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Heat Transfer/Heat Exchanger

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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 heat transfer. Fundamental equation of heat transfer Logarithmic-mean temperature difference. Heat transfer Coefficients. - PowerPoint PPT Presentation
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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 heat transfer. 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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Page 1: Heat Transfer/Heat Exchanger

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 heat

transfer.• Fundamental equation of heat transfer• Logarithmic-mean temperature difference.• Heat transfer Coefficients.• Heat flux and Nusselt correlation • Simulation program for Heat Exchanger

Page 2: Heat Transfer/Heat Exchanger

How is the heat transfer?

• Heat can transfer between the surface of a solid conductor and the surrounding medium whenever temperature gradient exists.ConductionConvection

Natural convection Forced Convection

Page 3: Heat Transfer/Heat Exchanger

Natural and forced ConvectionNatural convection occurs whenever heat flows

between a solid and fluid, or between fluid layers.

As a result of heat exchangeChange in density of effective fluid layers taken place, which causes upward flow of heated fluid.

If this motion is associated with heat transfer mechanism only, then it is called Natural Convection

Page 4: Heat Transfer/Heat Exchanger

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.

Page 5: Heat Transfer/Heat Exchanger

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

between two fluids is named a Heat Exchanger.

Page 6: Heat Transfer/Heat Exchanger

Applications of Heat ExchangersHeat Exchangers

prevent car engine overheating and

increase efficiency

Heat exchangers are used in Industry for

heat transfer

Heat exchangers are used in AC and

furnaces

Page 7: Heat Transfer/Heat Exchanger

• 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.

Page 8: Heat Transfer/Heat Exchanger

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

generatedsin out

outin ewqhmhmdtdE &&&&& +++⎟

⎠⎞⎜

⎝⎛

−= ∑ ∑ ˆ.ˆ.

∑∑ −=outin

hmhm ˆ.ˆ. &&h

hphh TCmAQ Δ= ... &

ccpcc TCmAQ Δ= ... &

0 0 0 0

•Control Volume

Qh

Cross Section Area

HOT

COLD

Thermal Boundary Layer

Page 9: Heat Transfer/Heat Exchanger

Q hot Q cold

Th Ti,wall

To,wall

Tc

Region I : Hot Liquid-Solid Convection

NEWTON’S LAW OF CCOLING

dqx = hh . Th − Tiw( ).dA Region II : Conduction Across Copper Wall

FOURIER’S LAW

dqx = −k. dTdr

Region III: Solid – Cold Liquid Convection

NEWTON’S LAW OF CCOLING

dqx = hc . Tow − Tc( ).dA

THERMAL

BOUNDARY LAYEREnergy moves from hot fluid to a surface by convection, through the wall by conduction, and then by convection from the surface to the cold fluid.

Page 10: Heat Transfer/Heat Exchanger

• Velocity distribution and boundary layerWhen 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

radius.

V = u2πrdrr=0

r=D/2

∫V = volumetric flowrate

u = average mean velocity

Page 11: Heat Transfer/Heat Exchanger

In turbulent flow, there is no such distribution.

• The molecule of the flowing fluid which adjacent to the surface 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

Page 12: Heat Transfer/Heat Exchanger

• Accordingly the temperature gradient is larger at the wall and through the viscous sub-layer, and small in the turbulent core.

• The reason for this is 1) Heat must transfer through the boundary layer by conduction.2) Most of the fluid have a low thermal conductivity (k)3) While in the turbulent core there are a rapid moving eddies, which they are equalizing the temperature.

heating

cooling

Tube wall

Twh

Twc

Tc

Metalwallδ

Warm fluiδ

colδ fluiδ

qx = hAΔTqx = hA(Tw − T)

qx = kδ

A(Tw − T)h

Page 13: Heat Transfer/Heat Exchanger

Region I : Hot Liquid – Solid Convection

Th − Tiw = qx

hh .Ai

qx = hhot . Th − Tiw( ).A

Region II : Conduction Across Copper Wall

qx =kcopper .2πL

ln ro

ri

To,wall − Ti,wall =qx .ln ro

ri

⎛ ⎝ ⎜

⎞ ⎠ ⎟

kcopper .2πL

Region III : Solid – Cold Liquid Convection

To,wall − Tc = qx

hc .Ao

qx = hc To,wall − Tc( )Ao

+

Th − Tc = qx1

hh .Ai

+ln ro

ri

⎛ ⎝ ⎜

⎞ ⎠ ⎟

kcopper .2πL+ 1

hc .Ao

⎢ ⎢ ⎢ ⎢

⎥ ⎥ ⎥ ⎥

qx = U.A. Th − Tc( )1

1.

ln.

.

⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢

+⎟⎟⎠⎞

⎜⎜⎝⎛

+=colδicopper

i

oo

ihot

o

hrkrrr

rhrU

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

Th − Tc = qx

R1 + R2 + R3

U = 1A.ΣR

ro

ri

Page 14: Heat Transfer/Heat Exchanger

Calculating U using Log Mean Temperature

coldhot dqdqdq =−=

ch TTT −=Δch dTdTTd −=Δ )(

hhphh dTCmdq ..&=

ccpcc dTCmdq ..&=

Hot Stream :

Cold Stream:⎟⎟⎠⎞

⎜⎜⎝⎛

−=Δ cpc

chph

h

Cmdq

CmdqTd

..)(

dATUdq ..Δ−=−⎟⎟⎠⎞

⎜⎜⎝⎛

+Δ−=Δ cpc

hph CmCm

dATUTd.1

.1...)(

∫∫ ⎟⎟⎠⎞

⎜⎜⎝⎛

+−=ΔΔΔ

Δ

2

1

2

1

..1

.1.)( A

Acpc

hph

T

TdA

CmCmU

TTd

( ) ( ) ( )[ ]outc

inc

outh

inhch TTTT

qAUTT

qAU

TT −−−−=Δ+Δ−=⎟⎟⎠⎞

⎜⎜⎝⎛

ΔΔ ...ln

1

2

∫∫ ⎟⎟⎠⎞

⎜⎜⎝⎛ Δ

−=ΔΔΔ

Δ

2

1

2

1

..)( A

Ac

c

h

hT

TdA

qT

qTU

TTd

⎟⎟⎠⎞

⎜⎜⎝⎛ΔΔΔ−Δ

=

1

2

12

ln.

TT

TTAUq

Log Mean Temperature

Page 15: Heat Transfer/Heat Exchanger

CON CURRENT FLOW

⎟⎟⎠⎞

⎜⎜⎝⎛ΔΔΔ−Δ

1

2

12

lnTT

TTTLn

731 TTTTT inc

inh −=−=Δ

1062 TTTTT outc

outh −=−=Δ

COUNTER CURRENT FLOW

1062 TTTTT inc

outh −=−=Δ

731 TTTTT outc

inh −=−=Δ

U =˙ m h . ˙ C p

h . T3 − T6( )A.ΔTLn

=˙ m c . ˙ C p

c . T7 − T10( )A.ΔTLn

T1 T2T4 T5

T3

T7 T8 T9

T10

T6

Counter - Current Flow

T1 T2T4 T5

T6T3

T7T8 T9

T10

Parallel Flow

Log Mean Temperature evaluation

T1

A

1 2

T2

T3

T6

T4 T6

T7 T8

T9

T10

Wall∆ T1

∆ T2

∆ A

A

1 2

Page 16: Heat Transfer/Heat Exchanger

T1

A

1 2

T2

T3

T6

T4 T6

T7 T8

T9

T10

Wall

q = hh Ai ΔTlm

ΔTlm = (T3 − T1) − (T6 − T2)

ln (T3 − T1)(T6 − T2)

q = hc Ao ΔTlm

ΔTlm = (T1 − T7) − (T2 − T10)

ln (T1 − T7)(T2 − T10)

Page 17: Heat Transfer/Heat Exchanger

Nu = f (Re,Pr,L /D,μb /μo)

DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGER

mr..Dv

kC p m.

kDh.

Nu = a.Reb .Pr c•Further Simplification:

Can Be Obtained from 2 set of experiments

One set, run for constant Pr

And second set, run for constant Re

q=kδA(Tw −T)

h

Nu=Dδ

Page 18: Heat Transfer/Heat Exchanger

•For laminar flowNu = 1.62 (Re*Pr*L/D)

•Empirical Correlation

14.03/18.0 .Pr.Re.026.0 ⎟⎟⎠

⎞⎜⎜⎝⎛

=o

bLnNu

mm

•Good To Predict within 20%•Conditions: L/D > 10

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

•For turbulent flow

Page 19: Heat Transfer/Heat Exchanger

ExperimentalApparatus

• 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

Page 20: Heat Transfer/Heat Exchanger
Page 21: Heat Transfer/Heat Exchanger

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

2.53

3.54

4.5

55.5

6

9.8 10 10.2 10.4 10.6 10.8 11

ln (Re)

ln (Nu)

Theoretical trendy = 0.8002x – 3.0841

Experimental trendy = 0.7966x – 3.5415

Theoretical trendy = 0.3317x + 4.2533

Experimental trendy = 0.4622x – 3.8097

Theoretical trend

y = 0.026x

Experimental trendy = 0.0175x – 4.049

Experimental Nu = 0.0175Re0.7966Pr0.4622

Theoretical Nu = 0.026Re0.8Pr0.33

Page 22: Heat Transfer/Heat Exchanger

0

5000

10000

15000

20000

25000

30000

35000

0 1 2 3 4

Velocity in the core tube (ms-1)

Heat Transfer Coefficient Wm

-2K-

hi (W/m2K)ho (W/m2K)U (W/m2K)

Effect of core tube velocity on the local and over all Heat Transfer coefficients


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