chapter one introduction mechanism of heat...

INTRODUCTION &

MECHANISM OF

HEAT TRANSFER

Chapter one

INTRODUCTION

• Relation of Heat Transfer to Thermodynamics

• Why we should learn Heat and mass transfer?

• Heat transfer?

• The mechanism of heat transfer?

Relation of Heat Transfer to Thermodynamics

Thermodynamics:

• deals with systems in equilibrium

• Predict the amount of energy required to change a system from one equilibrium state to another

• It may not be used to predict how fast the change will take place since the system is not in equilibrium during the process

Heat transfer supplements the first and second principles of thermodynamics used to establish energy transfer rate


• In thermodynamic, Q are only state function (contain by system) ∆Q

• In energy transfer, Q are associated with a process (path function). δQ

• “energy transfer: energy can cross the boundries of a closed system only in the form of heat (Q) or work (W)”

V is a state function

W is a path function


Example:

Cooling of hot steel bar placed in a

pail water 桶水

THERMODYNAMIC predict the final equilibrium temperature

of the steel bar-water combination.熱平衡

HEAT TRANSFER predict the temperature of both the bar and

the water as a function of time also the temperature of the bar

will be after a certain length of time.時間函數溫度變化

Heat Transfer??

• Heat is an energy transfer across a system boundary due to the temperature different between a system and its surroundings.

• There are 3 mechanisms of heat transfer

(1) Conduction: Surface to surface

(2) Convection: Surface to air熱對流

(3) Radiation: Direct exchange across space

熱傳導

熱輻射

(1) Conduction

• Direct transfer of heat (surface to surface)

# Transfer is affected by the ability of the touching objects to conduct heat

• Thermal conductivity, k

# expressed as W m-2 K-1

# It is a physical property for gas, liquid and solid

物質媒介溫度差

熱傳導係數

物理性質

(1) Conduction

• The heat is transferred as a result of the energy imparted between adjacent molecules.

• Conduction also arises from the movement of free electrons in the metals which accounts for the high thermal conductivities

• In fluids, it occurs as a result of the kinetic energy transfer between one molecule to another

傳授

(1) Conduction

• Temperature different: T1 and T2 [K]

• Thermal conductivity: k [W m-1 K-1]

• Heat transfer area: A [m2]

• Thickness of the material: x [m]

• Heat transfer rate by conduction: qc [??]

• Heat flux: q/A [??]

Since T2>T1, the heat flows from right

to left

Fourier’s Law

熱通量

Fourier’s Law

• Heat transfer by conduction from a high temperature region to the low temperature region

• The driving force of this heat transfer is the temperature gradient

Fourier’s Law

Example

The Resistance of heat flow:

Rod diameter

Rod length

Rod material type

Temperature difference

https://www.youtube.com/watch?v=UBcZsWJ5TNA

1d conduction

https://www.youtube.com/watch?v=UBcZsWJ5TNA

Heat conduction analysis

(1d and 3d)

Sec 1-1

Conduction

• Fourier’s Law

q : Heat transfer rate

: Temperature gradient in direction of the heat flow

*補充

Heat Conduction Analysis- 1D • 1-D (plane wall)

• So, the energy balance

Situation:

Consider general case where temp.

changing with time & heat source

present within the body.

Heat Conduction Analysis- 1D

General 1-Dimension Heat Conduction equation:

K=constant

Heat Conduction Analysis-3D

1) Cartesian coordinates

• So, the energy balance:


General 3-Dimension Heat Conduction equation:


If, k = constant

: Thermal Diffusivity of the material

Thermal Diffusivity

# The larger value of α, the faster heat will diffuse through the material.

# So, α can be higher value if

i) Thermal conductivity, K higher

ii) Thermal heat capasity, ρc lower

m2/s

Heat Conduction Analysis- 3D 3-Dimension Heat Conduction equation:

2) Cylindrical coordinates

3) Spherical coordinates

Cylinder Coordinates

Sphere Coordinates


：原點與點 P 之間的徑向距離 r ，原點到點 P 的連線與正 z-軸之間的天頂角 \theta ，以及原點到點 P 的連線，在

xy-平面的投影線，與正 x-軸之間的方位角 \phi

Analysis: conclusion

• All the general equation (1D & 3D): only used in special case

• So for developments in future chapter can reduced form of the general equations for several cases of practical interest under specified conditions

Analysis: conclusion Steady-state 1D heat flow (no heat generation):

Steady-state 1D heat flow in cylinder coordinates (no heat generation):

Steady-state 1D heat flow with heat sources:

2D Steady-state conduction without heat sources:

Fourier’s Law

Thermal conductivity, k

• Experiment measurement made to determine the value of k (different material, different k)

• The k value is a physical property of each solid, liquid and gas material

• k is strongly temp-dependent

• Unit W m-1 K-1 or W m-1 C-1

K of various materials at

0 °C


• The numerical value of k indicates how fast heat will flow in a given material.

• If molecules move fasters (gas), the faster they will transport energy. But structure collision harder

• So, value of k depends on the molecules structure (gas, liquid or solid)


1)Gas (Fig. 1-4)

• If temp. higher, the molecules have higher velocities

• Molecules are in continuous random motion and will colliding with one another and exchanging the energy and momentum

• The random motion of gas molecules happen whether/ not a temp. gradient exist in gas

• If a molecules move from higher temp. region to low temp. region, it transport kinetic energy to lower temp. part of system (through collisions molecules)

• The faster molecules move faster they will transport energy


2) Liquid (Fig. 1-5)

• The molecules are move closely space

• Exchange energy in collision process

3) Solid (Fig. 1-6)

• Thermal energy conducted in solid by 2 modes: lattice vibration and transport by free electron

電的絕緣體常是熱的絕緣體但鑚石例外


Why we should know k of each material???

Because to design the equipment in process esp. in storage and

transport.

(2) Convection • Transfer of heat between an object and air (Surface to air)

• Transfer of heat by bulk transport and mixing of macroscopic elements of warmer portions with cooler portion in a gas or liquid

# Transfer is affected by

i) the speed with which the air is moving

ii) the ability of the object to conduct heat

(2) Convection

• The velocity, u reduce to 0 at the plate as a result of viscous action. Because of that, heat must be transferred only by conduction at that point (wall).

• Convection heat transfer depends on the viscosity and the thermal properties of the fluid (k, cp, ρ)

• Viscosity influence the velocity profile

• Boiling & condensation example of convection phenomena

(2) Convection

• Temperature different between wall and fluid: Tw and Tf [K]

• Convective heat transfer coefficient: hcv [W m-2 K-1]熱對流傳遞係數

• Heat transfer area: A [m2]

• Heat transfer rate by convection: qcv [??]

• Heat flux: q/A [??]

Also referred to as the “Newton rate equation” or “Newton’s law of cooling”

Appproximate

value of h

(2) Convection Two types:

(i) Forced convection:

# Fluid is forced to flow past a solid surface by a mechanical means

(ii) Natural (free) convection:

# Heat circulation due to fluid density difference resulting from the temperature variation throughout a region of the fluid

q= m cp (Te-Ti) = h A ( Tw average – Tfluid, average)

m

Ti Te

(3) Radiation

• Transfer of energy across the space by means of electromagnetic waves- in the same way as the electromagnetic light waves transmitting light (Direct exchange across space)

(3) Radiation

• Electromagnetic radiation which is propagated because of temp. different called thermal radiation

• Ideal thermal radiation/ black body radiation, will emit energy at a rate proportional to the fourth power of the absolute temp. of the body and directly proportional to it’s surface area.

• Black-body = Black surface (a piece of metal recovered with carbon black)

q emitted = σ A T4

(3) Radiation

σ = 5.669 x 10-8 W/m2.K4

• Tefan-Boltzmann Law thermal radiation, it govern only radiation emitted by black-body

• The net radiant exchange between 2 surface proportional to the different in absolute temperature to the fourth power

q emitted = σ A T4

q emitted = σ A (T14 – T2

4)

(3) Radiation • Emissivity, ϵ relates the radiation on the ‘gray surface’

• Not all the radiation leaving on surface will reach the other surface since electromagnetic radiation leaving straight line & some be lost to the surroundings. Because of that, 2 new factors will be considered (i) Fϵ: Emissivity function and (ii) FG: Geometric “view factor’ function

(3) Radiation

Radiation in an enclosure

Simple radiation problem is encounter when a heat transfer surface at temp., T1 completely enclosed by a much large surface maintain at temp. T2. So that, the net radiant exchange:

Conclusion: Heat transfer mechanism

• Heat transfer may take place by 1 or > of 3 mode of mechanism

“Situation: Heat conducted through the plate is removed from

the plate surface by combination of convection & radiation.”

•So, the energy balance;

Heat conducted through wall = Heat convection + Heat radiation

Conclusion: Heat transfer mechanism

Conduction and convection- heat transfer mechanism through

a material medium. Therefore radiation mechanism through

electromagnetic radiation (thermal radiation/black body radiation)

Identify the mechanism of heat transfer..

Heat Transfer in unit operation 1) Shell and tube heat exchanger

Heat Transfer in unit operation

• Example of a chemical/bioprocess??

• Factors affecting heat transfer rate??

Example 1:

One face of copper plate 3 cm thick is maintained at 400 °C, and the other face is maintained at 100 °C. How much heat is transferred through the plate?

Ans: 3.7 MW/m2

Example 2:

Air at 20 °C blows over a hot plate 50 by 75 cm maintained at 250 °C. The convection heat transfer coefficient is 25 W/m2.K. Calculate the heat transfer.

Ans: 2.156 kW

Example 3.:

An electric current is passed through a wire 1 mm diameter and 10 cm long. The wire is submerged in liquid water at atmospheric pressure, and the current is increased until the water boils. For this situation h = 5000 W/m2.K, and the water temperature will be 100°C. How much electric power must be supplied to the wire to maintain the wire surface at 114 °C?

Ans: 21.99 W

Example 4:

Two infinite black plates at 800 °C and 300 °C exchange heat by radiation. Calculated the heat transfer per unit area.

Ans: 69.03 kW/m2

Exercise 1:

Calculate the rate of heat flow through a 0.5 m wide, 0.3 m high and 3 mm thick steel plate, having a thermal conductivity of 45 W/m.k when the temp. of the surface at x=0 is maintain at a constant temp. of 198 °C and its temp. at x=3 mm is 199.7 °C.

Exercise 2: A refrigerator stands in a room where the air temp. is

20 °C. The surface temp. on the outside of the refrigerator is 16 °C, the sides are 30 mm thick and have an equivalent thermal conductivity of 0.1 W/m.k. The heat transfer coefficient on the outside is 10 W/m2.k. Assuming 1D conduction through the sides, calculate the heat flow through refrigerator and the surface temp. on the inside

Assignment 1

Book: J.P. Homan 1) 1-1

2) 1-2

3) 1-3

4) 1-4

5) 1-10

6) 1-16

7) 1-19

8) 1-22

9) 1-29

10) 1-30

chapter one introduction mechanism of heat...

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