OPTIMIZING THE DESIGN AND SELECTION OF HEAT EXCHANGERS THROUGH LMTD CORRECTION FACTOR

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OPTIMIZING THE DESIGN AND SELECTION OF HEAT EXCHANGERS THROUGH LMTD CORRECTION FACTOR Divyanshu Shekhar*1 *1Mechanical

Engineer, Jaypee University of Engineering & Technology, Guna Madhya Pradesh, India.

ABSTRACT Optimizing the design and election of heat exchangers (HX) is a vital task. This piece of work becomes tougher in case of complex heat exchangers. Determination of the logarithmic mean temperature difference (LMTD) and the overall heat transfer coefficient are two vital steps in the thermal design of heat exchangers, which are crucial to compute the required heat transfer area. In a shell & tube HX (counter-current configuration) the LMTD value obtained is known as corrected logarithmic mean temperature difference (CLMTD) which is equals to the product of LMTD and a factor F which is known as LMTD correction factor. Ideally the value of F should be one i.e. for 1-1 counter-current configuration but for shell & HX it becomes 0 < F < 1. An optimal design gives the value of F very closer to 1.

MATLAB computer program for heat exchanger LMTD correction factor has been developed to make it easier. Itâ&#x20AC;&#x2122;s a tool for straight computation of the LMTD correction factors and also used in drawing the graphs. Obtained results are accurate enough for engineering applications, which is robust, user friendly, and flexible.

KEYWORDS: Heat Exchanger, LMTD, MATLAB, Correction Factor, Computer Program, Shell Passes.

I.

INTRODUCTION

A heat exchanger is a system used to transfer heat between two or more fluids of different temperatures.

They are used in both cooling and heating processes. The heat transferring process occurs through a solid separator, which prevents mixing of the fluids, or direct fluid contact. These devices are widely used in preheating, oil refining, industrial cooling process, steam generation, food processing, chemical processing, power plants, refrigeration, engines, aerospace, petroleum refineries, automobiles, etc.

Optimizing the design and election of heat exchangers (HX) is a vital task. This piece of work becomes tougher in case of complex, effective and efficient heat exchangers. Determination of the logarithmic mean temperature difference (LMTD) and the overall heat transfer coefficient are two vital steps in the thermal design of heat exchangers, which are crucial to compute the required heat transfer area.

Conventionally LMTD is calculated from the outlet and inlet temperatures of the cold and hot fluid streams. In a shell & tube HX (counter-current configuration) the LMTD value obtained is known as corrected logarithmic mean temperature difference (CLMTD) which is equals to the product of LMTD and a factor F which is known as LMTD correction factor. Ideally the value of F should be one i.e. for 1-1 counter-current configuration but for shell and tube heat exchangers it becomes 0 < F < 1. An optimal design gives the value of F very closer to one; F adopted for the design is selected using ad hoc criteria, F â&#x2030;Ľ 0.8. For higher value of shell passes (N) the value of F will be higher but the system becomes more expensive which is undesirable. So due to cost limitations the optimal design is selected in such a way that number of shell passes is chosen as minimum as possible.

MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. It is widely used in computation, modeling, simulation, data analysis, visualization, engineering graphics, etc.

II.

METHODOLOGY

1. Problem Formulation And Solution:The problem is to evaluating the LMTD correction factors for the widely used complex heat exchangers and also evaluating the minimum number of shell passes.

A. The LMTD correction factor (F) calculation:-

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Heat Capacity ratio,

(2) Thermal Effectiveness,

(3)

(4)

(5) CLMTD=F*LMTD, where 0 < F < 1 Where, T1 = inlet temperature of hot fluid, oC T2 = outlet temperature of hot fluid, oC t1 = inlet temperature of cold fluid, oC t2 = outlet temperature of cold fluid, oC N = number of shell passes

(6)

Q = mhCph (T1 â&#x20AC;&#x201C; T2) = mc Cpc (t2 â&#x20AC;&#x201C; t1), kW

(7)

Where, mh = mass flow rate of hot fluid, Kg/sec Cph = heat capacity of the hot fluid, kW/Kg- oC mc= mass flow rate of cold fluid, Kg/sec Cpc = heat capacity of the cold fluid, kW/Kg- oC, So, the heat transfer area (A) is then determined from the fundamental equation of heat transfer as, A=Q/ (U.CLMTD) (8) Where Q[kW] is the heat transfer rate and U[kW/(m2. oC)] is the overall heat transfer coefficient or the U-value.

B. Quick calculation of LMTD correction factor:The heat exchanger LMTD correction factor (F) can be calculated and graph is drawn quickly using the following MATLAB computer program which is given below;

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Table-1: Computer program for calculation of LMTD correction factor clear all; clc; %T1=Inlet Temperature of Hot Fluid %T2=Outlet Temperature of Hot Fluid %t1=Inlet Temperature of Cold Fluid %t2=Outlet Temperature of Cold Fluid %N=Number of Shell Passes p1='Enter N : '; p2='Enter T1 : '; p3='Enter T2 : '; p4='Enter t1 : '; p5='Enter t2 : '; N=input(p1); j=1 while j==1 T1=input(p2); T2=input(p3); t1=input(p4); t2=input(p5); R=(T1-T2)./(t2-t1); S=(t2-t1)./(T1-t1); S=0.1:0.1:1; p=((1-(((R*S)-1)./(S-1)).^(1/N)))./((R-(((R*S)-1)./(S-1)).^(1/N))); a=(sqrt(R*R +1 ))./(R-1); b=log((1-p)./(1-R*p)); d=(2./p)-1-R+(sqrt(R*R +1 )); e=(2./p)-1-R-(sqrt(R*R +1 )); c=log(d./e); F=a.*b./c; plot(S,F) grid on grid minor xlabel('S'); ylabel('LMTD Correction Factor,F'); hold on; p3='Continue 1 or 0 : '; j=input(p3); end

With the help of above computer program correction factor can be calculated and graph is drawn on MATLAB software for various R-value, for example two output graphs are shown below.

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From figures (a) and (b) we can see that LMTD correction factor (F) increases on increasing the number of shell pass.

C. The minimum number of shell passes calculation: 1. The Traditional Approach (explicit F approach) Traditionally, the designer would approach a problem requiring multiple shells by trial and error. By assuming a number of shells, usually one in the first instance, the F is evaluated. The number of shells in series is progressively increased until we get a satisfactory value of F is obtained for each shell, if the value of F is not acceptable. www.irjmets.com

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2. Method of Ahmad et al.

Ahmad et al. have given an analytical expression for calculating number of shells directly,

(9) Where, N is real (non-integer) number of shells, and

(10) Equation [9] gives a value of N that satisfies the chosen value of X. The problem now is what should be the design value of X? And how it will affect the temperature cross and consequently, F? Though emphasized the importance of temperature cross in exchanger design, they didn’t explain How X accounts for temperature cross. Their choice of value of X= 0.9 is based on F = 0.75 at R = 1, which is again arbitrary. What if a designer wants to use a lower value of X? 2. Method based on not allowing Temperature Cross This method is based on a dimensionless parameter G which explicitly accounts for temperature cross in the exchanger. It is defined as,

(11) F decreases moderately with decreasing positive G values, but falls suddenly both where the temperature meet (G = 0) and where the G values are negative (temperature cross). The parameter G is related to parameter R and S, by the equation, (12) For any value of R there exists a minimum asymptotic value of G (corresponding to F = -∞), say Gmin , which represents The maximum temperature crosses theoretically feasible in 1–2 exchanger.

The expression for Gmin is,

(13) It is shown that for G = 0, F is always above 0.8 (0.8 < F < 0.83), an acceptable value. Thus, following the criteria that temperature cross is not allowed in each shell ensures that F > 0.8. Using this fact, a simple equation is derived below to calculate the number of shells.

(14) Equation (14) can be used to estimate the number of shells for given R and G (calculated from the terminal temperatures).

3. Method based on allowing Temperature Cross Some authors recommend that in order to get the minimum number of shells it is necessary to allow some temperature crosses. For such cases a comprehensive criterion has been developed. A 1–2 exchanger designed for G < Gmin will not be feasible. Any hike in G from Gmin will make the exchanger feasible, and improve exchanger effectiveness and F. Let the desired increment be Y. Then

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(15) Where Y is a constant set by the designer. Now, the expression for estimating the number of shells can be written as

(16) Where GN is G for multi pass exchanger, and

(17)

Y can be correlated with XP as,

(18) Alternatively,

(19) Y is chosen by the designerâ&#x20AC;&#x2122;s decision on how much temperature cross he is going to allow in the design.

Author, also recommends that to be compatible with the existing design practices (F > 0.75; or XP = 0.9), a value of Y in the range 0.1 to 0.15 may be selected.

4. Methods based on F slopes An additional method of avoiding areas of steep slopes in the F chart is to consider a constant F slope.

Ahmad et al. have presented a constant slope criterion in a graphical form. However, their criterion, which is good to guarantee to stay away from those regions, is very complex to use and evaluate, as the authors recognized in their paper.

III.

RESULTS AND DISCUSSION

The MATLAB is popular computer software for curve fitting data points when there is no direct tool of curve fitting. The MATLAB was used to curve fit the charted correction factors. The interrelationship for the correction factor, F, as a function of the dimensionless temperature, S, at a specified ratio of the water equivalents of the two streams, R, in the interval are described in Table 1, corresponding to the heat exchanger arrangement type 1 shell pass, 2 or even number of tube passes (1-2n), 2 shell passes, 4 or multiple of 4 tube passes (2- 4n), 3 shell passes 6 or multiple of 6 tube passes (3-6n), 4 shell passes 8 or multiple of 8 tube passes (4-8n).

Table-2: LMTD correction factor, F variation at different number of shell passes, N, thermal effectiveness, S and heat capacity ratio, R; 1.

For N=1:R=0.1

R=0.2

R=0.3

R=0.4

R=0.5

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4

1.0 0.9999 0.9999 0.9968 0.9957

0.0 0.1 0.2 0.3 0.4

1.0 0.9999 0.998 0.995 0.990

0.0 0.1 0.2 0.3 0.4

1.0 0.999 0.997 0.993 0.988

0.0 0.1 0.2 0.3 0.4

1.0 0.998 0.9954 0.984 0.973

0.0 0.1 0.2 0.3 0.4

1.0 0.998 0.995 0.981 0.970

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e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science Volume:02/Issue:09/September-2020 0.5 0.6 0.7 0.8 0.9 0.95

0.9912 0.9843 0.9712 0.9433 0.8506 0.0

0.5 0.6 0.7 0.8 0.9

R=0.6

0.9814 0.9655 0.9352 0.865 0.0

Impact Factor- 5.354 0.5 0.6 0.7 0.8 0.85

R=0.7

0.976 0.951 0.894 0.751 0.0

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0.5 0.6 0.7 0.8

R=0.8

0.961 0.924 0.841 0.0

0.5 0.6 0.7 0.75

R=0.9

0.946 0.881 0.741 0.0

R=1.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.71

1.0 0.998 0.995 0.974 0.964 0.936 0.845 0.582 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.67

1.0 0.998 0.994 0.971 0.960 0.907 0.792 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.63

1.0 0.997 0.993 0.966 0.946 0.883 0.716 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

1.0 0.997 0.991 0.963 0.939 0.846 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.57

1.0 0.997 0.989 0.961 0.934 0.807 0.0

R=1.2

R=1.4

R=1.6

R=1.8

R=2.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.52

1.0 0.997 0.986 0.952 0.891 0.661 0.0

0.0 0.1 0.2 0.3 0.4 0.48

1.0 0.997 0.984 0.950 0.878 0.0

0.0 0.1 0.2 0.3 0.4 0.43

1.0 0.997 0.982 0.936 0.858 0.0

0.0 0.1 0.2 0.3 0.4

1.0 0.997 0.978 0.916 0.0

0.0 0.1 0.2 0.3 0.38

1.0 0.996 0.976 0.891 0.0

R=2.5

R=3.0

R=4.0

R=6.0

R=8.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.32

1.0 0.995 0.963 0.734 0.0

0.0 0.1 0.2 0.28

1.0 0.994 0.938 0.0

0.0 0.1 0.2 0.21

1.0 0.991 0.828 0.0

0.0 0.1 0.15

1.0 0.983 0.0

0.0 0.1 0.12

1.0 0.948 0.0

R=10.0

R=15.0

R=20.0

S

F

S

F

S

F

0.0 0.1

1.0 0.0

0.0 0.07

1.0 0.0

0.0 0.05

1.0 0.0

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For N=2:R=0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

R=0.2 1.0 0.999 0.9983 0.9974 0.9953 0.994 0.989 0.987 0.983 0.971 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.98

R=0.6

R=0.3 1.0 0.999 0.998 0.997 0.995 0.992 0.986 0.981 0.970 0.948 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.96

R=0.7

R=0.4 1.0 0.999 0.998 0.996 0.993 0.990 0.983 0.972 0.951 0.889 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.94

R=0.8

R=0.5 1.0 0.999 0.998 0.995 0.992 0.988 0.981 0.965 0.928 0.791 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

R=0.9

1.0 0.999 0.998 0.994 0.991 0.986 0.975 0.951 0.891 0.0

R=1.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.87

1.0 0.999 0.998 0.993 0.990 0.984 0.971 0.938 0.838 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.83

1.0 0.999 0.997 0.992 0.989 0.983 0.952 0.904 0.748 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.0 0.999 0.997 0.991 0.987 0.980 0.945 0.871 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.77

1.0 0.999 0.997 0.991 0.986 0.964 0.940 0.821 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.73

1.0 0.999 0.997 0.990 0.985 0.958 0.903 0.704 0.0

R=1.2

R=1.4

R=1.6

R=1.8

R=2.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.65

1.0 0.999 0.997 0.988 0.978 0.938 0.808 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

1.0 0.998 0.996 0.986 0.976 0.891 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.55

1.0 0.998 0.996 0.983 0.949 0.808 0.0

0.0 0.1 0.2 0.3 0.4 0.5

1.0 0.997 0.995 0.979 0.923 0.0

0.0 0.1 0.2 0.3 0.4 0.45

1.0 0.997 0.994 0.973 0.888 0.0

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R=3.0

R=4.0

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R=8.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.38

1.0 0.996 0.993 0.947 0.0

0.0 0.1 0.2 0.3 0.32

1.0 0.996 0.988 0.851 0.0

0.0 0.1 0.2 0.25

1.0 0.994 0.956 0.0

0.0 0.1 0.16

1.0 0.990 0.0

0.0 0.1 0.12

1.0 0.983 0.0

R=10.0

R=15.0

R=20.0

S

F

S

F

S

F

0.0 0.1

1.0 0.0

0.0 0.07

1.0 0.0

0.0 0.05

1.0 0.0

3.

For N=3:R=0.2

R=0.4

R=0.6

R=0.8

R=1.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.0 0.9996 0.9994 0.998 0.997 0.995 0.993 0.991 0.989 0.976 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.98

1.0 0.9995 0.9993 0.9988 0.996 0.994 0.992 0.988 0.972 0.926 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95

1.0 0.9995 0.9992 0.9984 0.996 0.993 0.984 0.973 0.941 0.803 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.0 0.9995 0.9992 0.9982 0.995 0.992 0.977 0.946 0.852 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.0 0.9995 0.9992 0.9981 0.993 0.981 0.958 0.894 0.0

R=1.2

R=1.4

R=1.6

R=1.8

R=2.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.73

1.0 0.9995 0.9992 0.998 0.992 0.968 0.924 0.726 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.65

1.0 0.9994 0.9992 0.9978 0.988 0.948 0.838 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.59

1.0 0.9994 0.9991 0.9976 0.974 0.926 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.53

1.0 0.9994 0.9991 0.9972 0.962 0.819 0.0

0.0 0.1 0.2 0.3 0.4 0.49

1.0 0.9994 0.9991 0.9968 0.9506 0.0

R=2.5

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R=3.0

R=4.0

R=6.0

R=8.0

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S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4

1.0 0.9992 0.9880 0.9754 0.0

0.0 0.1 0.2 0.3 0.32

1.0 0.9991 0.9872 0.932 0.0

0.0 0.1 0.2 0.25

1.0 0.9991 0.9782 0.0

0.0 0.1 0.16

1.0 0.999 0.0

0.0 0.1 0.12

1.0 0.988 0.0

R=10.0

R=15.0

R=20.0

S

F

S

F

S

F

0.0 0.1

1.0 0.0

0.0 0.07

1.0 0.0

0.0 0.05

1.0 0.0

4.

For N=4:R=0.2

R=0.4

R=0.6

R=0.8

R=1.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.0 0.99995 0.9999 0.9998 0.9997 0.9995 0.9993 0.9991 0.9961 0.9874 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99

1.0 0.9999 0.9998 0.9996 0.9993 0.9984 0.9966 0.9943 0.9877 0.958 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.97

1.0 0.9999 0.9997 0.9995 0.999 0.9971 0.9951 0.9879 0.964 0.903 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.92

1.0 0.9999 0.9996 0.9992 0.9971 0.9951 0.984 0.965 0.926 0.706 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.84

1.0 0.9999 0.9995 0.999 0.9963 0.9913 0.973 0.941 0.801 0.0

R=1.2

R=1.4

R=1.6

R=1.8

R=2.0

S

F

S

F

S

F

S

F

S

F

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.76

1.0 0.9999 0.9992 0.997 0.9956 0.981 0.951 0.852 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.67

1.0 0.9999 0.999 0.995 0.9943 0.973 0.908 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

1.0 0.9999 0.998 0.994 0.981 0.956 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.55

1.0 0.9999 0.997 0.993 0.979 0.908 0.0

0.0 0.1 0.2 0.3 0.4 0.5

1.0 0.9999 0.996 0.992 0.973 0.0

R=2.5 S

R=3.0 F

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S

R=4.0 F

S

R=6.0 F

S

R=8.0 F

S

F

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e-ISSN: 2582-5208 International Research Journal of Modernization in Engineering Technology and Science Volume:02/Issue:09/September-2020 0.0 0.1 0.2 0.3 0.4

1.0 0.9998 0.996 0.987 0.0

0.0 0.1 0.2 0.3 0.33

1.0 0.9997 0.995 0.963 0.0

R=10.0

Impact Factor- 5.354 0.0 0.1 0.2 0.25

1.0 0.9996 0.988 0.0

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0.0 0.1 0.17

1.0 0.9993 0.0

R=15.0

0.0 0.1 0.12

1.0 0.999 0.0

R=20.0

S

F

S

F

S

F

0.0 0.1

1.0 0.0

0.0 0.07

1.0 0.0

0.0 0.05

1.0 0.0

To obtain the LMTD correction factor (F) one substitutes S into the correlations in Table.1 that correspond to the heat exchanger flow arrangement under consideration and interpolates for F with R serving as the interpolation point.

3.1. EXAMPLE It is required to cool down 20 kg/s of an aqueous solution whose specific heat is 4,180J/(kg · K) from an inlet temperature of 67°C to 37°C. The operation will be performed with cooling water available at 17°C. Determine the number of shell passes of the heat exchanger using a water mass flow of (a) 40 kg/s and (b) 20 kg/s.

Solution a. With a water flow rate of 40 kg/s, the water outlet temperature can be calculated with the following heat balance: Q = mhCph (T1 – T2) = mc Cpc (t2 – t1) Or,

From which we get t2 = 32°C. Calculating the parameters we have

For a 1-2 heat exchanger with these parameters, we get F = 0.85. Thus it is possible to use this configuration for the required service. b. If a water mass flow of 20 kg/s is employed, the water outlet temperature calculated with a mass balance is 47°C and then

For a 1-2 configuration, a too low F factor is obtained with these parameters. This means that a 1-2 heat exchanger is not possible for these process conditions. With R = 1 and S = 0.6, if we move to a 2-4 configuration, we get F = 0.9, and it is thus the minimum configuration with this water flow rate. If the www.irjmets.com

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water mass, flow is reduced further, it may not be possible to use a 2-4 configuration, and a 3-6 unit may be necessary. In all cases, a countercurrent configuration is always possible because then F = 1. The reason for using multi-pass configurations is to increase the in-tube fluid velocity, improving the heat transfer coefficient, because in order to have good fluid velocity with only one tube pass, an excessively long heat exchanger may be necessary in some cases.

Additionally, in services requiring floating heads, the countercurrent configuration presents construction issues and is normally avoided. Obviously, U-tubes cannot be used in a one-pass configuration.

IV.

CONCLUSION

A MATLAB computer program for heat exchanger LMTD correction factor has been developed. It is a tool for direct computation of the LMTD correction factors and also used in drawing the graphs. Results obtained are precise enough for engineering application, which is robust, user friendly, and flexible. Apart from the stand-alone application of this MATLAB computer software, it can also be integrated into larger plant design software for improved productivity. The MATLAB if integrated into a larger plant can also be used by practicing engineers for heat exchanger design, and selection. We have also discussed the various methods for minimum number of shell passes calculation, and selection which are very effective.

ACKNOWLEDGEMENTS It is a matter of great pleasure and privilege for me to present this research paper on the basis of Practical & theoretical knowledge gained at Jaypee University of Engineering & Technology. Heartiest thanks to my guides, professors, Departments of Mechanical and Chemical Engineering, my mother Dr. Renu Jha, my family, friends, and my well wishers. We attribute hearties thanks to all Engineering departments for their Ample Guidance during my research period.

V.

REFERENCES

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[10] Wolverine Tube Heat Transfer Data Book.

[11] Effectively Design Shell-and-Tube Heat Exchangers - Rajiv Mukherjee, Engineers India Ltd.

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