FoE_ Heat Transfer.ppt

8/10/2019 FoE_ Heat Transfer.ppt

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ENERGY/REE

Foundations of Energy

Heat Transfer

Tapas Mallick


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Overview

Heat Transfer

Conduction

Heat transfer along a bar

Heat transfer across composite wall

Convection

Radiation

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3

Heat Transfer Mechanism:

Conduction

This is the intermolecular transfer of heat from

one part of a solid, liquid or gaseous body toanother part of the same body or from one

body to another body in physical contact,

without being displaced of the parts of the

body.

Hot ColdHeat Transfer from a hot solid body to cold

solid body, in physical contact.


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Heat Transfer Along a Bar

4

dx

dTkq

dx

dTkA

deltax

deltaTkAQ

Heat Transfer rateHeat flux

Fouriers Law of heatConduction

L

Ta Tb

Q

Thermal conductivity


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ENERGY/REE

Thermal Conductivity

5

11

2

KWm

m

Km

Watts

dX

dTA

Qk

dx

dTkAQ

Thermal Conductivity Unit: Wm-1K-1


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Thermal Conductivity

For any single material, k increases as vapour to

liquid to amorphous solid to solid Gases: thermal conductivity is very small, e.g. Air

0.0242 W/mK; Hydrogen: 0.167 W/mK

Liquid: thermal conductivity is small, e.g. Water:

0.569W/mK; Benzene: 0.159 W/mK

Solid: High thermal conductivity; e.g. Ice:

2.25W/mK; Steel 45.3W/mK; Copper 388 W/mK

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ENERGY/REE

Heat Transfer Across Composite

Wall

series thermal Resistance

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Heat Transfer Rate

A B C

xA xB xC

TA TB TC

T

QT1 T2 T3 T4

433221

TTx

AkTT

x

AkTT

x

AkQ

C

C

B

B

A

A


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CBA

C

C

B

B

A

A

C

C

B

B

A

A

RRR

TT

Ak

x

Ak

x

Ak

x

TTQ

TT

x

AkTT

x

AkTT

x

AkQ

4141

433221

Where, R=x/(kA) is the thermal resistance


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Composite Wall:

Parallel Resistance

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A TA

B TB

C TC

x

Q

AA

AB

AC

AQ

BQ

CQ

Heat Transfer Rate

T1 T2

Ak

x

T

Ak

x

T

Ak

x

TQ

C

C

C

B

B

B

A

A

A

CBA RRRTQ

111

or

Where, R=x/(kA) is the thermal resistance


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Conduction

Summary

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Through solid (mainly)

Q(dot) = - k A T / x = U A T= A T / R Two layers:

Resistance adds up

Two surfaces next to each other:

U-value and area add

Same as electrical network of resistors

(Ohms law)


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Example - 1

The wall of an industrial furnace is constructed from

0.15m thick fireclay brick having a thermal conductivity

of 1.7 W/m.K. Measurements made during steady-stateoperation reveal temperatures of 1400 and 1150 K at

the inner and outer surfaces, respectively. What is the

rate of heat loss through a wall that is 0.5 m by 3 m on a

side?

Answer: 4250 W


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Convection

This is the transfer of heat within fluids by

actual physical movement of the molecules Natural convection

The driving force is a difference of densities

Forced convection

The driving force is a mechanical mixing

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Cold

SolidHot Air

Hot air blowing over a cold solid will

heat up the solid after some time.

G /


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Convection

Heat is moved by fluid motion

Depends on geometries, temperatures, fluidproperties, and fluid velocities

Ignore all that and define a heat transfer

coefficient:

Q= hA T

ENERGY/REE


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Radiation

It is the transfer of heat as radiant energy from a

hot body in all directions, even without amedium.

14

SUN Earth

Heat transfer from Sun to Earth takes place by

radiant heat transfer through space

ENERGY/REE


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Radiation

Each object emits electromagnetic radiationaccording to its temperature

Blackbody radiation

Q= A (T14T2

4)

(T14T2

4)= (T12+ T2

2) (T12T2

2)

= (T12

+ T22

) (T1+ T2) T h= (T1

2+ T22) (T1+ T2)

Q= hA T

= Emissivity

Stephen Boltzmanns Constant

Here T1and T2are arbitrary

temperatures and T1>>T2

ENERGY/REE


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Example - 2

An uninsulated steam pipe passes through a room in

which the air and walls are at 25C. The outside

diameter of the pipe is 70mm, and its surfacetemperature and emissivity are 200C and 0.8,

respectively. What are the surface emissive power and

irradiation? If the coefficient associated with free

convection heat transfer from the surface to the air is 15W/m2. K, what is the rate of heat loss from the surface

per unit length of pipe?

Answer: Emissive power = 2270 W/m2

Irradiation = 447 W/m2

.Rate of heat loss = 998 W/m

ENERGY/REE


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Example - 3

The hot combustion gases of a furnace are separated

from the ambient air and its surroundings, which are at

25C, by a brick wall 0.15 m thick. The brick has athermal conductivity of 1.2 W/m . K and a surface

emissivity of 0.8. Under steady-state conditions an outer

surface temperature of 100C is measured. Free

convection heat transfer to the air adjoining the surface ischaracterised by a convection coefficient of h = 20

W/m2.K. What is the brick inner surface temperature?

Answer: 352C

ENERGY/REE


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Types of heat transfer

Through a solid object:

Conduction

By a moving fluid:

Convection

Through light:

Radiation

dx

dT

x

T kAkAQ ~

ThATTAQ ~4241

ThAQ ~dcomplicatetoo

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