ht-2081 (1)
Post on 24-Dec-2015
18 Views
Preview:
TRANSCRIPT
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
top related