HT-208:

Heat Transfer in Turbulent Flow

Telgote Devanand suresh-130020030

Gaurav choudhary-130020043

Gondi Venkat Narayan Reddy-130020110

Jayesh Bundel-130020039

Objective and Motivation

• The overall heat transfer coefficient is related to the total thermal resistance which includes thermal resistance for conduction and convection

• So it becomes very easy to calculate how much heat is going to be exchanged between the fluids at different temperature once we know the overall heat transfer coefficient at the given velocity of hot fluid

• To determine the overall heat coefficient by using the logarithmic mean temperature difference

• To find out the individual film heat transfer coefficient

• Verify the Dittus Boelter equation for the turbulant flow heat transfer.

Theory• The total thermal resistance provided to the heat

transfer is sum of the individual thermal resistances as the resistances are in series

where

• Ui :overall heat tansfer coefficient w.r.t. inner area

• Ai :inner area of the tube

• A0:outer area of the tube

• Alm:logarithmic mean area difference

• K:thermal conductivity

• ∆x=thichness of the metal wall

• hi=heat transfer coefficient of inner film

• h0=heat transfer coefficient of outer film

• Logarithmic mean temperature difference is defined by:

00

111

AhkA

x

AhAU lmiiii

• Multipliying by Ai we get

• Apply Dittus Boelter equation on the hot fluid :

Nu=0.023(Re)0.8(Pr)n

• The physical properties do not change much if the bulk

mean temperature of the hot fluid do not change much

as we change its flow rate,and so the equation can be

written a

Nu=constant x (velocity)0.8

• So the relationship is:

1/U=constant1/(u)0.8+constant2

• Now plot the graph between 1/U and 1/(u)0.8 this would

be a straight line and this plot is known as the wilson

plot.

00

11

Ah

A

kA

xA

hU

i

lm

i

ii

SCHEMATIC DIAGRAM OF THE

APPARATUS

Rotameter

Double temperature

indicator-controller

Double pipe heat

exchanger

Cold fluid

circulation pump

Heater

Hot fluid

circulation pump

Double pipe heat exchanger

Experimental Procedure

Switch on the double

temperature indicator

only and note down the

inlet and outlet

temperature to get the

zero error in digital

thermometer

Now switch on both the

pumps and adjust the

set point to around 650C

keeping the intial flow rate

around 400lph of both

fluids

Note down the inlet

and outlet temperature

of the hot and the

cold fluid when steady

state has reached

Now increase the hot

fluid flow rate keeping

the cold fluid flow rate

to be constant

Wait for 6-8 minutes

for the steady state to

come and then again

note down the inlet

and outlet tempeature

of the hot and the cold

fluid

Again repeat the

procedure and take 5

more readings for

different flow rate of

hot fluid

Calculation Procedure

Calculate the amount of

heat that is transfered

by the hot fluid using the

corrected temperatures

Calculate the overall

heat transfer coefficient

by using the amount of

heat transfered , LMTD

and inside area of heat

exchanger

Find out the velocity

of the hot fluid by

dividing the volume

flow rate by cross

sectional area of inner

tube

Plot the graph

between 1/Ui and

1/(u)0.8(Wilson plot),

whose intercept would

give the value of 1/h0

Plot the graph between

ln(Nu) and ln(Re),then

calcuate the slope of

the line that is obtained

by plotting the graph

Calculate the inner film

heat transfer coefficient

Observation Table

Inlet

Temperature

Outlet

TemperatureError

Hot Fluid 31.8 28.0 -3.8

Cold Fluid 27.2 27.8 +0.6

d1 (inner diameter of inner tube)=1.00cm

d2(outer diameter of the inner tube)=1.27cm

D1(inner diameter of the outer tube)=2.20cm

L(length of heat exchanger)=85cm

ρ(density of ethylene glycol)=1.085gm/cm3

μ(viscosity of ethylene glycol)=0.0052N.s/m2

Cp(specific heat capacity)=0.615Cal/gm.C

k(thermal conductivity)=0.258W/m.K

S.No.Flow Rate(lph)

Hin (0C) Hout(

0C)Hout

CorrectedCin(0C) Cout(

0C)Cout

Corrected

LMTD(0C)

1 400 65.8 58.0 61.8 26.8 31.3 30.734.743

2 460 65.8 58.2 62.0 26.7 31.5 30.934.494

3 520 65.8 58.5 62.3 26.6 31.8 31.234.537

4 580 65.8 58.5 62.3 26.6 31.5 30.934.69

5 640 65.8 58.7 62.5 26.6 31.7 31.134.686

6 700 65.8 58.8 62.6 26.5 31.8 31.234.733

7 760 65.8 59.0 62.8 26.5 31.9 31.334.778

y = 0.001x + 8E-06R² = 0.912

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Series1

Linear (Series1)

Graph between 1/U v/s 1/(u^0.8)

y = 0.753x - 0.931R² = 0.918

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8

Series2

Linear (Series1)

Graph between ln(Nu) v/s ln(Re)

Uncertainity in measured and estimated

parameters

• The uncertainity in measurement of the

temperature is 0.050C.

• The value of the slope of the line obtained

by plotting graph between ln(Nu) and

ln(Re) is 0.75 which differs from 0.8 by

0.05.

• So error in slope is 6.25%.

Q(Kcal/hr)U(Kcal/hr m2

0C)

u(m/sec)

Re Nu ln(Re) ln(Nu)hi(Kcal/hr

m2 0C)

907.493 978.155 1.415 2952.452 1.646 3.47 44.258 982.485

1166.399 1266.296 1.628 3396.885 1.758 3.531 57.325 1272.544

1214.437 1316.807 1.84 3839.231 1.776 3.584 59.679 1324.806

1354.567 1462.271 2.052 4281.577 1.821 3.632 66.263 1470.961

1409.287 1521.518 2.265 4726.01 1.839 3.674 69.003 1531.798

1494.693 1611.542 2.477 5168.356 1.864 3.713 73.031 1621.198

1521.386 1638.199 2.689 5610.702 1.871 3.749 74.357 1650.634

Result and Conclusion

Results and Conclusion

• As the volume flow rate of the hot fluid tube is increased then the heat transfer coefficient increase and the heat transfered also increases

• As the velocity of the flow increases reynolds number also increases and hence there would be more turbulent and more eddies developing in the flow so more heat transfer.

• Reynolds is basically the ratio of the inertial force to the viscous forces .So as the velocity of the flow increases the inertial force increases more as compared to the vicous forces and hence flow becomes turbulent

Result and Conclusions

• Also the nusselt number increases as the

velocity increases which is the ratio of the

convective heat transfer to the conductive

heat transfer

• So more and more heat tansferred by

convection as the velocity increases or the

flow becomes turbulent.

Precautions

• Surfaces of the hot fluid pipes should not

be touched

• Volume flow rate of the hot fluid should not

be too low so that there is no turbulent

flow

• Volume flow rate of the cold fluid has to be

constant so that resistance provided by

the outer film remains constant