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Advanced Heat TransferTheory & Application

Dr. S. Kamran Afaq

Professor

HITEC University

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Advanced Heat Transfer

Boiling and Condensation

Introduction

General Heat Conduction Equation

Convection Equation (Mass/Momentum/Energy)

Course Outline

In Rectangular, Cylindrical, Spherical Coordinate System

Steady (2-D) and Unsteady(1-D) Conduction

Various/Numerical Methods to Solve Conduction Equation

Laminar and Turbulent Heat Transfer Free and External/Internal Forced Convection

Fundamental of Radiation

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Introduction

Introduction

Basics of Heat Transfer

Heat & other Forms of Energy

Mechanism of Heat Transfer

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Introduction

Heat Transfer: A Practical Approach

Book:

By:Y A Cengel

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What is difference b/w Thermodynamicsand Heat transfer?

Thermodynamics :

Deals with the amount of heat transferas a system undergoesfrom one state to other equilibrium state.

Heat Transfer :

1. In engineering we are normally interested in the rate of heattransfer. How much heat is transfer per unit of time.

2. As well as the temperature distribution within the system at a

specified time.

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Introduction

Heat Transfer?

Heat Transfer :

1. Heat can transferred from one system to other due to the

temperature difference

2. It is science which predict the heat energy transfer betweenmaterial bodies as a result oftemperature difference.

Pipe flow

Pressure

Difference

Current flow

Voltage

Difference

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Introduction

Human Comfort

A human body iscontinuously rejecting

heat to surrounding.

Heat Transfer

Human comfort is directly related to rate of heat

rejection (Heat Transfer rate). We adjust this rate

by our clothing to the environmental condition.

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Introduction

Daily Life Examples

Heat Transfer

Heating & Air-Conditioning System

Refrigerator, Iron

Computer

Energy Efficient Home

Car Radiators Solar Collectors

(Min. Heat loss in winter and

gain in summer)

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Introduction

Why we need a detailed study ofHeat Transfer ?

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Introduction

Heat Transfer indicates how long process will take.

Why we need a detailed study ofHeat Transfer ?

A designer of thermosnormally interested in

that how long coffee will

sustain its temperature

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Introduction

Engineering Heat TransferApplications

1. Heat Exchangers

2. Boilers

3. Condensers

4. Radiators

5. Heaters

Rating : Determination of HT for an

existing system at a specific


Sizing : Determination of size of asystem in order to transfer heat as

a specified rate for a specific


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Introduction

Thermal Energy (Q) = 1 joule

UNITS

Heat Transfer rate (q-dot) = 1 joule/sec = 1 watt

Heat Flux (q/A) = 1 watt/m2

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Introduction

Energy :

Heat & other forms of Energy

Thermal

Chemical, Nuclear

K.E, P.E

Mechanical

Electrical

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Introduction

Internal Energy (U) :


Sum of all microscopic forms of energy of molecules.

U = K.E + P.E

Portion of K.E = Sensible Energy or Heat

Heat :

Temperature :

Total K.E of molecules

Average K.E of molecules

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Introduction

Internal Energy


Associated Atomic bonds

in a molecule is called

Chemical energy

Associated with bond within the

Nucleus of the atom is calledNuclear Energy

This energy is released during the chemical or Nuclear reaction

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Introduction

Calorie :


Calorie is a unit of Heat Energy. Like Joule

1 Cal = 4.1868 Joule

1 Cal =Amount of heat required

raise the temperature of one gram

of water at 14.5C by 1C

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Introduction

Specific Heat:


Amount of heat required raise the temperature of a

unit mass of a substance by 1C

At Constant Volume

(Cv)

At Constant Pressure

(Cp)

Forincompressible substance it is constant

C = f( P,T)UNIT ?

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Introduction

Specific Heat:


For an ideal gas , specific heat normally depends

only on temperature.

du = Cv(T) dT dh = Cp(T) dT

Sum of internal energy and energy required to flow of fluid

h = u + Pv

Enthalpy

At low

pressure real

gas also

behave as

Ideal gas

UNIT ?

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Introduction

Latent Energy or Heat :


If energy (Heat) supplied to the system is greater than

Molecular force phase change

Amount of heat require to change the phase is called Latent heat.

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Introduction

First law of Thermodynamics :

In rate

0 systemE

dt

dEEE

system

outin

outin EE

systemoutin EEE

Steady State :


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Introduction

In the absence of electric, magnetic, gravity effect, normally the

change in total energy of the system is the simply change in

internal energy of the system;


systemsystemoutin UEEE

TmCEE voutin (fixed mass system)

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Introduction

In Heat Transfer, Normally we are interested in the Thermal

energy which is transferred due to temperature difference.

And, All Nuclear, Chemical, etc energies consider in the form of

thermal energies as heat generation;


systemthermalgenoutin EEQQ

Energy Balance in Heat Transfer

Heat Transfer

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Introduction

Example-1 Heat Transfer

V = D3 / 6

SA = D2

I t d ti

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Introduction

Example-2

Assumption Heat loss is negligible Specific heats are constant

systemsystemoutin UEEE

TmCEE voutin (fixed mass system)

Heat Transfer

pot

vwater

vin TmCTmCE

I t d ti

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Introduction

1. Conduction

2. Convection

3. Radiation

Modes of Heat Transfer

I t d ti

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Introduction

Modes of Heat Transfer Conduction :

Transfer of heat through solids or stationary fluids

Introduction

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Introduction

Modes of Heat Transfer Convection :

In this mode heat is transfer due to the movement

of the fluids

Introduction

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Introduction

Modes of Heat Transfer Radiation :

It does not require any medium for heat transfer. Inthis mode the electromagnetic radiation is emitted by an

object for heat transfer.

Conduction

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Conduction

Heat Conduction Conduction :

Heat Transfer through solids or stationary fluids

How this take place?

In solids

Atoms are bound to each other by series of bonds analogous tospring.

When there is a temperature difference in the solid. The hot side of the solid experiences more vibration. The vibrations are transmitted through the springs to the cooler side. Eventually, they reach an equilibrium

Conduction

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Conduction

Heat ConductionMathematical Modeling :

,1

,

,

xQ

AQ

TQ

x

Ak-

T

Q

x

A

T

Q

0)x(x

kA- ddTQ

Fouriers law of conduction

Conduction

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Conduction

Heat ConductionMathematical Modeling :

x

kA-d

dTQ

k = Thermal Conductivity

-ive sign shows that heat is conducted in the

direction ofdecreasing temperature.

T becomes negative, so heat transfer is + ive.

A is er to the heat transfer

Conduction

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Conduction

Heat ConductionThermal Conductivity :

kA

x

T

Q

x

Ak-

T

Q

Rate of heat transfer through a unit

thickness of material per unit area and

per unit temperature difference.

UNIT ?

Conduction

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Conduction


Why Gases have

lower thermalconductivity than

Solids?

Why metals have

higher thermal

conductivity than

Solids?

Conduction

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Conduction


For Gases

Mk

Tk

1

(Temperature Effect)

Helium (M=4) having higherk

than Argon (M=29)

Conduction

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Conduction



For Liquids

Mk

Tk

1

1

Liquid metals such as Mercuryand Sodium having higher

thermal conductivity.

For high heat transfer they are

used in Nuclear Power plant.

Conduction

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Co duct o



For Solids

Normally it is constantbut for certain solids in certain

range of temperature it is

increased dramatically.

e.g.

Copper 401 at 300 KCopper 20,000 nearabsolute zero ( 20 K )

Super Conductors

Conduction

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Bronze =

Cu (90%) + Al (10%)

k 401 + 237

What about the k ofMetal Alloys like

Bronze

k (bronze) = 52 w/m/K

Conduction

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Heat CapacityHeat Transfer

Storage capability of material per unit volume

Thermal Diffusivity

How fast heat diffuses through a materials

pC

pC

k

StoredHeat

ConductedHeat

Higher or lower, which

one is better ?

UNIT ?

Conduction

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Example-1

Conduction

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Heat ConductionThermal Resistance Concept :

x

A

T

-kQ

Electrical Circuit:

21

eRVVI

Current Flow

Electric Resistance

Potential Difference

Thermal Circuit:

x

kA

T-Q

21

tR

TTQ

Conduction

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21

tR

TTQ


x

A

T

-kQ

Heat Flow

Thermal Resistance

Temperature Difference

x

kA

T

-Q

Conduction

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21

tR

TTQ


Unit ?

x

kA

T-Q

x

Ak

Rt

k

R

AR

xR

t

t

t

1

1

Conduction

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Heat ConductionMultiwall Heat Conduction:

x2x1

1

211R

TTQ

2

32

2R

TTQ

QQQ 21

21

31

RR

TTQ

T

t

R

Q allover

x

1

1

1Ak

R

x

2

2

2Ak

R

Walls in Series

Conduction

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Heat ConductionMultiwall Heat Conduction:

1

211R

TTQ

2

212R

TTQ

21 QQ

11

1

21

t

RR

R

x

1

1Ak

R

x

2

2Ak

R

Walls in Parallel

Conduction

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Conduction in Circular Pipes

l

d=2r

l>>>rFor Pipes

Conduction

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l>>>r

Q

Q

Heat Transfer along the pipe length is neglected

Radial Heat Transfer

Conduction

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T1

T2

Q

QQ

Q


ri

roQ

Radial Heat Transfer

Conduction

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T1

T2

Q


x

d

dT

-kAQ

Conduction in walls

Fouriers Law

ri

ro

Conduction

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T1 T2

Q


dr

dT-kAQ

ri

ro

x

d

dT-kAQ

For Walls

For pipes

r

Fouriers Law

Conduction

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l

d=2r

A=2rl

Conduction

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x

d

dT-kAQ

Area is Constant

ri

ro

dr

dT-kAQ

Area is variable

A

A=2rlA=lxb

l

b

Conduction

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T1 T2

Q

ri

ro

r

dr

dT-kAQ

2dr

dTlr-kQ

A=2rl

ln

2 21

io rr

TTlkQ

Conduction

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T1 T2

Q

ri

ro

r

A=2rl

ln2 21

io rr

TTlkQ

21

tRTTQ

2

ln21

lk

rr

TTQ

io

2

lnt

lk

rrR io

pipe

Thermal

Resistancein Pipes

Conduction

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Conduction in Hollow Sphere

T1 T2

Q

ri

ro

r

A= 4r2

Sphere

Conduction

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Conduction in Hollow Sphere

T1T

2

Q

ri

ro

r

4

21

krr

rr

TTQ

io

io

4

tkrr

rrR

io

io

sphere

Thermal

Resistance

in Sphere

dr

dT-kAQ

r4

2

dr

dT

-kQ

A= 4r221

tR

TTQ

Conduction

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Conduction in Multilayer Pipes

ri

ro

Pipe

Insulations

Conduction

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pipe

Insulation-Layer

Insulation-Layer

Conduction

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Thermal

Circuit

Conduction

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Rt = R1 + R2 + R3

41

tRTTQ

Conduction

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Steam at 320C flows in a cast iron pipe (k = 80 W/m C)

whose inner and outer diameters are 5 cm and 5.5 cm,

respectively. The pipe is covered with 3-cm-thick glass woolinsulation with k = 0.05 W/m C. Heat is lost to the

surroundings at 5C . Find the Heat loss with and without

insulation.

Example

Convection

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Modes of Heat Transfer

Convection :

In this mode heat is transfer due to the movement of the

fluids

Free Convection Forced Convection

Convection

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Heat ConvectionFree ConvectionForced

Convection

Convection

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Hot Iron Block(T1 = 400C)

Cool Air

(T = 15C) By Speed

Type of fluid

(Water)

, , C, v ..

Roughness, Geometry of the

object

Nature of the

flow

Convection

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Heat Convection

Mathematical Modeling :

The rate of heat convection over a medium depends on the:

Nature of the flow (Re.Laminar or Turbulent) Nature of the fluid (

Viscosity, k, density, C, etc)

Surface Area of the medium

Temperature Difference

Unlike conduction, convection is not concerned

with medium properties

s

AQ

TQ

Convection

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Heat Convection

Mathematical Modeling :

,

,

AQ

TQ

As ThQ

As TQ

Newtons law ofcooling

Convective heat

transfer Coefficient

(Nature of the fluid)

where; T = (Ts -T)

Convection

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Convective heat transfer Coefficient (h)Heat Convection

Rate ofHeat transferb/w solid surface and a fluid perunit surface

area perunit temperature difference

Units :

As T

Qh

h : (W/m2/C)

Convection

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Heat Convection

Thermal Resistance Concept :

In conduction

condthR

TQ

kA

xRcondth

In convection

As ThQ

Convection

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Heat Convection

Thermal Resistance Concept :

sA1

h

TQ

As ThQ

convthR

TQ

or

but

1

s

convthhA

R so,

Convection

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Consider a 0.8-m-high and 1.5-m-wide glass windowwith a thickness of8 mm and a thermal conductivity ofk= 0.78 W/m C. Determine the steady rate of heattransfer through this glass window and the temperature

of its inner surface for a day during which the room is

maintained at 20C while the temperature of theoutdoors is 10C. Take the heat transfer coefficients on

the inner and outer surfaces of the window to be h1 =10 W/m2 C andh2 =40 W/m

2 C.

Example

Convection

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Heat Conduction/Convection

Over All Heat Transfer Coefficient

TUAQ s

AhkA

x

Ah

Rth

21

11

1

s

thUA

R

thR

TQ

Over all Heat Transfer

Coefficient (U)

Convection

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Thank You

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