Small Shell and Tube Heat ExchangerUniversity 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

1

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

2

Nomenclature

Variable Description Units

Qh Heat duty of the hot side WattsQc Heat duty of the cold side WattsQL Heat lost to the environment WattsCp 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 °CΔTlm Log mean temperature difference °CF Correction factor No units

3

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

4

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)

5

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

6

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

7

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

8

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%

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

ΔTlm (°C) 18.80 15.82 14.39 13.47

U (W/°C*m2)

1522.1

6 1866.95

2020.0

3 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%

Shell Side Flow Rate (L/min) 1.24 2.44 3.83 5.22

Tube Side Flow Rate (L/min) 3.92 3.91 3.90 3.90

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

9

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%

Shell Side Flow Rate (L/min) 1.24 2.44 3.83 5.22

Tube Side Flow Rate (L/min) 3.92 3.91 3.90 3.90

ΔTlm (°C) 17.77 16.00 14.51 13.50

U (W/°C*m2)

1457.9

5 1810.38

2009.6

2 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.

10

1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50550.00

600.00

650.00

700.00

750.00

800.00

850.00

572.21

749.02 752.81

840.17

742.92

775.01789.78

702.85

Heat Loss vs Volumetric Flow RateVarying Tube Side Varying Shell Side

Volumetric Flow Rate (L/min)

Heat

Loss

(J/s

or W

)

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

11

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 ×C p× ∆ 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

12

Qh=mh ×C p× ∆ 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.

13

Lastly, the heat 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 × ∆ T lm× 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

14

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.

15

16

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/ [Accessed: Oct. 10, 2015].

[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. [Accessed: Oct. 11, 2015].

[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. [Accessed: Oct. 13, 2015].

[10] J. Welty, C. Wicks, R. Wilson, G. Rorrer, Fundamentals of Momentum, Mass and Heat Transfer, 2008, pp. 344.

17

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

18

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 4.7838Shell (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

Mass Flow Rate (L/min) 1.2736 3.854 3.870 3.743

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

Mass Flow Rate (L/min) 1.243 2.436 3.828 5.222Tube (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

Mass Flow Rate (L/min) 3.9235 3.9081 3.897 3.9039

19

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 × ∆ T lm× F . (2)

The equation for heat duty of the tube side is:

Qc=mc ×C p× ∆ T , (3)

where mc is the mass flow rate of the tube side, C p 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 Lmin

× 1min60 seconds

× 1000 mL1 L

×.998207 g

mL+.997047 g

mL2

× 4.184 Jg° C

× (24.00 °C−20.87 ° C )

=905.44 W

The equation for heat duty of the hot-side flow is:

Qh=mh ×C p× ∆ 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.

Example Equation 4:

20

Using data from technical objective 2 when the shell side is 30% open:

Qh=2.44 Lmin

× 1min60 seconds

× 1000 mL1 L

×.99565 g

mL+.990216 g

mL2

× 4.184 Jg ° 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:

Using data from technical objective 2 when the shell side is 10% open:

QL=|−1374.69W|−|802.47W|=572.21 W

Equation (2) is solved for the overall heat transfer coefficient as

U=Qc

A × ∆ T lm × 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:

Using data from technical objective 2 when the shell side is 70% open:

U= 893.52 W

50¿2 × (1m )2

¿¿¿ ¿

21

=2137.88 W/(°C*m2)

The equation for ∆ T lm (log mean temperature difference) is

∆ T lm=¿¿¿ . (7)

Example Equation 7:

Using data from technical objective 2 when the shell side is 10% open:

∆ T lm=(48.79−23.70 )° C−(32.80−20.76 )° C

ln( 48.79−23.7032.80−20.76

° C° C )

=17.77 °C

22