# heat exchanger

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• 8/11/2019 Heat Exchanger Lecture.ppt

1/22

Heat Transfer/Heat Exchanger How is the heat transfer?

Mechanism of Convection

Applications .

Mean fluid Velocity and Boundary and their effect on the rate of heattransfer.

Fundamental equation of heat transfer

Logarithmic-mean temperature difference.

Heat transfer Coefficients.

Heat flux and Nusselt correlation

Simulation program for Heat Exchanger

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How is the heat transfer?

Heat can transfer between the surface of a solid conductorand the surrounding medium whenever temperaturegradient exists.

ConductionConvection

Natural convection

Forced Convection

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Natural and forced Convection

Natural convection occurs whenever heat flows

between a solid and fluid, or between fluidlayers.

As a result of heat exchange

Change in density of effective fluid layers takenplace, which causes upward flow of heated

fluid.

If this motion is associated with heat transfer mechanism

only, then it is calledNatural Convection

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Forced Convection

If this motion is associated by mechanical means such as

pumps, gravity or fans, the movement of the fluid is

enforced.

And in this case, we then speak of Forced convection.

• 8/11/2019 Heat Exchanger Lecture.ppt

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Heat Exchangers A device whose primary purpose is the transfer of energy

between two fluids is named a Heat Exchanger.

• 8/11/2019 Heat Exchanger Lecture.ppt

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Applications of Heat Exchangers

Heat Exchangers

prevent car engine

overheating and

increase efficiency

Heat exchangers areused in Industry for

heat transfer

Heat

exchangers are

used in AC and

furnaces

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The closed-type exchanger is the most popular one.

One example of this type is the Double pipe exchanger.

In this type, the hot and cold fluid streams do not come

into direct contact with each other. They are separated by

a tube wall or flat plate.

• 8/11/2019 Heat Exchanger Lecture.ppt

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Principle of Heat Exchanger First Law of Thermodynamic: Energy is conserved.

generateds

in out

outin ewqhmhmdt

dE

..

outin

hmhm .. h

h

phh TCmAQ ...

c

c

pcc TCmAQ ...

0 0 0 0

Control Volume

Qh

Cross Section Area

HOT

COLD

Thermal Boundary Layer

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Q hot Q cold

T

h

Ti,wall

To,wall

Tc

Region I : Hot Liquid-

Solid Convection

NEWTONS LAW OF

CCOLING

dqxhh. ThTiw .dA Region II : ConductionAcross Copper Wall

FOURIERS LAW

dqx

k.dT

dr

Region III: Solid

Cold Liquid

Convection

NEWTONS LAW OF

CCOLING

dqxhc.TowTc .dA

THERMAL

BOUNDARY LAYER

Energy moves from hot fluid

to a surface by convection,

through the wall by

conduction, and then byconvection from the surface

to the cold fluid.

• 8/11/2019 Heat Exchanger Lecture.ppt

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Velocity distribution and boundary layer

When fluid flow through a circular tube of uniform cross-

suction and fully developed,

The velocity distribution depend on the type of the flow.

In laminar flow the volumetric flowrate is a function of the

V u2rdrr0

rD / 2

V = volumetric flowrate

u = average mean velocity

• 8/11/2019 Heat Exchanger Lecture.ppt

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In turbulent flow, there is no such distribution.

The molecule of the flowing fluid which adjacent to thesurface have zero velocity because of mass-attractive

forces. Other fluid particles in the vicinity of this layer,

when attempting to slid over it, are slow down by viscous

forces.

r

Boundary

layer

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Accordingly the temperature gradient is larger at the walland through the viscous sub-layer, and small in theturbulent core.

The reason for this is

1) Heat must transfer through the boundary layer byconduction.

2) Most of the fluid have a low thermal conductivity (k)3) While in the turbulent core there are a rapid movingeddies, which they are equalizing the temperature.

heating

cooling

Tube wall

Twh

Twc

Tc

Metalwall

Warm fluid

cold fluid

qxhATqxhA(Tw T)

qx

k

A(T

w

T)h

• 8/11/2019 Heat Exchanger Lecture.ppt

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Region I : Hot Liquid

Solid Convection

ThTiw qxhh.Ai

qxhhot. ThTiw .A

Region II : Conduction

Across Copper Wall

qxkcopper.2L

lnrori

To,wallTi,wall

qx.ln ro

ri

kcopper.2L

Region III : Solid

Cold Liquid Convection

To,wall Tc qx

hc.Ao

qxhcTo,wallTc Ao+

ThTc qx1

hh.Ai

ln rori

kcopper.2L

1

hc.Ao

qxU.A. T

hT

c

1

1

.

ln.

.

coldicopper

i

oo

ihot

o

hrk

r

rr

rh

rU

U = The Overall Heat Transfer Coefficient [W/m.K]

ThTc qx

R1R2R3

U 1

A.R

r

o

r

i

• 8/11/2019 Heat Exchanger Lecture.ppt

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Calculating U using Log Mean Temperature

coldhot dqdqdq

ch TTT

ch dTdTTd )(h

h

phh dTCmdq ..

ccpcc dTCmdq ..

Hot Stream :

Cold Stream:

c

pc

c

h

ph

h

Cm

dq

Cm

dqTd

..

)(

dATUdq ..

c

pc

h

ph CmCmdATUTd

.

1

.

1...)(

2

1

2

1

..

1

.

1.

)( A

Ac

pc

h

ph

T

TdA

CmCmU

T

Td

outc

inc

outh

inhch TTTTq

AUTTq

AU

T

T

...

ln1

2

2

1

2

1 ..

)( A

Ac

c

h

hT

T dAq

T

q

T

UT

Td

1

2

12

ln

.

T

T

TTAUq

Log Mean Temperature

• 8/11/2019 Heat Exchanger Lecture.ppt

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CON CURRENT FLOW

1

2

12

lnT

T

TTTLn

731 TTTTT in

c

in

h

1062 TTTTT out

c

out

h

COUNTER CURRENT FLOW

1062 TTTTT in

c

out

h

731 TTTTT out

c

in

h

Umh.

Cph. T3T6

A.TLn

mc.Cpc. T7T10

A.TLn

T1 T2T4 T5

T3

T7 T8 T9

T10

T6

Counter - Current Flow

T1 T2T4 T5

T6T3

T7

T8 T9

T10

Parallel Flow

Log Mean Temperature evaluation

T1

A

1 2

T

2

T

3 T

6

T

4

T

6

T7

T

8 T

9 T10

WallT1

T2

A

A

1 2

• 8/11/2019 Heat Exchanger Lecture.ppt

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T1

A

1 2

T

2

T

3 T

6

T

4T6

T

7

T

8 T

9 T10

Wall

qhhAiTlm

Tlm(T3 T1) (T6 T2)

ln(T3 T1)

(T6 T2)

qhcAoTlm

Tlm(T1T7) (T2T10)

ln(T1T7)(T2T10)

• 8/11/2019 Heat Exchanger Lecture.ppt

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Nu f(Re,Pr,L /D,b /

o)

DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGER

..Dvk

Cp .

k

Dh.

Nua.Reb.PrcFurther Simplification:

Can Be Obtained from 2 set of experiments

One set, run for constant Pr

And second set, run for constant Re

q k

A(TwT)

h

NuD

• 8/11/2019 Heat Exchanger Lecture.ppt

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For laminar flow

Nu = 1.62 (Re*Pr*L/D)

Empirical Correlation

14.0

3/18.0 .Pr.Re.026.0

o

bLnNu

Good To Predict within 20%

Conditions: L/D > 10

0.6 < Pr < 16,700Re > 20,000

For turbulent flow

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Experimental

Apparatus

Two copper concentric pipes

Inner pipe (ID = 7.9 mm, OD = 9.5 mm, L = 1.05 m)

Outer pipe (ID = 11.1 mm, OD = 12.7 mm)

Thermocouples placed at 10 locations along exchanger, T1 through T10

Hot Flow

Rotameters

Temperature

Indicator

Cold Flow

rotameter

Heat

Controller

Switch for concurrent

and countercurrent

flow

Temperature

Controller

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0

50

100

150

200

250

150 2150 4150 6150 8150 10150 12150

Pr^X Re^Y

Nus

Examples of Exp. Results

4

4.2

4.4

4.6

4.8

0.6 0.8 1 1.2 1.4

ln (Pr)

ln(Nu

)

2

2.5

3

3.5

4

4.5

5

5.5

6

9.8 10 10.2 10.4 10.6 10.8 11

ln (Re)

ln(Nu)

Theoretical trend

y = 0.8002x 3.0841

Experimental trend

y = 0.7966x 3.5415

Theoretical trend

y = 0.3317x + 4.253