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Thermal Fluid System Design

Design #3

2

Table of Contents

Nomenclature Listing ……………………………………………………………………….3

Executive Summary ……………………………………………………………………….4

Introduction ……………………………………………………………………………….4

Analysis ……………………………………………………………………………….6

Results/Discussion ……………………………………………………………………...14

Conclusion ……………………………………………………………………………...24

References ……………………………………………………………………………...25

Appendix A: Detailed Calculations ……………………………………………………...26

Appendix B: Excel Data Tables ……………………………………………………...32

Appendix C: Shell and Tube Analysis ……………………………………………...44

3

Nomenclature Listing

T: refers to temperature of warmer fluid

t: refers to temperature of the cooler fluid

w: subscript refers to warmer fluid

h: subscript refers to hydraulic diameter

c: subscript refers to cooler fluid

a: subscript refers to the annular flow area / dimension

p: subscript refers to the tubular flow area / dimension

1: subscript refers to an inlet condition

2: subscript refers to an outlet condition

e: subscript refers to equivalent diameter

4

Executive Summary

This project entails the optimization of a heat exchanger. The system’s requirements are

oil coming from an engine at 4 lbm/s with an initial temperature of 300°F, being cooled by water

with an initial temperature of 55°F. The outlet requires oil to be within the range of 120°F and

165°F, with water not exceeding 180°F. Tubing is comprised of schedule 40 steel pipes and the

desired system is to implement a double pipe heat exchanger. Using Microsoft Excel to simplify

the calculations, the optimized system would be a double pipe heat exchanger of 2,930 feet, mass

flow rate of water of 2.34 lbm/s, and an outlet temperature of 165°F for the oil. If the customer

is interested in minimizing the length further, an 8 foot shell and tube heat exchanger could be

used, with a 171/4

” shell inner diameter, coupled with ¾” inner diameter tubing.

Introduction

Heat exchangers exist in many different configurations. Whether it is a double pipe, shell

and tube, cross flow, or a plate and frame heat exchanger, each system has specific uses.

Nevertheless, the analysis doesn’t differ greatly between each configuration. This project

examines a double pipe heat exchanger and the relationship between the placement of the given

fluids (such as in the annulus or tube) and the subsequent effect on length and pressure drop of

the system. As with any heat exchanger, a main objective for the system is to transfer as much

heat as possible, while minimizing the cost. To achieve this goal, it is necessary to keep the

system as small as possible. Figure 1 is an example of a double pipe heat exchanger.

Figure 1: Double Pipe Heat Exchanger

5

As Figure 1 suggests, the fluids have two separate inlets, which leads to the two concentric pipes.

For the project at hand, the heat exchanger is used to cool oil coming from an engine at 4 lbm/s

and 300°F to at least 165°F (but no less than 120°F). Water acts as the cooling fluid and is

available at 55°F and cannot exceed 180°F at the outlet. Schedule 40 piping will be used for the

heat exchanger and counterflow will be assumed as it is notably more effective, as compared to

parallel (unidirectional) flow. Figures 2 and 3 show the temperature graphs for both parallel

flow and counterflow.

Figure 2: Parallel Flow

Figure 3: Counterflow

These figures make it apparent as to why counterflow is a more logical choice when analyzing

the system. Note that counterflow could potentially allow the outlet of the hot fluid to be cooler

than the outlet for the cold fluid. This is not the case in parallel flow as the outlet of the cold will

never be above the outlet of the hot1.

6

To be able to optimize this system, careful consideration will be given to pipe size,

associated heat exchanger length, placement of the fluids, and the mass flow rate of water. With

this exposition for the project completed, it is appropriate to look at the mathematical model used

to solve this problem. While this model is applicable to solve the project by hand, the fact is that

many of the parameters aren’t specified, thus, Microsoft Excel is chosen to make the

computations simpler and iterative processes quicker.

Analysis

Like most thermal fluid applications, this project can be analyzed in two sections.

Firstly, with respect to heat transfer and secondly, with respect to fluid mechanics. To begin the

analysis it is necessary to determine the fluid properties at their average temperatures. This is

done for the oil over a range of 210°F to 233°F (as the oil outlet could vary) and at 118°F for the

water (as the water inlet and outlet were fixed). Next, it is appropriate to choose pipe sizes for

the flow. Figure 4 is a diagram showing the associated diameters of the heat exchanger.

Figure 4: Associated Diameters

While choosing the pipe sizes may seem random, it is necessary to ultimately look at the length

and pressure drop each pipe combination offers for the system, as will be discussed in the

Results section. Having these properties for the system, it is appropriate to start with Equation

(1).

IDa

ODp

IDp

7

(1)

Where is the area of the pipe in ft2 and is the inner diameter of the pipe in ft. Equation

(2) then allows the annulus area, , to be calculated using the outer pipe diameter, .

(2)

Having the areas associated with the pipe and annulus, the fluid velocities can then be computed,

as shown in Equations (3) and (4).

(3)

(4)

Where the pipe velocity in ft/s, the annulus velocity in ft/s, and is the mass flow rate of

the specified fluid in lbm/s.

8

Using the tubing sizes, it is appropriate to calculate the hydraulic and equivalent diameters of the

annulus. Equation (5) allows the hydraulic diameter to be computed, while Equation (6) allows

the equivalent diameter to be computed.

(5)

(6)

Where is the hydraulic diameter and is the equivalent diameter, both in feet.

With the associated diameters, it is feasible to compute the Reynolds Numbers for the pipe and

annulus. Equation (7) does so for the pipe while Equation (8) does so for the annulus.

(7)

(8)

With and being the Reynolds Numbers for the pipe and annulus, respectively. Note that

ν, the kinematic viscosity, is a fluid property and in ft2/s.

9

Having the Reynolds Numbers allows the Nusselt Numbers for the pipe and annulus to be

calculated. Equation (9) is appropriate if the flow is laminar (Re < 2200), while Equation (10) is

appropriate for turbulent flow (Re > 10000).

(9)

(10)

Where L is the length of the heat exchanger in feet, Pr is the Prandtl number (listed as a fluid

property), and n is .3 for a fluid being cooled, or .4 for a fluid being heated. Note that L is going

to require an iterative approach as it is an unknown. Coupling Equation (9) with Equation (20),

the length must be iterated until the results converge.

Using the Nusselt numbers, the convection coefficients for the pipe and annulus can be

computed. This is shown in Equations (11), (12), and (13).

(11)

(12)

10

(13)

With being the heat transfer coefficient of the inner pipe, being the coefficient of the entire

pipe, including the pipe wall, being the coefficient of the annulus, and is the fluid’s

thermal conductivity, a property of the fluid. Note that the convection coefficients are in Btu/(h-

ft2-°R). Having these coefficients it is possible to compute the exchanger coefficient, , as

shown in Equation (14).

(14)

Where is in Btu/(h-ft2-°R). Thus far this analysis has followed the Janna text

1, but due to the

project’s requirements, certain alterations are now necessary; primarily, obtaining mass flow rate

values. While economic velocities can be used to set limits on a mass flow rate, this project aims

to minimize the length of the system, thus the economic velocity range may not be met. This is

simply due to the fact that this system is trying to be economic elsewhere, more specifically with

respect to the length of the heat exchanger and pressure drop.

By knowing all of the temperatures for this project, it is possible to compute the log mean

temperature difference, as depicted in Equation (15). Also, by setting up a heat balance across

the system, it is appropriate to ultimately compute the mass flow rate of water, as displayed in

Equations (16) and (17).

11

(15)

Note that Equation (15) is applicable only for counterflow.

(16)

Where is the heat transfer due to the warm fluid in Btu/s, is the mass flow rate of the

warm fluid, and is the specific heat of the warm fluid in Btu/(lbm-°R). Using a heat balance,

Equation (17) is appropriate.

(17)

With being the specific heat of the cool fluid.

Recognizing that is an ideal exchanger coefficient, it is necessary to look at the fouling

factors the fluids have on the system. Equation (18) calculates the design coefficient, , also in

Btu/(hr-ft2-°R).

12

(18)

Where and are the fouling factors of the two fluids on the inner and outer pipe,

respectively. Having the actual exchanger coefficient, it is appropriate to calculate the area of

the heat exchanger. Equation (19) shows this computation.

(19)

With being the heat transfer area in ft2. Using , Equation (20) allows the length of the

system, L, to be computed. As previously stated, the fact both Equations (9) and (20) have

length in them, a separate input box in Microsoft Excel allows the lengths to be iterated until

convergence is achieved.

(20)

With L in feet. While Reynolds Numbers were computed in Equations (7) and (8), it is now

necessary to look at the Reynolds Numbers to be able to obtain friction factors, as shown in

Equations (21) and (22).

13

(21)

(22)

Note that Equation (22) requires the hydraulic diameter. Furthermore, coupling these equations

with the roughness factor of the piping, it is possible to obtain the friction factor from the moody

chart (if the flow is turbulent) or using 64/Re (if the flow is laminar). Having the friction factors

allows the pressure drop to be computed for both the pipe and the annulus, as depicted in

Equations (23) and (24)

(23)

(24)

Where and are the pressure drops, in lb/ft2, in the pipe and annulus, respectively. is

the friction factor for the pipe, is the friction factor in the annulus, is the density of the fluid

in the pipe, and is the density of the fluid in the annulus. Note that to get the pressure drop

into psi, simply divide and by 144.

With Equations (1) – (24), the mathematical analysis is completed. It is now appropriate

to look at the results that this analysis yields, for the case of water in the annulus and oil in the

annulus. Furthermore, Appendix A denotes detailed calculations for one case.

14

Results / Discussion

One of the first steps shown in the analysis is choosing pipe sizes. This process is a very

crucial one, as it is quite possible to have multiple tubing combinations that may appear to satisfy

the pressure drop requirement, yet doesn’t necessarily optimize the length of the system.

Similarly, the pressure drop is a function of the mass flow rate of water as well. This can be seen

in Table 1.

Tubing Size Pressure Drop

(psi) in Pipe and

Annulus

Mass Flow Rate

of Water (lbm/s)

Length of

System (ft)

8” x 5” 4.3 ; 1.3 3.06 17,450

10” x 8” .6 ; 2.8 2.90 14,710

10” x 8” .5 ; 2.1 2.75 12,550

8” x 6” 1.1 ; 3.0 2.65 10,930

8” x 6” .9 ; 2.3 2.49 9,300

8” x 6” .7 ; 1.7 2.39 7,910

Table 1: Tubing Sizes

As this table suggests, each tube combination satisfies the requirement of pressure drop being

less than 10 psi, for both the annulus and pipe, yet it is obvious that the 8” x 6” tubing

combination optimizes the length. While this data is for water in the annulus, comparative

results are applicable for oil in the annulus, with Table 1 simply displaying the iterative process

that must take place in order to optimize the system. Regarding this data, Appendix B contains

the entire workbook along with all the associated calculations. With this being said, it is

appropriate to look at the two cases presented in the Introduction and decide whether it is best to

place water or oil in the annulus. For the remainder of the report, Case 1 will pertain to water in

the annulus, while Case 2 will pertain to oil in the annulus.

Due to the fact that there are certain restrictions on the outlet temperatures of both the oil

and water, it is necessary to assume some parameters. Because economic flow velocity is not

going to be of interest, a heat balance was used to gain the mass flow rate of water (as shown in

15

Equation (17) ). Furthermore, because the outlet temperature of the oil can vary from 120°F to

165°F, six subsections are made for each case, that increases the oil outlet temperature 9°F per

section. This is done because water has very similar properties and by fixing its outlet

temperature at 180°F, the properties have an effect on the calculations. Oil on the other hand is

very much affected by temperature. For example: when temperature varies from 176°F to 212°,

Prandtl number varies from 490 to 276. Thus, this assumption is valid. By using Microsoft

Excel, a spread sheet is programmed to compute the characteristics for each case and the results

for the two best scenarios of each case will be compared. On the other hand, using the data for

the six subsections per case, certain trends will be apparent when comparing outlet temperature,

mass flow rate of water, pipe size, length, and pressure drop.

Starting with the case of water in the annulus of the heat exchanger, the system’s

characteristics are obtained. This is displayed in Table 2.

16

Table 2: Case 1: Water in the Annulus

Similarly, it is appropriate to look at the system’s characteristics for the case of oil in the

annulus. This is displayed in Table 3.

Dimensionsri (ft) 0.25

ro (ft) 0.28

Ri (ft) 0.33

L (ft) 7914.30

Temperatures UsedTc, in (°F) 55.00

Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 165.00

Heat Transfer Coefficientshi (Btu/hr-ft2-°R) 0.67

ho (Btu/hr-ft2-°R) 121.30

Mass Flow Rate of Watermc (lbm/s) 2.34

Overall Heat Transfer CoefficientUi (Btu/hr-ft2-°R) 0.67

Pressure DropsWater (psi) 1.72

Oil (psi) 0.72

Heat Transfer AreaAi (ft2) 13727.14

Effectivenessε 0.55

Heat Exchanger Ratingq (Btu/s) 291.60

17

Table 3: Case 2: Oil in the Annulus

By simply looking at these two tables, it appears that placing oil in the annulus is the optimal

design, as the length is shorter by nearly 5000 ft. Nevertheless, it is of sound engineering

practice to perform a cost analysis for each of these systems since the necessary pipe size of

having oil in the annulus is larger than the case of water in the annulus. This is of importance as

the increase in diameter of the pipe size may contribute to a cost greater than the extra 5000 ft of


ro (ft) 0.36

Ri (ft) 0.42

L (ft) 2925.55


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 165.00






Oil (psi) 7.13




18

the smaller diameter pipe. Obtaining prices from Metals Depot2, Table 4 displays the cost

analysis for both cases.

Tubing

Sizes

Cost / ft Overall Cost

10” x 8” $207.26 $606,345.5

8” x 6” $150.99 $1,187,065.9

Table 4: Cost Analysis

With the cost analysis performed, it is clear that placing oil in the annulus is indeed the

optimal design for this system. Another point of interest is the fact that by having the oil (the

hotter fluid) in the annulus, the surrounding environment will also help with respect to heat

transfer. Lastly, it is of importance to note the fouling factors associated with the two fluids.

Due to the fact that water and oil have comparable fouling factors (both nearly .001 ft2-hr-

°R/Btu), the placement of the fluids won’t affect quality of the pipes. If the oil were to have a

fouling factor more than the water, it may be more appropriate to place it in the pipe, as only the

inner pipe would have to be replaced over time, versus the chance of replacing both pipes if the

greater fouling agent were placed in the annulus. With the optimal design for the system being

selected, by placing oil in the annulus, using 10” x 8” tubing, it is of interest to look at the heat

exchanger’s characteristics for the oil outlet temperature varying from 120°F to 165°F.

The first parameter to be altered when varying the outlet temperature is the mass flow

rate of water. Figure 4 displays this relationship.

19

Figure 4: Mass Flow Rate vs. Outlet Temperature

Note that regardless of placement of the fluids, whether it is oil in the annulus or water, the trend

is exactly the same, as this figure is predicated solely from the heat balance. Figure 4 is

affirming in the fact that it is congruous with the computation performed in Equation (17). By

increasing outlet temperature, the water mass flow rate must decrease in order to conserve

energy. Also interesting is the effect that the outlet temperature has on effectiveness. This is

shown in Figure 5.

Figure 5: Effectiveness vs. Outlet Temperature

110.0000

120.0000

130.0000

140.0000

150.0000

160.0000

170.0000

2.25 2.45 2.65 2.85 3.05 3.25

Ou

tle

t Te

mp

ear

ture

(°F

)

Mass Flow Rate of Water (lbm/s)

Mass Flow Rate of Water vs. Outlet Temperature

115.0000

125.0000

135.0000

145.0000

155.0000

165.0000

175.0000

0.50 0.60 0.70 0.80

Ou

tle

t Te

mp

era

ture

(°F

)

Effectiveness (ε)

Effectiveness vs. Outlet Temperature

20

The importance of Figure 5 is that for the system to operate with the highest efficiency, the oil

outlet temperature must be a minimum. This makes sense as the system must remove the most

heat to cool the outlet temperature to such a degree, thus increasing effectiveness. Nevertheless,

the system with the highest efficiency isn’t always the optimized design. Figure 6 displays this

fact, that length and effectiveness are directly related.

Figure 6: Effectiveness vs. Length

This figure demonstrates that by having more pipe, the effectiveness will increase as the fluids

will travel a longer length, allowing for more heat transfer. While it is appropriate to fit a linear

trendline to the data set, it is apparent the points don’t particularly fit a certain equation. This is

due to the fact that in order to keep pressure drop below 10 psi, while minimizing the heat

exchanger length, pipe sizes must change. The drastic drops in pipe length are indicative of this

fact.

A main factor in determining the length of the heat exchanger is the exchanger

coefficient, . Figure 7 shows this relationship.

0.0000

5000.0000

10000.0000

15000.0000

20000.0000

25000.0000

0.50 0.55 0.60 0.65 0.70 0.75 0.80

Len

gth

(ft

)

Effectiveness (ε)

Effectiveness vs. Length

21

Figure 7: Exchanger Coefficient vs. Length

This relationship is important, as to minimize the area (and subsequently the length), must be

maximized. Because the oil has such a low Nusselt number, due to the laminar flow, the

controlling heat transfer coefficient is due to the oil. This in turn minimizes the exchanger

coefficient and thus makes the length exuberant. This effect is due to the 4 lbm/s flow rate of oil

coming from the engine. While I was the original person to question the 4 lbm/min flow rate, as

economic flow velocity yielded no valid pipe sizes, the fact economic flow velocity isn’t a goal

of this project, 4 lbm/min would have yielded much better results. To prove this, Tables 5 and 6

list the specifications of both cases with the original 4lbm/min mass flow rate, as given in the

problem statement.

0.3500

0.5500

0.7500

0.9500

1.1500

1.3500

1.5500

2000 7000 12000 17000 22000 27000

Exch

ange

r C

oe

ffic

ien

t (B

tu/h

r-ft

2 -°R

)

Length (ft)

Length vs. Exchanger Coefficient

22

Table 5: Case 1: 4 lbm/min Mass Flow Rate


ro (ft) 0.05

Ri (ft) 0.06

L (ft) 145.89


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 165.00






Oil (psi) 0.25




23

Table 6: Case 2: 4 lbm/min Mass Flow Rate

While the lengths are still 145 ft and 85 ft, these lengths are significantly lower than when the oil

flow rate is 4 lbm/s. While some assume this is an engine in a car, and having a heat exchanger

of 85 ft is quite long, if this were an engine in a larger system (such as a ship), having a heat

exchanger that is 10’ x 9’ isn’t that unreasonable. The importance of Tables 5 and 6 is to depict

the effect oil flow rate has on the system. Another point to note is the amount of heat that must


ro (ft) 0.04

Ri (ft) 0.04

L (ft) 85.07


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 165.00






Oil (psi) 10.12




24

be removed for the oil to be cooled to 165°F (or below for that matter). Having such a steep

temperature gradient requires a greater pipe length. Lastly, if 4 lbm/min were the required flow

rate, the cost of the optimal system (oil in the annulus) would be only $2,168, a considerable

savings.

Another consideration for this project is to analyze the system as a shell and tube heat

exchanger. The properties used to compute the shell and tube analysis are taken from the

optimal case of the double pipe heat exchanger, where engine outlet temperature is 165°F. This

is a valid assumption, as using the higher outlet temperature will lower the amount of heat

transfer, and thus minimize the length of the heat exchanger. Performing a shell and tube

analysis yielded the following results; a shell of 171/4

” ID, with ¾” ID 13 BWG tubes, on a 1”

square pitch. Appendix C contains the spreadsheet used to calculate the analysis. This data

indicates that a shell and tube heat exchanger would be a more reasonable heat exchanger design

for this system if the customer were willing to have this configuration.

Having this data and the presented evaluation complete, a conclusion of the knowledge

gained is appropriate.

Conclusion

This project displays the fact that designing a heat exchanger is very dependent on the

flow rates used, as well as the necessary temperature difference that the exchanger must supply.

Furthermore, in selecting a certain type of heat exchanger, it is important to look at the given

parameters, as well as the requirements, and choose the most suitable system. The fact that a

shell and tube can handle these requirements, with a length of 8 feet is a lot more realistic than a

double pipe heat exchanger that is nearly 3,000 feet. Nevertheless, whether the calculated results

and the expected results differ or are synonymous, it is important to note the relationships

between the parameters. Such as; that mass flow rate and outlet temperature are inversely

related. That effectiveness and outlet temperature are inversely related. Effectiveness and length

are directly related and lastly, that length and exchanger coefficient have an inverse relationship

as well. Being able to obtain these relationships is the important part of any project and while

the resulted values, such as length of the system, are exuberant, the knowledge gained regarding

heat exchangers is immeasurable.

25

References

1) Design of Fluid Thermal Systems. 3rd ed. Stamford, CT: Cengage Learning, 2010. Print.

2) Metals Depot® - Buy Small Quantity Metal Online! Steel, Aluminum, Stainless, Brass.

Web. 03 May 2010. <http://www.metalsdepot.com/index.phtml?aident=>.

26

Appendix A: Detailed Calculations

(See Attached)

32

Appendix B: Excel Data Tables

Case 1:

Table B-1: Oil Outlet Temperature of 120°F


ro (ft) 0.23

Ri (ft) 0.33

L (ft) 17449.04


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 120.00






Oil (psi) 4.29




33



ro (ft) 0.36

Ri (ft) 0.42

L (ft) 14712.92


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 129.00






Oil (psi) 0.58




34



ro (ft) 0.36

Ri (ft) 0.42

L (ft) 12519.72


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 138.00






Oil (psi) 0.46




35



ro (ft) 0.28

Ri (ft) 0.33

L (ft) 10927.17


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 147.00






Oil (psi) 1.12




36



ro (ft) 0.28

Ri (ft) 0.33

L (ft) 9309.36


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 156.00






Oil (psi) 0.91




37



ro (ft) 0.28

Ri (ft) 0.33

L (ft) 7914.30


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 165.00






Oil (psi) 0.72




38

Case 2:



ro (ft) 0.28

Ri (ft) 0.42

L (ft) 22439.73


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 120.00






Oil (psi) 5.50




39



ro (ft) 0.28

Ri (ft) 0.42

L (ft) 19041.11


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 129.00






Oil (psi) 4.67




40

Table B-9: Oil Outlet Temperature 138°F


ro (ft) 0.28

Ri (ft) 0.42

L (ft) 16190.07


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 138.00






Oil (psi) 3.71




41



ro (ft) 0.28

Ri (ft) 0.42

L (ft) 14139.64


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 147.00






Oil (psi) 3.01




42



ro (ft) 0.36

Ri (ft) 0.42

L (ft) 3422.72


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 156.00






Oil (psi) 8.93




43



ro (ft) 0.36

Ri (ft) 0.42

L (ft) 2925.55


Tc, out (°F) 180.00

Th, in (°F) 300.00

Th, out (°F) 165.00






Oil (psi) 7.13




44

Appendix C: Shell and Tube Analysis

L 8

A. Fluid Properties

Oil: Evaluated at 233°F

mw (lb/s) 4.00 T1 (°F) 300

ρ (lbm/ft3) 52

Cp (Btu/lbm-

°R) 0.54

kf (Btu/hr-

ft-°R) 0.079 α (ft2/hr) 0.0028

nu (ft2/s) 0.000169 Pr 217

Water: Evaluated at 118°F

mc (lb/s) 2.34 t1 (°F) 55

ρ (lbm/ft3) 61.7

Cp (Btu/lbm-

°R) 0.9987

kf (Btu/hr-

ft-°R) 0.37 α (ft2/hr) 0.0059

4

nu (ft2/s) 6.11E-06 Pr 3.68

B. Tubing Sizes

IDt(ft) 0.0467 ODt (ft) 0.0625

Nt 124.0000 Np 2

C. Shell Data

Ds 1.4375

B 0.1450

Nb 7.0000

Pt 0.1667

C 0.1042

D. Flow Areas

At 0.1060

As 0.1303

45

E. Fluid Velocities

Vt 0.3570

Vs 0.5905

F. Shell Equivalent Diameter

De 0.5034

G. Reynolds Numbers

Ret 2726.639

6

Res 1758.788

8

H. Nusselt Numbers

Nut 21.7055

Nus 131.8226

I. Convection

46

Coefficients

hi 172.0934 ht 128.49636

87

ho 20.6879

J. Exchanger Coefficient

Uo 17.8191

K. Outlet Temperature

R 1.2500 Ao 194.77874

45

UoAo/mcC

pc 0.4133 S 0.46

t2 167.7000

T2 159.1250

L. Log Mean Temperature Difference

Counterflow:

LMTD 117.6508

M. Heat Balance

qw 304.2900

47

qc 262.9066

N. Overall Heat Balance for Exchanger

F 0.9300

q 105.4877

O. Fouling Factors and Design Coefficient

Rdi 0.0002 Rdo 0.001

U 17.46125

78

P. Area Required to Transfer Heat

Ao 198.7701

L 8.1639 (Ideal length as contaminates will

build up)

Q. Friction Factors

ft 0.0235

fs 0.4301

R. Pressure Drop Calculations

Δpt 0.0136

Δps 0.019206

Table C-1: Shell and Tube Analysis

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