101 Tuesday A-2 Small Shell and Tube

1
Small Shell and Tube Heat Exchanger
University of Pittsburgh
ChE 0101 Section 1080
Foundations of Chemical Engineering Laboratory
Authors:
Kaitlin Muzic, Kaylene Kowalski, Kayla LeMaster,
Emily Connor, Kelly Schreiber, and Taylor Shaffer
Tuesday A-2

2
Table of Contents
Nomenclature 3
1.0 Introduction and Background 4
2.0 Experimental Methodology 6
2.1 Equipment and Apparatus 6
2.2 Experimental Procedures 7
3.0 Results 8
3.1 Technical Objective 1 Results 8
3.2 Technical Objective 2 Results 9
3.3 Graphical Representation of Results 10
4.0 Analysis and Discussion of Results 11
5.0 Summary and Conclusions 14
References 16
Appendix A-1 18
Appendix A-2 19

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Nomenclature
Variable Description Units
Qh Heat duty of the hot side Watts
Qc Heat duty of the cold side Watts
QL Heat lost to the environment Watts
Cp Specific heat J/(g*°C)
U Overall heat transfer coefficient W/(°C*m2)
A heat transfer surface area of the tubes m2
T Temperature °C
ΔT Change in temperature °C
ΔTlm Log mean temperature difference °C
F Correction factor No units

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1.0 Introduction and Background
Heat exchangers transfer heat between fluids of two different temperatures. They are
used in chemical and food industries, refrigeration systems, car radiators, venting, and much
more. There are two general types of heat exchangers: direct contact and indirect contact [1].
Direct contact heat exchangers, such as cooling towers, are used with two immiscible substances,
and there is no wall separating the two fluids. Mass and heat transfer generally occur at the same
time [1]. In an indirect contact heat exchanger, a wall separates the two fluids, and thermal
energy is exchanged through the heat transfer surface [1]. A shell and tube heat exchanger is an
example of an indirect contact heat exchanger.
There are different geometries, or configurations, of heat exchangers, such as tubular,
plate, and extended surface [1]. A shell and tube heat exchanger has a tubular configuration;
tubes inside run parallel to the axis of the shell, as seen in Figure 1. One fluid flows on the inside
of the tubes (the tube side) while another fluid flows on the outside of the tubes (the shell side).
In general, if a fluid is corrosive or has a high pressure, it is used on the tube side [3]. A
corrosive fluid will damage only the inside of the tubes and not the entire shell, thus saving
money when equipment needs to be replaced. Special alloy coatings can also be put on the inside
of the tubes to help prevent damage [3]. High pressure fluids are used on the tube side because
the tubes have a smaller diameter than the shell [3]. Thus, the tubes have a higher pressure rating
than the shell.
FIGURE 1: Representation of a shell and tube heat exchanger [2]
The main design objectives of a heat exchanger are ease of cleaning, low cost, and
accommodation for thermal expansion [1]. Shell and tube heat exchangers are relatively less
expensive compared to other types of heat exchangers. They are easy to clean because they can
be dismantled. The utilization of a U-shaped tube can give way to essentially unlimited thermal

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expansion [1]. Shell and tube heat exchangers also have great design flexibility, meaning that the
tube diameter and length, the number of tubes, and the arrangement of tubes can conveniently be
altered for specific applications [1].
Advantages and disadvantages of shell and tube heat exchangers coincide with the
efficiency of the heat transfer. The tubes can undergo vibrations caused by the shell side of the
exchanger which can damage the tubes [4]. This can lead to a short operation time of the heat
exchanger because damaged tubes need to be replaced [4]. To help solve this problem, baffles
are sometimes used [4]. Baffles also direct the shell side flow back and forth over the tube
bundle which initiates a higher heat transfer rate. However, dead zones are created in the corners
between the baffle and the shell [5]. This leads to a decreased efficiency of heat transfer. Fins
can be added to the tubes to increase the heat transfer surface area, thus increasing the amount of
heat transfer. Insulation around the shell is frequently required to help minimize the heat loss to
the environment [5]. This can be in the form of a second wall around the shell or a special
coating painted on the outside of the shell of the heat exchanger.
The amount of heat transfer and the overall heat transfer coefficient can be found by
using known and experimental quantities at steady state. Steady state means that an equilibrium
has been reached and the inlet and outlet temperatures of the shell and tube sides are no longer
changing. Heat transfer can be found by calculating the heat duty for the tube side and for the
shell side. Heat duty is calculated by multiplying the mass flow rate of the liquid, the specific
heat, and the change in temperature. Under ideal conditions, the heat duty of the tube side and
the heat duty of the shell side are equivalent. To account for heat loss to the environment, the
energy balance has to be adjusted. The energy balance becomes
|Qh|= |Qc| + QL, (1)
where Qh is the heat duty of the shell side, Qc is the heat duty of the tube side, and QL is the heat
loss to the environment. Using this equation and the heat duties of the shell and tube sides, the
heat loss to the environment can be calculated. The overall heat transfer coefficient is a measure
of the overall ability to transfer heat. It can be determined using the equation
Qc = U × A × ΔTlm × F, (2)

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where U is the overall heat transfer coefficient, A is the heat transfer surface area of the tubes,
ΔTlm is the log mean temperature difference, and F is the correction factor. A large overall heat
transfer coefficient corresponds to heat being more easily transferred between two fluids. Heat
loss and the overall heat transfer coefficient can be used to determine the relative efficiency of a
shell and tube heat exchanger.
The flow rate of a fluid can have an effect on the steady state heat transfer, the heat loss
to the environment, and the overall heat transfer coefficient. The following experiment was
conducted to determine this effect by varying the flow rate of the tube (cold) side while keeping
the shell (hot) side flow rate constant and vice versa.
2.0 Experimental Methodology
2.1 Equipment and Apparatus
To collect the data in this experiment, the small shell and tube heat exchanger is set up as
illustrated in Figures 2 and 3.
FIGURE 2: Annotated diagram of entire small shell and tube heat exchanger

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FIGURE 3: Annotated detailed diagram of small shell and tube heat exchanger
As shown in Figure 3, the cold water flows from the chiller, through the tube side valve
that regulates the flow rate, and into the small shell and tube heat exchanger. When it exits the
heat exchanger it flows back into the chiller to be cooled again. As this is occurring, the hot
water flows from the heater, through the shell side valve that regulates the flow rate, and into the
small shell and tube heat exchanger. The hot water then exits the small shell and tube heat
exchanger, via the shell side flow out, and enters the heater again. When the shell and tube sides
enter the heat exchanger, the hot water passes over the cold water in the tubes, and heat transfer
occurs. The temperatures of the shell and tube flows are recorded in the LabVIEW program as
they enter and exit the small shell and tube heat exchanger. The flow rates are varied and
recorded by using the LabVIEW program to set the percent valve openings. The data recorded is
used to determine the heat transfer and heat loss of the small shell and tube heat exchanger in
each trial run.
2.2 Experimental Procedures
The first technical objective was to determine how the tube side flow rate affects the heat
transfer and heat loss of the small shell and tube heat exchanger. In this objective, the initial shell
side valve opening was set to 50% and was kept constant for the entire objective. The initial

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tube side valve opening was set to 10% open. The temperatures were then allowed to stabilize,
and once the system reached steady state, the data was recorded. The tube side valve opening
was then increased to 30% open, and the system was allowed to come to steady state again. The
tube side valve opening was adjusted to 60% open, and the system was once again allowed to
reach steady state. In the last trial, the tube side valve opening was increased to 100% open and
the system was allowed to reach steady state.
The second technical objective was to determine how the shell side flow rate affects the
heat transfer and heat loss of the small shell and tube heat exchanger. In this technical objective,
the initial shell side valve opening was set to 10% open and the initial tube side
valve opening was set to 50% open. The tube side valve opening was kept constant for the entire
second objective. When temperatures were stabilized and the system was at steady state, the data
was recorded. The shell side valve opening was then adjusted to 30% open, and the system was
allowed to stabilize again. The shell side valve opening was then increased to 50% open, and the
system was allowed to come to steady state. Finally, the shell side valve opening was increased
to 70% open, and the system came to steady state again. As in the last objective, every time the
system reached steady state, the data was recorded.
3.0 Results
3.1 Technical Objective 1 Results
The tube side was varied while the shell side remained at 50% open constantly.
Table 1. Heat Duty Results for Technical Objective 1
Tube Side Open 10% 30% 60% 100%
Tube Side Flow Rate (L/min) 1.27 2.86 4.16 4.78
Shell Side Flow Rate (L/min) 3.83 3.85 3.87 3.74
Heat Duty Cold-side Flow
(Watts) 870.34 907.47 905.44 895.23
Heat Duty Hot-Side Flow
(Watts) -1613.27 -1682.47 -1695.22 -1598.08
Heat Loss
(Watts) 742.92 775.01 789.78 702.85

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The flow rate of the tube side was fairly inconsistent (yet always increased) as changes
were made to adjust the tube side flow while the corresponding shell side flow rates were very
consistent. With the exception of when the tube side is 10% open, the heat duty of the cold-side
flow decreased overall. The heat loss increased as the tube side flow rate increased until the final
adjustment was made to the system, resulting in a drastic drop in heat loss relatively.
Table 2. Heat Transfer Coefficient for Technical Objective 1
Tube Side Open 10% 30% 60% 100%
ΔTlm (°C) 18.80 15.82 14.39 13.47
U (W/°C*m2) 1522.16 1866.95 2020.03 2378.56
The log mean temperature difference (ΔTlm) used to calculate the heat transfer coefficient
inconsistently decreased. The heat transfer coefficient (U) showed a strong positive trend.
3.2 Technical Objective 2 Results
The shell side was varied while the tube side remained at 50% open constantly.
Table 3. Heat Duty Results for Technical Objective 2
Shell Side Open 10% 30% 50% 70%
Heat Duty Hot-side Flow
(Watts) -1374.69 -1646.22 -1655.60 -1733.69
Heat Duty Cold-Side Flow
(Watts) 802.47 897.20 902.78 893.52
Heat Loss
(Watts) 572.21 749.02 752.81 840.17

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The flow rate of the shell side was fairly inconsistent (yet increased) as changes were
made to adjust the shell side flow while the corresponding tube side flow rates were extremely
consistent. The heat duty of the hot-side flow decreased overall. The heat loss increased as the
shell side flow rate increased.
Table 4. Heat Transfer Coefficient for Technical Objective 2
Shell Side Open 10% 30% 50% 70%
ΔTlm (°C) 17.77 16.00 14.51 13.50
U (W/°C*m2) 1457.95 1810.38 2009.62 2137.88
The log mean temperature difference (ΔTlm) used to calculate the heat transfer coefficient
inconsistently decreased. The heat transfer coefficient (U) showed a strong positive trend.
3.3 Graphical Representation of Results
By varying the tube side (as in technical objective 1), the calculated heat loss data is
confined to a certain range of values. The altered shell side (as in technical objective 2) displayed
an increasing trend upward over a larger range comparatively.

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FIGURE 4: Heat Loss vs Volumetric Flow Rate
The calculated heat transfer coefficient was fairly similar in both technical objective one
and technical objective two. The final plotted point at which the tube side was 100% open and
the shell side is 70% open differed by about 200 W while the rest of the plotted data of similar
shell and tube side flow rates were within 100 W of each other.
FIGURE 5: Heat Transfer Coefficient vs Volumetric Flow Rate
742.92
775.01
789.78
702.85
572.21
749.02 752.81
840.17
550.00
600.00
650.00
700.00
750.00
800.00
850.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00
HeatLoss(J/sorW)
Volumetric Flow Rate (L/min)
Heat Loss vs Volumetric Flow Rate
Varying Tube Side Varying Shell Side

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4.0 Analysis and Discussion of Results
In this experiment, the inlet and outlet temperatures of the tube side and the shell side
streams were recorded when the system reached steady state. Then, by taking the density of the
water at a certain temperature and multiplying it by the volumetric flow rate of the fluid, the
mass flow rate was found. The variation of the flow rate of a liquid had a great effect on the
steady state heat exchanger, the heat loss to the environment, and the overall heat transfer
coefficient.
For the first technical objective, the initial tube side valve opening was varied by
percentages ranging from 10% to 100%, while the shell side valve was kept constant at 50%. The
key results from this trial were the decrease in temperatures of both the shell and tube sides, the
heat duty of the tube and shell side flow, and the heat loss to the environment. To begin, the tube
side flow rate was varied and the inlet temperature of the tube side remained around 20.7 ºC,
while the outlet temperature decreased from 30 ºC to 23 ºC. Then, the shell side valve was
observed while the opening remained at a constant 50%. The inlet temperature of the shell side
decreased from 48 ºC to 39 ºC, and the outlet temperature decreased from 41 ºC to 32 ºC. The
decrease in temperature of the tube side in the first objective and of the shell side in the second
objective indicates that heat was transferred from the shell side to the tube side. Heat is always
transferred from the hot liquid to the cold liquid to increase the entropy of the system.
Conceptually, the tube side should have increased in temperature due to the flow of heat.
However, increasing opening of the valve forced the temperature to decrease due to an increase
in the mass flow rate of the tube side. Another key feature is the heat duty calculated for the tube
and shell side flows, which are Qc and Qh, respectively. From equation (3) and equation (4), Qc
and Qh were calculated. The equation for heat duty of the tube side flow is
Qc = mc × Cp × ∆T, (3)
where mc is the mass flow rate of the tube side, Cp is the specific heat of water, and ∆T is the
change in temperature of the tube side flow. At these temperatures, Cp has a value of 4.186 J/g ºC
[6]. The equation for heat duty of the shell side flow is

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Qh = mh × Cp × ∆T, (4)
where mh is the mass flow rate of the shell side, Cp is the specific heat of water, and ∆T is the
change in temperature of the shell side flow.
For the first technical objective Qc was a large positive number due to Tcold out - Tcold in
being positive. Then, Qh was found to be a large negative number due to Thot out - Thot in being
negative. Finally, the heat lost to the environment, QL, was another key feature that was
calculated from equation (1a).The equation for the heat balance is
|Qh| = |Qc| + QL, (1)
which was rearranged as
QL = |Qh| − |Qc| (1a)
to solve for the heat loss to the environment. From calculation, Qh was a large negative number,
which shows that heat was lost to the surroundings.
For the second technical objective, the initial shell side valve opening was varied by
percentages ranging from 10% to 70%, while the tube side valve was kept constant at 50%. The
key results from this trial were the increase and decrease in temperature for both the inlet and
outlet of the shell and tube side valves, the heat duty of the tube and shell side flow, and the heat
lost to the environment. To begin, the tube side flow rate was varied and the inlet temperature
remained around 20.7℃, while the outlet temperature increased from 23℃ to 24℃. By increasing
the flow rate of the shell side, the tube side temperature increased. Next, the shell side valve was
varied and the inlet temperature decreased from 48 ℃ to 38℃ and the outlet temperature
increased from 32℃ to 33℃. Another key feature is the heat duty calculated for the tube and
shell side flow, which is Qc and Qh respectively. Qc and Qh had been calculated by equation (3)
and equation (4), respectively. From the calculation, Qc for the second technical objective is a
large negative number due to Tcold out - Tcold in being negative. Futhermore, Qh is a large positive
number due to Thot out - Thot in, which is the change in temperatures being positive. Lastly, the heat

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lost to the environment QL was another key feature calculated from equation (1a). From
calculation, Qh was a large negative number, which shows that the heat loss was gained by the
environment.
From equation (2), the overall heat transfer coefficient was found. The equation for the
overall heat transfer coefficient is
Qc = U × A × ∆Tlm × F, (2)
In the experiment, the overall heat transfer coefficient represents the overall resistance to
heat transfer over the surface area of the tubes, the change in temperature, and the correction
factor. From the data and calculations, when the shell and tube side valves were varied, the heat
transfer coefficient increased. These results are reasonable because the heat transfer coefficient
depends greatly on the amount of heat transferred over a certain area and the change in
temperatures.
After steady state was reached and calculations were completed, the degree of heat loss to
the environment was interpreted. For the first technical objective, QL was negative because the
system lost heat. This shows that Qc and Qh both decrease because, theoretically, energy was
being subtracted from the overall system. In the second objective, QL was also negative because
heat was gained by the surroundings. This shows that both Qc and Qh both decreased, which in
turn means energy again was being added to the environment. In this experiment, there was a
great amount of heat loss because the hot liquid was in the shell side, which is on the outside,
and therefore more heat was lost to the environment.
5.0 Summary and Conclusions
A small shell and tube heat exchanger was used to evaluate the effects of varying either
the shell or tube side flow rate, while keeping the other constant. The purpose of this experiment
was to assess how changing the flow rates affected the steady state heat duty, the overall heat
transfer coefficient of the heat exchanger, and to estimate the heat loss to the environment.
The data collected through the first trial of the experiment involved varying the tube side
and keeping the shell side fixed at 50% open. As the percent opening of the tube side increased,
the temperature of hot fluid going in and out of the exchanger clearly decreased, and the

15
temperatures of the cold fluid going in and out decreased slightly, but not as noticeably. The flow
rate of the hot fluid decreased slightly with each increase of the tube opening, while the flow rate
of the cold fluid increased with each change. This increase in the cold side flow rate was
expected as increasing the valve opening allowed more fluid to flow through. The data collected
from the second trial, with the tube side fixed at 50% open and the shell side changing, showed
similar results in the temperature changes. The flow rates varied oppositely, though, in
comparison to the first trial. The flow rate of the hot fluid increased as the percent valve opening
of the shell increased, and the flow rate of the cold fluid decreased. This was again expected,
since the hot side valve opening was increased each time. It can be determined from both trials
that the shell side temperatures were more affected by the flow rate changes than the tube side.
After all of the data was collected and recorded, some calculations were performed to
better evaluate the results of the experiment. The heat duty was calculated, which is the amount
of heat, or energy, transferred from the hot side to the cold side [7]. For the first technical
objective, the heat duty of the cold side was a large positive number that overall increased with
each percent valve opening increase in the tube side. For the hot side, this value was a negative
number that did not vary significantly. The heat duties of the second technical objective were the
opposite. For the cold side, it was a very negative number that decreased with each change in
flow rate. The heat duty of the hot side was a positive number that had no conclusive trend. The
negative values are the result of cooling, while the positive values indicate that heating occurred
[8]. The overall heat transfer coefficient was also calculated. This number refers to how well heat
is conducted through the fluid [9]. The larger the coefficient, the easier the heat is transferred
from the source to what is being heated [9]. For both technical objectives, the coefficient was a
large number that was positive for the first trial when the tube flow rate was varied, but negative
for the second, when the shell side was varied. Positive means that temperature decreased, and
negative means that temperature increased. Lastly, the heat lost to the environment was
evaluated. For both trials, the heat loss is a very large value. This is because the hot fluid on the
shell side transferred heat to the tube side and the environment.

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References
[1] A. Pramuanjaroenkij, H. Liu, and S. Kakac, Heat Exchangers: Selection, Rating, and
Thermal Design. Boca Raton, Florida: CRC Press, 2012. pp.8-22.
[2] A.P., “Analysis of a Shell and Tube Heat Exchanger,” oocities.org, 2003. [Online].
Available: http://www.oocities.org/ucoproject/index.htm. [Accessed: Oct. 12, 2015].
[3] Alfa Laval, “Basic Construction of Shell and Tube Heat Exchangers,” Jul 2010. [Online].
Available: http://local.alfalaval.com/en-us/key-technologies/heat-transfer/shell-and-tube-
heat-exchangers/process-
industrial/Documents/TEMA%20basics%20of%20construction%20-%2007.10.pdf.
[Accessed: Oct. 12, 2015].
[4] A. Roberts, E. Giuffrida, J. Palazzolo, K. Minbiole, M. Africa, and R. Kendrick, “Heat
Exchangers,” in Encyclopedia of Chemical Engineering Equipment. University of
Michigan, [online document], 2014. Available: http://encyclopedia.che.engin.umich.edu/
[5] G. Chen, M. Zeng, Q. Chen, and Q. Wang, “Numerical investigation on combined
multiple shell-pass shell-and-tube heat exchanger with continuous helical baffles,”
International Journal of Heat and Mass Transfer, vol. 52, no. 5-6, February, 2009.
[Online serial].
Available: http://www.sciencedirect.com/science/article/pii/S001793100800536X.
[Accessed Oct. 11, 2015].
[6] “Specific Heat Capacity Table,” [Online]. Available:
http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html.
[7] O. Araromi, A. Oyelaran, and L. Ogunleye. "Design and Development of a Small Heat
Exchanger as Auxiliary Cooling System for Domestic and Industrial Applications,"
International Journal of Engineering Trends and Technology, vol. 5, no. 6, November,
2013. [Online serial]. Available: http://ijettjournal.org/volume-5/number-6/IJETT-
V5N6P157.pdf. [Accessed Oct. 13, 2015].
[8] “Simple Heat Exchanger,” syscad.net, Mar 13, 2014. [Online]. Available:
http://help.syscad.net/index.php/Simple_Heat_Exchanger. [Accessed: Oct. 13, 2015].
[9] “Overall Heat Transfer Coefficient,” tlv.com. [Online]. Available:
http://www.tlv.com/global/TI/steam-theory/overall-heat-transfer-coefficient.html.
[10] J. Welty, C. Wicks, R. Wilson, G. Rorrer, Fundamentals of Momentum, Mass and Heat
Transfer, 2008, pp. 344.

18
[11] “Water Density Calculator,” [Online]. Available:
http://antoine.frostburg.edu/chem/senese/javascript/water-density.html. [Accessed: Oct.
11, 2015].

19
Appendix A-1
Experimental Data
Table 1. Technical Objective 1
Tube (cold) Open: 10% 30% 60% 100%
Temp In (oC) 20.91 20.83 20.87 20.95
Temp Out (oC) 30.74 25.39 24.00 23.64
Mass Flow Rate (L/min) 3.828 2.8606 4.1582 4.7838
Shell (hot) Open: 50% 50% 50% 50%
Temp In (oC) 47.74 42.10 40.04 38.92
Temp Out (oC) 41.63 35.79 33.72 32.76
Table 2. Technical Objective 2
Shell (hot) Open: 10% 30% 50% 70%
Temp In (oC) 48.79 43.37 40.13 38.39
Temp Out (oC) 32.80 33.61 33.89 33.60
Tube (cold) Open: 50% 50% 50% 50%
Temp In (oC) 20.76 20.62 20.79 20.84
Temp Out (oC) 23.70 23.92 24.12 24.13

20
Appendix A-2
Example Calculations
The equation for the energy balance to determine heat loss to the environment is
|Qh| = |Qc| + QL. (1)
The equation for the overall heat transfer coefficient is
Qc = U × A × ∆Tlm × F. (2)
The equation for heat duty of the tube side is:
Qc = mc × Cp × ∆T, (3)
where mc is the mass flow rate of the tube side, Cp is the specific heat of water, and ∆T is the
change in temperature of the tube side.
Example Equation 3:
Using data from technical objective 1 when the tube side is 60% open:
𝑄𝑐 = 4.16
𝐿
𝑚𝑖𝑛
×
1 𝑚𝑖𝑛
60 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
×
1000𝑚𝐿
1𝐿
×
. 998207
𝑔
𝑚𝐿 + .997047
𝑔
𝑚𝐿
2
× 4.184
𝐽
𝑔 °𝐶
× (24.00°𝐶 − 20.87°𝐶)
=905.44 W
The equation for heat duty of the hot-side flow is:
Qh = mh × Cp × ∆T, (4)
Where mh is the mass flow rate of the shell side, Cp is the specific heat of water, and ∆T is the
change in temperature of shell side.

21
Example Equation 4:
Using data from technical objective 2 when the shell side is 30% open:
𝑄ℎ = 2.44
𝐿
𝑚𝑖𝑛
×
1 𝑚𝑖𝑛
60 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
×
1000𝑚𝐿
1𝐿
×
.99565
𝑔
𝑚𝐿
+ .990216
𝑔
𝑚𝐿
2
× 4.184
𝐽
𝑔 °𝐶
× (33.61°𝐶 − 43.37°𝐶)
=-1646.22 W
Equation (1) is solved for heat loss as
QL = |Qh| − |Qc|, (5)
where Qh is the heat duty of the hot-side flow and Qc is the heat duty of the cold-side flow.
Example Equation 5:
𝑄𝐿 = |−1374.69 𝑊| − |802.47 𝑊| = 572.21 𝑊
Equation (2) is solved for the overall heat transfer coefficient as
U =
Qc
A×∆Tlm×F
, (6)
where Qc the heat duty of the cold-side flow, A is the heat transfer surface area for the tubes
which is 50 in2 that can be converted for dimensional homogeneity to 0.03225812903 m2, F is
.96, and ∆Tlm is expanded upon below [11].
Example Equation 6:

22
𝑈 =
893.52 𝑊
50 𝑖𝑛2 ×
(1 𝑚)2
(39.37 𝑖𝑛)2 × 13.50 °𝐶 × .96
=2137.88 W/(°C*m2)
The equation for ∆Tlm (log mean temperature difference) is
∆Tlm =
(T(hot,in)−T(cold,out))−(T(hot,out)−T(cold,in))
ln(
T(hot,in)−T(cold,out)
T(hot,out)−T(cold,in)
)
. (7)
Example Equation 7:
∆𝑇𝑙𝑚 =
(48.79 − 23.70)°𝐶 − (32.80 − 20.76)°𝐶
ln (
48.79 − 23.70
32.80 − 20.76
°𝐶
°𝐶
)
=17.77 °C

101 Tuesday A-2 Small Shell and Tube

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