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Shell and Tube Heat Exchanger, James Anstey
Heat Transfer in Shell and Tube Exchangers: A Further
Study of the Reliability of Current Theoretical Methods.
Submitted By : James Anstey (SID: 9506654)
Group 13 : Anne Claxton
Anna Schlunke
Date Performed : 23-3-99
Date Submitted : xx-4-99
Date Re-Submitted : x-5-99
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Executive Summary:
The focus of this work is to take existing correlations between heat exchanger
design and heat transfer rate (for example Kerns or Bells methods) and test
their reliability and accuracy for the determination of overall heat transfer
coefficients and pressure drops. The overall heat transfer coefficient was
determined experimentally and subsequently compared to the sum of the
individual heat transfer coefficients for the tube and shell sides as calculated
theoretically (appropriate fouling resistances and wall thermal conductivity
were also taken into consideration for this summation).
The results obtained demonstrate that the calculation of the overall heat
transfer coefficients using Kerns method appears more reliable when there
exists a highly turbulent flow regime in the shell-side. It is postulated that this
effect may be due to the reduced contribution of the shell-side coefficient,
with fouling factors becoming increasingly dominant in the overall coefficient.
Conversely Bells method displays a better agreement with experimental
results with a lower shell-side Reynolds number. Hence it is concluded that
Bells method gives a more reliable shell-side heat transfer coefficient than
that obtained with Kerns. It was not possible to differentiate the accuracy of
the various fouling resistances due to error involved in calculating the overall
heat transfer coefficients arising from both the log mean temperature driving
force and the temperature correction factor. Errors ranged from 10 130 %,
averaging around 25 %.
There was a significant disagreement between the calculated overall
pressure drops for the shell side with Kerns and Bells methods when
compared to the experimental values. It has not been elucidated if this result
is an experimental artifact (due to equipment failure: for example nozzle
blockage) or a reflection on the performance of the two methodologies.
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Table of Contents:
HEAT TRANSFER IN SHELL AND TUBE EXCHANGERS: A FURTHER STUDY OF THE
RELIABILITY OF CURRENT THEORETICAL METHODS..............................................................1
EXECUTIVE SUMMARY:...............................................................................................................................2
TABLEOF CONTENTS:................................................................................................................................3
INTRODUCTIONAND THEORETICAL BACKGROUND:..........................................................................................4
EXPERIMENTAL METHODOLOGY:..................................................................................................................8
RESULTS:...............................................................................................................................................10
DISCUSSION:...........................................................................................................................................13
Experimental Reliability.................................................................................................. ........ .......13
Evaluation of Theoretical Methods............................................................................................. ....14
CONCLUSION:..........................................................................................................................................17
REFERENCES:..........................................................................................................................................18
APPENDICES:...........................................................................................................................................19
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Introduction and Theoretical Background:
Shell and tube heat exchangers are common in industrial practice. It is
necessary to test the reliability and accuracy of existing correlations between
heat exchanger design and heat transfer rate (for example Kerns or Bells
methods) for the determination of overall heat transfer coefficients and
pressure drops.
The calculation of individual heat transfer coefficients resulting from fluid flow
is possible due to the experimentally determined correlation between the
Nusselt (Nu), Reynolds (Re) and Prandtl (Pr) numbers. The Nusselt number
acts to define the heat transfer properties of the fluid which is proportional (not
linearly) to the fluid flow (as defined by the Reynolds number) and the heat
capacity of that fluid (the Prandtl number). For a non-viscous fluid (such as
water) this relationship is of the form:
baxNu .(Pr).(Re)=
For water the equation contains no correction for changes in viscosity with
temperature, as this effect is negligible over the temperature range
considered. The parameters a, b, x have been fitted experimentally to provide
a working relationship under constrained geometric parameters (for instance
the Sieder-Tate relationship for fluid flow in pipes). The values of Nu, Re, and
Pr are described by:
k
dhNu e
.=
edu ..Re =
k
Cp .Pr=
Where:
=h heat transfer coefficient (W/m2.K)
=ed equivalent diameter (m)
=k thermal conductivity (W/m.K)
=u fluid velocity (m/s)
= fluid density (kg/m3
)= fluid viscosity (kg/m.s)
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=pC heat capacity of the fluid (J/kg.K)
Kerns and Bells methods both use this general relationship between fluid
flow and heat transfer, but in addition define means of calculating appropriate
shell side fluid velocities. Hence it is possible to use the general relationshipfor heat transfer, modified by supplying specific dimensionless numbers
(specifically the Reynolds number) which are dependent on the arrangement
of the shell and tube exchanger. These two correlations differ by the means in
which each calculate the shell-side velocities and account for non-ideal heat
transfer; for instance Bells method includes correction factors for fluid leakage
and bypass in the heat exchanger, terms not present in the Kerns method
calculation. Sample calculations for both of these methods are presented inAppendix A, and the reader is referred to Coulson and Richardson Volume 6
for a thorough detailing of both procedures.
Now once the individual heat transfer coefficients have been calculated for the
shell and tube sides, and with the inclusion of appropriate fouling resistances
and wall conductivity and overall heat transfer coefficient can be derived.
o
o
osoi
i
it A
F
AhAA
F
AhUA++++=
.
1
..
11
Where:
=U overall heat transfer coefficient (W/m2.K)
=A overall heat transfer area (m2)
=th tube side heat transfer coefficient (W/m2.K)
=iA tube inside area (m2)
=iF inside fouling resistance (m2
.K/W)
= tube wall thickness (m)
= wall thermal conductivity (W/m.K)
=oA tube outside area (m2)
=sh shell side heat transfer coefficient (W/m2.K)
=oF outside fouling resistance (m2.K/W)
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As the overall heat transfer coefficient can also be determined experimentally
it is possible to test the reliability of individually determined heat transfer
coefficients (from both Kerns and Bells methods) after their summation to
give an overall coefficient. The experimental overall heat transfer coefficient
can be calculated from the following formula:
mav TUAQ =
Where:
2/)( chav QQQ +=
cpcch TCmQQ = ..
=cm cold stream flow-rate (kg/s)
= cT change cold stream temperature (between inlet and outlet)
lmtm TFT = .
=tF temperature correction factor, a function of two dimensionless
temperature ratios R, S.
)(
)(tube
i
tube
o
shell
o
shell
i
TT
TTR
=
)()(
tube
i
shell
i
tube
i
tube
o
TTTTS
=
Ft can be read off temperature correction factor plots specific for the geometric
design of the heat exchanger.
)(
)(ln
)()(
tube
i
shell
o
tube
o
shell
i
tube
i
shell
o
tube
o
shell
i
lm
TT
TT
TTTTT
=
=shelliT inlet shell side fluid temperature
=shelloT outlet shell side fluid temperature
=tubeiT inlet tube side fluid temperature
=tubeoT outlet tube side fluid temperature
Hence by measuring the heat transfer of the exchanger under different flow
regimes (laminar to transitional to turbulent) the accuracy of the two methods
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can be evaluated, particularly when the shell side coefficient is the dominant
resistance.
The shell-side pressure drop can be calculated with the following formula
(Kerns method):
2
.8
2
s
Be
sfs
u
l
L
d
DjP
=
Where:
=fj shell side friction factor
=sD diameter of the shell
=L length of shell
=Bl distance between baffles
=su shell-side fluid velocity
The shell-side pressure drop can also be estimated with Bells method, which
attempts to provide a more reasonable representation of the pressure drop by
summing the calculated pressure drops for individual parts of the exchanger.
The exchanger is broken up into three compartments: a) the end zones, b) the
flow across the tubes, and c) the window zones. Again the reader is referred
to Coulson and Richardson Volume 6 and Appendix A for a full description of
the calculations.
From the theory presented above it is possible to estimate the values for
individual heat transfer coefficients, and subsequently calculate an overall
heat transfer coefficient for the shell and tube exchanger. Pressure drops for
both shell and tube sides can also be estimated using the Kern and Bell
correlations. Both the pressure drops and the heat transfer coefficient can be
compared to those calculated from experimental results.
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Experimental Methodology:
Experimental work was performed on a 96 tube heat exchanger; with eight
tube passes for one shell pass, and with 34 baffle plates (20 % baffle cut).
Temperatures of the tube and shell flow were measured at point of entry and
exit. The flow rate and pressure drops of both the shell and tubes were also
measured.
Figure 1: Overall schematic of the shell-tube exchanger set-up.
The tube arrangement is square pitch with bundle diameter of 190 mm and
heat transfer length of 178 cm. Each tube is made of drawn copper with an
inside diameter of 7.1 mm and wall thickness of 1.2 mm. The shell contains
34 baffles spaced 50.8 mm apart and has an internal diameter of 195 mm.
Flow-rates and temperatures were allowed to equilibrate for 20 minutes after
each change in condition.
8
Hot Water
Cooling
Tower
12 tubes per
pass, 8 passesShell in
Shell out
Tube in
Tube out
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Table 1: Experimental conditions for operation of the shell and tube HX.
Run Fshell (kg/min) Ftube (kg/min) Thot tank (C) Tcold tank (C)1 42.3 2.5 40 20
2 42.3 10.6 40 20
3 41.3 23.4 40 204 41.0 39.3 40 20
5 41.3 29.6 40 20
6 41.0 49.6 40 20
7 29.6 7.2 40 20
8 25.7 16.6 40 20
9 27.8 21.2 40 20
10 28.5 36.6 40 20
11 27.4 29.7 40 20
12 28.1 44.2 40 20
13 28.3 28.6 60 20
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Results:
All raw data can be found in appendix A. Figure 2 shows that, for all but two
runs, the heat gained by the cold stream was within experimental
uncertainties of that lost by the hot stream, confirming the energy balance for
these data and hence the reliability of the results.
y = -1.0592x
0
20000
40000
60000
-60000 -40000 -20000 0
Heat Loss Hot Stream (W)
HeatG
ainColdStream
(W)
Figure 2: Plot of the shell-side heat loss against the tube-side heat gain.
Gradient of the line is the heat balance. X-errors bars are calculated by the
maximum heat loss to the surroundings at steady-state. Y-error bars are
negligible as they represent the possible temperature deviation between the
inlet and outlet of the tubes (less than 1 % error).
Propagation of error calculations, shown in Table 2, demonstrate the strong
sensitivity of the temperature correction factor (Ft) and the log mean
temperature difference (Delta Tlm) to temperature fluctuations of 0.2 degrees
Celsius and flow-rate oscillations of 0.5 L/min.
Figure 3 shows that the agreement between theory and experiment in the low
heat transfer range is poor for both Bells and Kerns methods, but that. Bell's
method is much better at higher heat-transfer coefficients.
Figure 4 demonstrates that low heat transfer occurs for tube-side laminar flow.
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Table 2: Propagation of error to the log mean temperature and the
temperature correction factor.
Run Err Ft Err Delta Tlm Total Err
1 13 40 49
2 8 7 9
3 6 9 12
4 5 25 34
5 6 11 18
6 5 104 133
7 8 7 9
8 7 9 14
9 6 17 23
10 6 23 32
11 6 44 5812 5 14 22
13 3 30 40
0
100
200
300
400
500
600
700
800
900
1000
0 200 400 600 800 1000 1200
Experimental U (W/m2.K)
EstimatedU(W/m2.K)
Figure 3: Plot of all calculated vs experimentally determined heat transfer
coefficients. Error bars are included for Bells and Kerns methods with the
maximum fouling. Derivation of experimental error is attached in appendix C.
Diamonds Kerns method (minimum fouling), squares Kerns method
(maximum fouling), triangles Bells method (minimum fouling), crosses
Bells method (maximum fouling).
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200
300
400
500
600
700
800
0 5000 10000 15000
Tube-side Reynolds' Number
EstimatedOHTC(W/m2.K)
Figure 4: Plot of the Reynolds number across the tube-side against the
overall heat transfer coefficient (calculated using Bells method minimum
fouling). Squares 50 % flow shell-side, diamonds 100 % flow shell-side.
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Discussion:
Experimental Reliability
The temperature fluctuations in the steady-state regime are estimated as 0.2
degrees Celsius, and flow-rate oscillations at 0.5 L/min. Initially the maximum
heat loss to the surroundings was calculated for the heat exchanger operating
in a steady-state regime. This value was obtained by measuring the
temperature drop the hot flow with zero cold flow through the tube-side. A
value of 1452 W was obtained, although this value itself comprises significant
error from the small change in temperature (error of 70 %). The reliability of
the other experimental results can be seen with a heat balance between the
shell and tube flows.
tpt
sps
TCm
TCmeHeatBalanc
=
..
..
Where:
=sm flow-rate of shell-side
=tm flow-rate of tube-side
=pC heat capacity
= sT inlet outlet temperature for shell-side
= tT inlet outlet temperature for tube-side
Under ideal steady-state conditions (where heat loss to the surroundings is
negligible) the heat loss from the shell side should equal the heat gain in the
tube flow. Figure 2 demonstrates that most of the experimental values are in
fact at steady-state, with the gradient of the linear regression (which is in fact
the heat balance) equal to 1 and lying within the error range of almost all
points. Although the heat balance may be valid, the calculation of the overall
heat transfer coefficient in the low heat transfer regime can give rise to large
uncertainty as the changes in flow-rates and temperatures are small. In this
case values such as the log mean temperature difference and the
temperature correction factor can propagate a large error to the heat transfer
coefficient.
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This result is seen in Table 2 where the calculated uncertainty in the
parameters S and R (defined in the introduction) can result in errors of up to
10% in the temperature correction factor. Such high error results from the
nature of the function (Ft) which displays a drop-off in the region of < 0.8,
hence small perturbations in the inlet and outlet temperatures can result in a
large change in the Ft value (drop-off). Note that the methodology for the
calculation of errors is presented in appendix C. The total calculated error for
the mean temperature difference across the heat exchanger is also presented
in Table 2, which includes error from both the log mean temperature and the
temperature correction factor. As the log mean temperature driving force
involves the difference of the inlet and outlet temperatures the small errors
become very significant. This is readily apparent when the inlet tube side and
shell side temperatures are very close as with the exit temperatures (as for
run 6).
Evaluation of Theoretical Methods
For the theoretical calculation of the overall heat transfer coefficients two sets
of reasonable fouling resistances were used to investigate the size of the
effect of these resistances on the final coefficient. These values were:
A) Inside tube fouling resistance = 1.75 104 (m2.K/W)
Outside tube fouling resistance = 1.75 104 (m2.K/W)
Wall Conductivity = 401 (W/m.K)*
B) Inside tube fouling resistance = 3.5 104 (m2.K/W) b
Outside tube fouling resistance = 1.75 104 (m2.K/W)
Wall Conductivity = 401 (W/m.K)*
() Treated cooling tower water (Hewitt pg 872)
(b) Treated cooling tower water (Hewitt pg 872)
() Closed loop treated water (Hewitt pg 872)
(*) Drawn copper at 300 K (Hewitt pg 1022)
Figure 3 clearly shows the poor agreement between theory and experiment in
the low heat transfer range, with both Bells and Kerns methods performing
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poorly. In all runs the flow through the shell-side of the exchanger is turbulent
with the shell-side Reynolds number > 2000. Hence such a result suggests
that the heat transfer coefficient for the tube-side is in error when the flow in
the tubes is laminar. This is consistent with the deviation occurring for both
Bells and Kerns methods, as the same tube-side coefficient is used for the
calculation of the overall heat transfer coefficient. This study is particularly
concerned with a situation where the shell-side coefficient gives a significant
contribution to the overall heat transfer coefficient as this will more rigorously
test the theoretical methods employed. Figure 4 demonstrates that the low
heat transfer occurs when there exists a laminar flow through the tube-side.
Therefore it is sufficient to evaluate the most reliable theoretical heat transfer
coefficients (those which lie within the error of the experimental values)
against the experimental values. Figure 3 clearly shows that Bells method
most successfully models overall heat transfer, with most calculated values
lying within the error of the experimental values. The actual fouling would
appear to be between the two extreme values taken, with the minimum and
maximum fouling Bells method lying on either side of the line representing
agreement between theory and experimental.
It is also apparent that Kerns method displays less error when the shell-side
heat transfer coefficient is not controlling the overall heat transfer (ie a high
shell-side fluid flux). Bells method displays a trend counter to this with an
improvement in the overall heat transfer coefficient as the shell-side becomes
more dominant. Such a trend suggests that Bells method can more
accurately evaluate the shell-side coefficient whereas the agreement seen
with Kerns method may arise only when fouling resistances provide a large
contribution to the overall heat transfer coefficient.
For the calculation of pressure drops across the shell-side of the exchanger
both methodologies significantly underestimate the value of the pressure
drop. For Bells method this is almost a factor of ten on all occasions, and with
Kerns method by a factor of five. With such a large discrepancy found
between the experimental values and the theoretical calculations it is
speculated that some of the error may be attributable to the experimental
value rather than across the board poor agreement. Equipment failure such
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as nozzle blockage or anomalous pressure readings could account for this
increase in shell-side pressure.
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Conclusion:
The overall heat transfer coefficient as determined using the two theoretical
methods were tested against the experimentally determined values; where the
experimental values were chosen in the high heat transfer regime and at
when the heat exchanger was operating under steady-state conditions
(determined through a heat balance). Bells method (minimum fouling)
provided the most reasonable agreement with the experimental results.
The calculated pressure drops for the shell-side were not in agreement with
experimental results by upwards of a factor of ten as calculated with Bells
method. This discrepancy may be experimental artefact, hence no evaluation
of either theoretical method was possible.
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References:
1. Coulson and Richardson, Volumes 1 and 6
2. Kern, D Q, Process Heat Transfer McGraw Hill, 1950
3. Hewitt, Shires, Bott, Process Heat Transfer CRC Press, 1994
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Appendices:
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Appendix A
Table 1: Experimental values obtained for the overall heat transfer coefficient
and pressure drops across shell and tube-sides.
Run Number Qh/Qc Uoverall (W/m2.K)
Pshell (kPa) Ptube (kPa)1 1.62 109 12.04 -0.142 1.12 334 12.04 3.02
3 1.06 608 12.11 10.9
4 0.88 733 11.97 24.38
5 0.88 645 12.13 15.12
6 0.79 817 12.06 32.91
7 1.09 214 7.37 1.1
8 0.97 432 7.25 6.56
9 0.99 432 7.01 10.02
10 0.95 655 7.17 24.3
11 0.83 540 7.16 15.5312 0.86 658 7.46 31.91
13 1.05 590 7.18 15.62
Table 2: Calculated shell-side pressure drops using Kerns and Bells
methods.
Run 1 2 3 4 5 6 7 8 9 10 11 12
Kern (kPa) 2.3 2.3 2.2 2.2 2.2 2.2 1.5 1.4 1.3 1.4 1.3 1.3
Bell (kPa) 1.6 1.6 1.5 1.5 1.5 1.5 0.8 0.7 0.7 0.7 0.7 0.7