.5 years

=(1000kW*$3/W) /

[(1000kW-80kW)

×7000hr×$0.1/kWh]

< 1.5 years

=(1000kW*$1/W) /

[(1000kW-80kW)

×7000hr×$0.1/kWh]

*Ideal efficiency assumes constant hot and cold junction temperatures which deems unrealistic.

**Prices were estimated with commercial product values.

6. Experience – (Discuss your experiences in low temperature waste heat recovery,

including number of projects.)

I have taught a course of Design of Thermal Systems at WMU since 1999. Meanwhile, I

have developed a new graduate course of Advanced Thermal Design for 8 years, where

thermoelectric generators is one of the topics. Low grade heat recovery is often taken by

students as a term projects. This is the rationale for me to develop optimal design of

thermoelectric devices. I wrote a textbook with a title of Thermal Design: Heat Sinks,

Thermoelectrics, Heat Pipes, Compact Heat Exchangers and Solar Cells to help students

for their thermal design projects. The optimal design developed is particularly good in

nature for low grade heat recovery. The finding are under publications.

7. Expertise – (Share the team expertise, discuss other work of a similar nature, highlight

other capabilities or competencies that augment your ability perform the proposed

project, provide the years in this field.)

One of my students, Sean Weera, conducted experiments to verify the effective material

properties which is one of important features of the optimal design methods with a good

agreement compared to the theoretical equations (Weera, 2014). Another PhD student,

Alaa Attar, developed automotive air conditioner using the optimal design method found

a good way of design and proved the method is essential for his design (Attar, 2014).

Low-grade waste heat conversion to electricity has drawn much attention toward

reduction of production cost (Matsuura, Rowe et al. 1992, Rowe 1995, Ebrahimi, Jones et

al. 2014). Organic Rankine cycle has been recently proved as a feasible solution with

about 7% thermal efficiency and initial cost of about $2/watt for a high temperature of

116 °C and low temperature of 25 °C (Imran, Park et al. 2014, Matsuda 2014, Minea

2014). Thermoelectric generators is thought to be an alternative solution. The barriers for

thermoelectric generators are the low conversion efficiency of about 3% and high initial

cost of about $20/watt (Rowe 2012, Ebrahimi, Jones et al. 2014). However, recent

development of optimal design on thermoelectric generators indicates that significant

improvement in both performance and cost could be achieved (Lee 2010, Lee 2013,

Attar, Lee et al. 2014, Weera 2014). Together particularly with a small operating cost due

to no moving parts, thermoelectric generators turned out to be a good and reliable

candidate for low-grade waste heat recovery with the present optimal design. I have been

working in this field since 1999. I am a director of Advanced Thermal Science at Western

Michigan University.