IJMET Shell and Tube Heat Exchanger Design

INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME
AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
IJMET
Volume 3, Issue 3, September - December (2012), pp. 378-386
© IAEME: www.iaeme.com/ijmet.asp ©IAEME
Journal Impact Factor (2012): 3.8071 (Calculated by GISI)
www.jifactor.com

A PRACTICAL APPROACH TO DESIGN AND OPTIMIZATION OF
SINGLE PHASE LIQUID TO LIQUID SHELL AND TUBE HEAT
EXCHANGER

Ajeet Kumar Rai * and Mustafa S Mahdi**
*Deptt of Mech. Engg. SSET, SHIATS-DU Allahabad (U.P.) INDIA-211007
**Deptt of Mech. Engg. University of Diyala, Republic of Iraq-32001
E mail-raiajeet@rediffmail.com, Mustafa.sabah@yahoo.com

ABSTRACT

In this paper a method for thermal-hydraulic design of single phase liquid to liquid
shell and tube heat exchanger is established based on Tinker method. Modification suggested
by Kern and Kakac are also incorporated. A computer program has been developed to ease
the design procedure. The program determines the overall dimensions of the shell, the tube
bundle, and optimum heat transfer surface area required to meet the specified heat load by
utilizing the allowable shell-side pressure drop and other optimum parameters like fixed tube
side velocity and fixed baffle cut. The capability of the proposed model was verified through
a case study of a shell and tube heat exchanger used in a locomotive for cooling of the
lubricating oil of the engine. The design shows a comparable result with the case study with
deviation of 10%.

Keywords: Heat exchanger; Shell and tube; Sizing; Single-phase flow

INTRODUCTION

Shell and tube heat exchanger have a wide application, it is worth noting that more than
ninety percent of heat exchangers used in industry are of the shell and tube heat exchanger
type as these heat exchangers are capable of handling a quite high load in a moderate size,
they offer a great flexibility to meet almost any service requirement, they can be designed for
handling high pressures and they can be easily cleaned. Consequently many researches and
investigation are done towards establishing better and efficient design procedures with
optimization with its characteristics and cost. Kern [1] provided a simple method for
calculating shell side pressure drop and heat transfer coefficient. However, this method
cannot adequately account the baffle to shell and tube to baffle leakage. The concept of
considering the various streams through the exchangers was originally proposed by Tinker

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

[2]. He suggested a schematic flow pattern, which divided the shell side flow in a number of
individual streams. Tinker’s original analysis was quite complex and hard to understand but it
presents a much better approximation than the analysis given by Kern, a simplified form of
Tinker’s analysis is present by Frass [3], which is suitable for computer program, which has
been depended on this work for thermal and hydraulic design. In the context of development
of new design technique, this work presents a design and optimization procedure integrate
with an practical design guidelines with the help of simple user friendly computer program.

METHOD
Design strategy: Shell and tube heat exchanger design is an inherently iterative process;
the main steps can be summarized as follows: (1) Obtain an initial configuration for the heat
exchanger. (2) Obtain a thermal and hydraulic design which is suitable for given data. (3)
Iterate until acceptable design is obtained. (4) Optimize the design by testing all the design
parameters to get an optimum and economic design; this can be done by using the computer
program that has been developed in this work.
Thermal and hydraulic design: In thermal design, the heat exchanger is sized, which means
that all the principal construction parameters such as shell diameter, number of tubes, tube
length, tube, baffle spacing and cut, are determined as the following procedure:
1- Calculate the total number of tubes
‫ݓ‬ଵ ݂ଵ ∗ ‫ܰ ∗ ܮ‬ଵ ଷ
݊= ∗ඨ
1.11 ߩଵ ∗ ݀௜௡ ∗ ∆ܲଵ
Use 2.25 m/s as a fluid velocity in tube side which is the most efficient velocity to utilize the
allowable pressure drop to heat transfer coefficient for determination of Reynolds number
that required for determination of friction factor[4].
2- Calculate the tube matrix diameter and shell inside diameter [5].
0.87 ‫ݏ‬
݀௠ = 0.637 ∗ ඨ ∗ [ߨ ∗ ݀௢௨௧ ∗ ݊ ∗ ( )ଶ ]଴.ହ
0.9 ݀௢
݀௦ = ݀௠ ∗ 1.075
3- Calculate nozzles diameter [1].
݀ே = ݀௦ ∗ 0.2
4- Calculation of correction factors to allow the deviation from ideality for shell side, each
baffle cut has a particular correction factors [3], however in present work the baffle cut is
fixed to 25% as it’s the most efficient cut so the correction factors is:
M = 0.88, ܰ௛ = 0.54, Y = 4.7, ܰ௣ = 0.3
‫ܨ‬௛ = (1 + ܰ௛ ∗ ඥ݀௦ ⁄‫ି)ݏ‬ଵ
‫ܨ‬௣ = (0.8 + ܰ௣ ∗ ඥ݀௦ ⁄‫ି)ݏ‬ଵ
5- Calculate the coefficients ‫ܥ‬௔ and ‫ܥ‬௕ which use in calculation of ‫ܩ‬ଶ , ℎଶ and ݂ଶ . this step

ℎ
adopted from the experimental work of Tinker [2].

‫ܥ‬௔ = ଴.ହ଺
‫ܩ‬௛
Where for this step

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24
ℎ=
݀௢ ଵ ߤ
∗ ܲ‫ݎ‬ଶ ିଷ ∗ (ߤ )ି଴.ଵସ
݇ଶ ௪

ܴ݁ଶ ∗ ߤଶ ∗ ‫ܯ‬
And
‫ܩ‬௛ =
݀௢∗ ‫ܨ‬௛
And for ‫ܥ‬௕
0.8
‫ܥ‬௕ = ି଴.ହଷ
‫ܩ‬௣

ܴ݁ଶ ∗ ߤଶ
And
‫ܩ‬௣ =
݀௢ ∗ ‫ܨ‬௣
6- Calculate the logarithmic mean temperature difference.
‫ܶܨ ∗ ܦܶܯܮ = ܦܶܯܮ‬
∆ܶଶ − ∆ܶଵ
‫= ܦܶܯܮ‬
݈‫ܶ∆(݃݋‬ଶ ⁄∆ܶଵ )
൫√ܴ ଶ + 1൯ ln (1 − ‫)ݏܴ − 1(⁄)ݏ‬
‫= ܶܨ‬
2 − ‫ ܴ√ − 1 + ܴ(ݏ‬ଶ + 1)
(ܴ − 1) ݈݊
2 − ‫ + 1 + ܴ(ݏ‬ඥܴ ଶ + 1)

1.86 ∗ ‫ܥ‬௔ ∗ ߨ ∗ ݀௢ ∗ ∆ܲଶ ‫ܷ ܦܶܯܮ‬ ߤ
7- Calculate shell side mass flow rate through the tube bundle

‫ܩ‬ଶ ଷି௔ି௕ = ∗ ∗ ∗ ( )଴.ଵସ
‫ܥ‬௕ ∗ (‫݀ − ݏ‬଴ ) ∗ ‫ܨ‬௣ ∗ (1 − ‫݀⁄ܪ‬௦ ) ∗ (1 + ܻ(‫݀⁄ݏ‬௦ )) ∗ ܿ௣ଶ
ଶ ∆‫ݐ‬ଶ ℎଶ ߤ௪
௎
௛మ
is the ratio of overall heat transfer coefficient to shell side heat transfer for first design it
can be approximate to unity from the fact that the most shell and tube heat exchangers are
employing organic liquid in the shell side and cooling water is insensitive to the tube side h
this makes possible a simplifying approximation [3].
8- Calculate Reynolds number for shell side that modified to the calculation of friction
factor ܴ݁௣ and heat transfer coefficient ܴ݁௛ [2].
‫ܩ‬ଶ ∗ ݀௢ ∗ ‫ܨ‬ ௣
ܴ݁௣ =
ߤଶ
‫ܩ‬ଶ ∗ ݀௢ ∗ ‫ܨ‬௛
ܴ݁௛ =
ߤଶ ∗ ‫ܯ‬
9- Calculate shell side friction factor
݂ଶ = ‫ܩ‬௣ ௕ ∗ ‫ܥ‬௕
10- Calculate shell side heat transfer coefficient
ℎଶ = ‫ܥ‬௔ ∗ ‫ܩ‬௛ ௔

ܳ
11- Calculate of baffle spacing
݈= ଴.ହ ∗ (‫ܿ ∗ ݐ∆ ∗ ) ܩ( ∗ ) ݀ − ݏ‬
‫ܥ‬௠ ∗ ݊ ௢ ଶ ଶ ௣ଶ

380


2 ∗ ∆ܲଶ ∗ ߩଶ ∗ ‫ܥ‬௠
12- Calculate baffles number
ܰଶ = ߤ
݂ଶ ∗ ‫ܩ ∗ ܨ‬ଶ ∗ ݊଴.ହ ∗ (1.075 ∗ (1 − ‫݀⁄ܪ‬௦ ) ∗ (1 + ܻ(‫ݏ‬ൗ݀௦ )) ∗ (ߤ )଴.ଵସ
ଶ
௣
ଶ
௪
13- Calculate tube length of the heat exchanger
‫ܰ ∗ ݈ = ܮ‬ଶ
This is the step to check the value of the assumed length, which it was necessary to assumed
it to precede the calculation; it is provide the bases for the second trail, where the second
assumed value should be closer and higher to the value of calculated length.

݇ଵ ∗ ܰ‫ݑ‬
14- Calculate tube side heat transfer coefficient.

ℎଵ =
݀௜௡

‫ݓ‬ଵ
15- Calculate tube side mass flow rate.
‫ܩ‬ଵ = ݊ ߨ
∗ ∗ ݀௜௡ ଶ
ܰଵ 4
16- Calculate tube side pressure drop
݂ଵ ∗ ‫ܩ‬ଵ ଶ ∗ ‫ܰ ∗ ܮ‬ଵ
∆ܲଵ =
2 ∗ ߩଵ ∗ ݀௜௡

1 1 1
17- Calculate the overall heat transfer coefficient
ܷ = ( + + )ିଵ
ℎଶ ℎଵ ܶ௖
19- Calculate the total heat transfer area, for the purpose of cost estimation
‫݀ ∗ ߨ ∗ ݊ = ܣ‬௢ ∗ ‫ܮ‬
Following above steps are the calculations of thermal design, which find the dimensions of
the heat exchanger and the quantity of some feature, such as nozzles, baffles, shell and tubes.
As it seems very lengthy and the error is not avoidable in manual calculation and the iteration
is required to get the final and optimum design of given data which makes the design very
lengthy. Therefore a computer program is developed in present work to ease the calculation
and minimize the time. This would make the design an enjoyable task to get the optimum
design with the help of computer.
A C code is developed based on the method described above. Baffle cut is fixed to 25% as
it’s the most efficient cut and for simplicity. The program allows the user to choose the
different fluid for shell and tube side. The flow diagram of the computer program is
illustrated in the Fig. 1.

RESULT AND DISCUSSION
The performance of the proposed model is illustrated through the analysis of the results
obtained in an example of design tasks and comparing the solution reached with a shell and
tube heat exchanger that employed in a locomotive for cooling the lubricating oil of the
engine, the data had taken from diesel locomotive works, Varanasi. And the heat exchanger is
employing to maintain the lubricating oil temperature between 65.6 C° and 60 C°. The
requirement data to design the shell and tube heat exchanger is illustrated in table (1). Table
(2) shows three columns. Run1 (with the same data of locomotive heat exchanger column)
gives the acceptable design for a given data that the length assumed was 1.4 m and the

381


calculated length is 1.37 m which it is quite close to the assumed one. The last column show
the result of real heat exchanger (DLW, Varanasi) the design result is comparable with a
deviation of 5-10%. Run2 contains the result of different input data (different in tube
diameters only in Run1=0.019, in Run2=0.025) and is an example of how the designers
(users) can use the program and examine the variable input parameters to get an optimum
design for a particular task, following are the difference observed between Run1 and Run2:
(1)The heat exchanger first cost has increased due to the increase in the heat transfer area.
(2)Tube side heat transfer coefficient is not much affected with the change due to the fact
that the velocity in tubes in both cases had been fixed at 2.25 m/s.
(3)Shell side heat transfer coefficient is decreased.
(4)Tube side pressure drop is less in Run2.
(5)The overall heat transfer coefficient has decreased in Run2.
This comparison shows that Run1 is the optimum design, which has a better utilization of
allowable pressure drop to heat transfer coefficient, which Leads to a more economic design
(less heat transfer area or the smaller heat exchanger) for a particular heat load.

Table 1 Data of case study

Heat load = 211000 W
Flow configuration = 2 passes
Matrix geometry = triangular pitch
Tube size (m) = 0.019m outside diameter, 0.0166 inside diameter
shell tube

Temperature in ( ௢ ‫) ܥ‬
Fluid oil water
65.6 32.2
Temperature out ( ௢ ‫)ܥ‬ 60 43.52

Density (݇݃/݉ ଷ )
Allowable pressure drop (Pa) 14000 10355

Heat capacity (‫)݇ .݃݇⁄ܬ‬
849 993
2100 4200

Thermal conductivity (‫)݇ .݉⁄ݓ‬
Viscosity (Pa . s) 0.031 0.00075
0.156 0.614
Total flow rate (kg/s) 18.2 60

382


Figure 1 Flow chart of the program

Table 2 Thermal-hydraulic result

Geometry present work present work Locomotive
Run1 Run2 SHTH
no. of tubes 241 138 253
shell diameter (m) 0.439 0.438 0.4439
nozzles diameter (m) 0.088 0.087 N.A.
baffle spacing (m) 0.274 0.29 0.25
baffle cut 25% 25% 34%
baffle number 5 8 6
tube length (m) 1.37 2.4 1.5
heat transfer area (݉ଶ ) 19.7 25.28 N.A.

tube side heat coefficient (ܹ ⁄݉ଶ . ଴ ‫)ܥ‬
tube side pressure drop (Pa) 10167 9674.3 N.A.

shell side heat coefficient(ܹ ⁄݉ଶ . ଴ ‫)ܥ‬
8278 7755.4 N.A.

over all heat coefficient(ܹ ⁄݉ଶ . ଴ ‫)ܥ‬
456.88 413.8 N.A.
429.03 390.13 N.A.
(N.A.= not available)

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CONCLUSION

The design strategy is based mainly on Tinker method which provides a good
prediction for shell side flow. The design model was very close to the ideality. The
optimization strategy is based on two things, (i) assumptions made for tube side velocity,
utilization of all shell side pressure drop, and the fixed baffle cut. And (ii) the need of a
computer aided design, that can be used to examine all the design parameters for a given heat
load to get the economic design. This work and specially the computer program is useful for
both the customers and the designers. A customer can get a first idea about the size and the
component of the required heat exchanger and can select it from hundreds of the heat
exchangers provided in manufacturer’s catalogues. And for the designer to test all the design
parameters to get an economical design, and this can be made easily with the help of the
computer program.

NOMENCLATURE

Q Heat load (ܹ)
The area of heat transfer (݉ଶ )
݊
A

‫ ݓ‬
Total number of tubes

݂
Total flow rate (݇݃/‫)ݏ‬

‫ܮ‬
Flow friction factor

݀௜௡
Tube length (݉)

݀௢
Tube inside diameter (݉)

ܰଵ
Tube outside diameter (݉)

݀௠
Number of tube side passes

ܴ݁
Diameter of circle circumscribed (݉)

ܴ݁௣
Reynolds number

ܴ݁௛
Reynolds number for pressure drop calculations

݀௦
Reynolds number for heat transfer coefficient calculations

݀ே
Shell diameter (݉)
Nozzle diameter (݉)

‫ ܯ‬ Ratio of the effective flow passage area for cross flow through the
tube matrix to the total flow passage area
ܻ A factor which when multiplied by ‫݀⁄ݏ‬௦ gives the ratio of the
baffle window pressure drop to the tube matrix pressure drop for

‫ݏ‬
the shell side flow
Tube spacing (݉)

‫ܨ‬௣ Fraction of the shell side flow passing through the tube matrix for
the determination of the pressure drop
ܰ௣ Factors used in the calculation of ‫ܨ‬௣

‫ܨ‬௛ Fraction of the shell side flow passing through the tube matrix for
the determination of the heat transfer coefficient
ܰ௛ Factors used in the calculation of ‫ܨ‬௛

384


‫ܩ‬௣ Shell side mass flow rate for the determination of pressure drop (݇݃⁄݉ ଶ ‫)ݏ‬
‫ܩ‬௛
coefficient (݇݃⁄݉ଶ ‫)ݏ‬
Shell side mass flow rate for the determination of heat transfer

‫ܥ‬௕
‫ܥ‬௔
Coefficient in step 5

ℎ Heat transfer coefficient (ܹ ⁄݉ ଶ ݇)
Coefficient in step 5

‫ܦܶܯܮ‬
cold fluids ( ௢ ‫) ܥ‬
The logarithmic mean temperature difference between the hot and

‫ܶܨ‬ Correction factor applied to calculate ‫ܦܶܯܮ‬௦௛௘௟௟ ௔௡ௗ ௧௨௕௘
ܿ௣ Specific heat (‫)݇݃݇⁄ܬ‬
∆‫ݐ‬ଶ The temperature difference at shell side ( ௢ ‫) ܥ‬
݈
‫ܥ‬௠
Baffle spacing (݉)
The square root of (average number of tubes per transverse row/number of

‫ ܩ‬ Mass flow rate (݇݃⁄݉ ଶ ‫)ݏ‬
tubes rows)

ܰଶ
ܰ‫ݑ‬
Baffles number

݇ Thermal conductivity (ܹ ⁄݉ ݇ )
Nusslet number

ܲ‫ ݎ‬
ܶ௖
Prandtl number

wall by the tube thickness (ܹ ⁄݉ ଶ ݇)
Tube conductance obtained by dividing the thermal conductivity of the

ܷ Overall heat transfer coefficient (ܹ ⁄݉ଶ ݇ )
ܾ௪
݇௪ Tube-wall conductivity (ܹ ⁄݉ଶ ݇)
Tube-wall t thickness (݉)

‫ݒ‬ Fluid velocity (݉⁄‫)ݏ‬

ߤ
Greek symbols

∆ܲ
Fluid viscosity (ܲܽ ‫)ݏ‬

ߩ Fluid density (݇݃⁄݉ଷ )
Pressure drop (ܲܽ)

REFRENCES
1. Kern D.Q. (1950), “Process heat transfer”, McGraw Hill, New York.
2. Tinker T. (1951) “Shell-side characteristic of shell-and-tube heat exchangers”, Parts
II, III, and I, in: Proceedings of General Discussion on Heat Transfer, Institute of
Mechanical Engineers and American Society of Mechanical Engineers, London, New
York, pp. 89.
3. Frass A.P. (1989), “Heat Exchanger Design”, John Wiley & sons, New York.
4. Bell K. J. Delaware method for shell-side design, in: Serth R.W., Process heat transfer
principles and applications, Elsevier Science & Technology Books, 2007, pp. 145.
5. Kakac S., Hongtan L. (2002), “Heat exchangers selection, rating and thermal design”,
CRC Press.

385


6. El-Fawal, Fahmy and Taher. (2011), “Modelling of Economical Design of Shell and
Tube Type Heat Exchanger Using Specified Pressure Drop”, Journal of American
Science, Vol 7, pp. 32-40.
7. Polley G.T., Shahi M.H. and Nunez M.P. (1991), “Rapid design algorithms for shell
and tube and compact heat exchangers”, Trans Chem, Vol. 69(A), November, pp.
435-444.
8. Kara Y. A., Guraras O. (2004), “A computer program for designing of shell-and-tube
heat exchangers”, Elsevier Applied Thermal Engineering, Vol. 24, PP. 1797–1805.
9. Adelaja, Ojolo and Sobamowo M. G. (2012), “Computer Aided Analysis of Thermal
and Mechanical Design of Shell and Tube Heat Exchangers”, Advanced Materials
Research, Vol. 367, pp. 731-737.
10. LEONG K. C., TOH K. C. (1998), “Shell and Tube Heat Exchanger Design Software
for Educational Applications”, Int. J. Engng Ed. Vol. 14[3], pp. 217-224.
11. Incropera F.P., Dewitt D.P. (1988), “Fundamentals of heat transfer”, John Wiley &
sons, New York.
12. Serth R.W. (2007), “Process heat transfer principles and applications”, Elsevier
Science & Technology Books.
13. Poddar T.K. and Polley G.T. (1996), “Heat Exchanger Design through Parameter
Plotting”, Transactions of the Institution of Chemical Engineers, Vol. 74[A], pp 849–
852.

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IJMET Shell and Tube Heat Exchanger Design

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