DESIGN OF SHELL AND TUBE HEAT EXCHANGER
USING SPECIFIED PRESSURE DROP
Vimalkumar B. Bilimoria
B.E., Pune University, India, 2005
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
MECHANICAL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2010
DESIGN OF SHELL AND TUBE HEAT EXCHANGER
USING SPECIFIED PRESSURE DROP
A Project
by
Vimalkumar B. Bilimoria
Approved by:
__________________________________, Committee Chair
Akihiko Kumagai, Ph.D.
____________________________
Date
ii
Student: Vimalkumar B. Bilimoria
I certify that this student has met the requirements for format contained in the University format
manual, and that this project is suitable for shelving in the Library and credit is to be awarded for
the Project.
__________________________, Graduate Coordinator
Kenneth S. Sprott, Ph.D.
Department of Mechanical Engineering
iii
________________
Date
Abstract
of
DESIGN OF SHELL AND TUBE HEAT EXCHANGER
USING SPECIFIED PRESSURE DROP
by
Vimalkumar B. Bilimoria
The pressure drops used in heat exchange of shell and tube type, the situations are particular and
put ahead of the design exercise. In such situations, it is very desirable to make full use of the
acceptable pressure drops in order to minimize the size of the heat exchanger. Heat exchanger
design is Complex due to large number of design variables like shell diameter, tube pitch, baffle
cut, tube diameter, baffle spacing, tube layout etc. in shell and tube type of heat exchanger. This
design method is a taking time and intervening procedure. This is mandatory to design thermal
and hydro mechanical procedure for this project performance. While fulfilling heat transfer
requirements, it has anticipated to estimate the minimum heat transfer area and resultant
minimum cost for a heat exchanger for given pressure drops. Effectiveness-NTU approach is the
way developed for the design of shell-and-tube heat exchanger. The total number of transmit
units, NTU, is scattered between shell and tube side. The methodology accounts for full use of
given pressure drops on both sides of exchanger to yield the smallest exchanger for a given duty.
_______________________, Committee Chair
Akihiko Kumagai, Ph.D.
_______________________
Date
iv
ACKNOWLEDGMENTS
It is my distinct honor and proud privilege to acknowledge with gratitude to keen interest taken
by Professor Akihiko Kumagai, his ever-inspiring suggestions; constant supervision and
encouragement that made it possible to pursue and complete this project efficiently. Here I also
thank to the department of Mechanical Engineering and graduate coordinator Professor Kenneth
sprott who always guide me on proper way.
Finally I thank all the people who extended their support directly or indirectly to make this
project a complete success. In addition, it is a great pleasure to acknowledge the help of many
individuals without whom this project would not have been possible.
v
TABLE OF CONTENTS
Page
Acknowledgments..................................................................................................................... v
List of Tables ......................................................................................................................... viii
List of Figures .......................................................................................................................... ix
Chapter
1. INTRODUCTION ..................... ………………………………………………………… 1
2. LITERATURE REVIEW ................................................................................................... 3
3. SHELL AND TUBE HEAT EXCHANGER .................................................................... 23
3.1 Construction Details of Shell and Tune Heat Exchanger .......................................... 23
3.2 Design Method of Shell and Tube Heat Exchanger .................................................. 27
3.3 Log Mean Temperature Difference Method ............................................................. 28
3.4 Effectiveness – NTU Method.................................................................................... 30
3.5 Calculation of Heat Transfer Coefficient and Pressure Drops .................................. 31
3.6 Heat Transfer Efficient.............................................................................................. 33
3.7 Pressure Drop ............................................................................................................ 36
4.
DESIGN OF SHELL AND TUBE HEAT EXCHANGER USING SPECIFIED
PRESSURE DROP........................................................................................................... 40
4.1 Input Date................................................................................................................ 40
4.2 Formulation of Design Procedure ........................................................................... 41
4.3 Shell Side Procedure ............................................................................................... 43
4.4 Tube Side Procedure ............................................................................................... 46
4.5 Optimization of Shell and Tube Heat Exchanger.................................................... 48
4.6 Mechanical Design of Shell and Tube Heat Exchanger ......................................... 51
vi
4.7 Tube Sheet .............................................................................................................. 52
4.8 Channel Cover......................................................................................................... 53
4.9 End Flanges and Bolting ......................................................................................... 53
4.10 Baffle Design .......................................................................................................... 53
4.11 Costing of Shell and Tube Heat Exchanger ............................................................ 56
4.12 Shell Cost ................................................................................................................ 56
4.13 Tube Costs............................................................................................................... 56
4.14 Installed Nozzle Cost .............................................................................................. 58
4.15 Front and Rear Head Cost ........................................................................................ 58
4.16 Miscellaneous Cost ................................................................................................. 60
5.
DEVELOPMENT OF ALGORITHEM AND OPTIMIZATION FOR DESIGN OF
SHELL AND TUBE HEAT EXCHANGER ................................................................... 61
6.
RESULT, DISCUSSION, CONCLUSION AND FUTURE SCOPE OF WORK.......... 63
6.1 Area Targeting .......................................................................................................... 67
6.2 Optimization Results of Components of Shell and Tube Heat Exchanger ............... 68
6.3 Cost Analysis ............................................................................................................ 69
6.4 Conclusion ................................................................................................................. 70
6.5 Future Scope of Work ............................................................................................... 71
References ............................................................................................................................... 72
vii
LIST OF TABLES
Page
1.
Table 3.1 Features of TEMA Type Heat Exchangers ................................................ 25
2.
Table 3.2 Linear Equations for FT ............................................................................. 30
3.
Table 4.1 Baffle Diameter........................................................................................... 54
4.
Table 4.2 Baffle Thickness ........................................................................................ 55
5.
Table 4.3 Diameter of Holes in Baffle Plate ............................................................... 55
6.
Table 4.4 Preparation Cost......................................................................................... 57
7.
Table 4.5 Material Cost ............................................................................................. 58
8.
Table 4.6 Shell Cost Factors for Selected Shell Constructions.................................. 59
9.
Table 6.1 Shell and Tube Heat Exchanger Design Problem-Physical Properties ....... 64
10.
Table 6.2 Shell and Tube Heat Exchanger Design Problem-Geometry...................... 64
11.
Table 6.3 Comparison of Shell and Tube Heat Exchanger Design-Geometry .......... 67
12.
Table 6.4 Comparison of Shell and Tube Heat Exchanger Design-Performances .... 67
13.
Table 6.5 Optimized Result of Mechanical Assembly .............................................. 68
14.
Table 6.6 Cost Analysis ............................................................................................. 69
viii
LIST OF FIGURES
Page
1.
Figure 2.1 Pressure Drop Constraints ........................................................................ 14
2.
Figure 2.2 Area Requirement ..................................................................................... 15
3.
Figure 2.3 Region of Feasible Design on the Pressure Drop Diagram ...................... 22
4.
Figure 3.1 Fixed Tube Sheet Shell and Tube Heat Exchanger .................................. 24
5.
Figure 3.2 Mechanical Clearances in Shell and Tube Heat Exchanger ..................... 32
6.
Figure 3.3 Flow Path on Shell Side; A Cross Flow; B Window;
C Shell Baffle Leakage; D Tube Baffle Leakage; E Bundle Bypass .......................... 32
7.
Figure 3.4 Jh/f Versus Re for Shell Side Flow ............................................................. 45
8.
Figure 3.5 Jh/f Versus Re for Tube Side Flow…. ........................................................ 48
ix
1
Chapter 1
INTRODUCTION
Heat exchangers are devices in which heat is transfer from one fluid to another. The most
commonly used type of heat exchanger is a shell-and-tube heat exchanger. Shell-and-tube heat
exchangers are used extensively in engineering applications like power generations, refrigeration
and air-conditioning, petrochemical industries etc. These heat exchangers can be designed for
almost any capacity. The main purpose in the heat exchanger design is given task for heat transfer
measurement to govern the overall cost of the heat exchanger.
The heat exchanger was introduced in the early 1900s to execute the needs in power
plants for large heat exchanger surfaces as condensers and feed water heaters capable of operating
under relatively high pressures. Both of these original applications of shell-and-tube heat
exchangers continued to be used; but the design have become highly sophisticated and
specialized, subject to various specific codes and practices. The broad industrial use of shell-andtube heat exchangers known today also started in the 1900s to accommodate the demands of
emerging oil industry.
The steadily increasing use of shell-and-tube heat exchangers and greater demands on
accuracy of performance prediction for a growing variety of process conditions resulted in the
explosion of research activities. These included not only shell side flow but also, equally
important, calculations of true mean temperature difference and strength calculations of
construction elements, in particular tube sheets.
The objective of the thesis is to formulate the design algorithm and optimization
procedure for a shell-and-tube exchanger in which exchanger geometry is determined from
2
required performance for fixed pressure drops. First step in the effective consideration of
allowable pressure drops is to establish a quantitative relationship between velocity, friction
factors, pressure drop of the stream and number of transfer units. The solution of this equation
provides the core of such an algorithm.
The first chapter deals with the brief introduction of shell-and-tube heat exchangers. The
second chapter gives the development in the design methodology considering pressure drops as
constraint over the years for shell-and-tube heat exchangers. The third chapter gives the brief
outlines of various methods of design of shell-and-tube heat exchangers and constructional details
of various class of shell-and-tube heat exchanger. In the fourth chapter, the design procedure is
developing for a given heat exchanger specifications and pressure drops. In this design, both the
thermal and mechanical design is doing for a tube and shell exchanger. Various cost equations are
developing for tubes (including preparation and material), shell, nozzles, front and rear end heads,
baffles, and saddle of exchanger. The algorithm for exchanger with specified pressure drops is
present in the fifth chapter. In the sixth chapter, the heat exchanger design derived using the new
algorithm is comparing with the original one. The results and conclusion of the present work are
discussing in the sixth chapter.
3
Chapter 2
LITERATURE REVIEW
Detailed design of shell-and-tube heat exchanger generally proceeds through the testing
of a range of potential exchanger geometries in order to find those that satisfy three major design
objectives:
1. Transfer of required heat duty
2. Specified cold side pressure drop
3. Specified hot side pressure drop

The allowable pressure drops determine the operating cost of heat exchanger in
the process; they also determine the capital requirement of the installed heat exchanger
surface area.

Different authors have long recognized the importance of considering pressure
drops during heat exchanger analysis. McAdams [1] was one of the earliest workers to
quantitatively demonstrate this. His analysis was simple and based on tubular heat exchanger.
By taking into account the cost of power and fixed cost of the exchanger, per unit heat
transferred, simple expressions for estimating the optimum mass velocities for both inside
tubes and outside tube fluids are developed. However, his equations are deriving on the basis
that each side of the exchanger can be treating independently of the other. It is assume that
the streams do not interact and the effect of opposing resistance is neglecting. This is an
erroneous assumption.
4

Jenssen [2] in an attempt to provide a quickly and general method for estimating
the economic power consumption in plate exchangers introduced the so-called ‘J’ parameter
(i.e. the specific pressure drop per heat transfer unit parameter). He produced graphs showing
economic optimum based on the assumption that the streams on the either side the exchanger
have the same flow rates and the same physical properties. The use of such graphs in design
only requires the knowledge of the ratio of the capital cost influence to the power cost
influence. The capital cost influence is given as the annual investment increment for added
unit heating surface area. The power cost influence is the annual unit power cost. One major
weakness in this work that has perhaps limited its practical application is the assumption that
the streams have identical fluid properties and identical geometries. These are highly limiting
assumptions. While the method may apply under restricted conditions to plate exchangers, its
extension to shell-and-tube heat exchangers appears too far from straightforward.

Since the cost of heat exchanger, is usually a major item in the overall process,
the design of heat exchangers based on minimum total cost. The total annual heat exchanger
cost to be minimized may be represented by the following general equation:
TC  AK F C Ao 

QtCu
3.5
4.75
 A T hT tKT  A S tK S hS
C pu T1  T2  T1  T2 
FT T2  T1 
Q ln T2  T1 

  Dt

1


 RF 
A  Dti hT hS

Where
Q = Heat transfer rate
C Ao = Installed cost of heat exchanger per unit of outside heat transfer area
(2.1)
5
K T  Cost for supplying fluid through the inside of the tubes
K S  Cost for supplying fluid through the shell side of the exchanger
C pu  Cost of utility
FT  Correction factor on logarithmic-mean temperature difference
h  Film heat transfer coefficients
t  Hours of operation per year
RF  Combined resistance of tube wall and scaling or dirt factors
T  Temperatures on shell or tube side
  Lagrangian multiplier
  Dimensional factors for evaluation of power loss per unit heat transfer coefficients
TC = Total cost
Sidney and Jones [3] have developed separate programs for the price optimum design of
shell-and-tube heat exchangers for four cases: (a) no phase change occurs, pumping costs of tube
side and shell side is given. Estimation of inside heat transfer coefficient is accomplished by
differentiating equation (2.1) w.r.t. hT and A. Addition of the two differential equations
eliminated A and  , yielding an equation in which hT is the only unknown. Estimation of inside
heat transfer coefficient is accomplished by differentiating equation (2.1) w.r.t. h S and A.
Elimination of A and the multiplier yield an equation from which h S can be computed directly.,
(b) no change in phase and negligible costs on tube side: Under these conditions, the outside heat
transfer coefficient and the tube fluid velocity are fixed. Based on the assumptions that hT is
constant and CT is equal to zero. The optimum value of h S is determined by differentiation of
6
equation (2.1)., (c) no change in phase and negligible pumping costs on shell side: Under these
conditions, the outside heat transfer coefficient and shell side velocity are fixed. Estimation film
heat transfer coefficient on shell side is accomplished in a similar manner to that used in case (b)
but using a Nusselt type equation and the pressure drop equation for shell side, and (d) change in
phase on shell side: Under this condition, tube side power cost are significant but the
pressure drop and power costs for the fluid on the shell side are assumed to be zero and shell side
heat transfer coefficient is assumed to be constant. Optimum tube diameter is not obtained since
the tube diameter has little effect on the total cost
Steinmeyer [4, 5] has attempted to apply Jenssen’s [2] approach to shell-and-tube heat
exchangers. He produced separate relationships for shell side and tube side geometries. However,
in producing the relationships he, like McAdams [1], assumed that he could ignore the conditions
on the opposite side of the exchanger. Again, this assumption is incorrect and application on his
procedure can lead to serious errors. The result of McAdams [1], Jenssen [2] and Steinmeyer [4,
5] can be considered very useful. Their analysis on single heat exchanger at the optimum, the
annual power cost ranges from 20% to 50% of the heat exchanger cost. The lower value is valid
for non-viscous liquids and the higher value is valid for high viscosity liquids, with low viscosity
liquids and gases being in contact. This ratio can be used to warn (both the heat exchanger
designer and the process network designer), whether or not they are using reasonable coefficients.
Peter and Timmerhaus [6] recognized the importance of optimizing tube side pressure
drop; shell side pressure drop and heat transfer area simultaneously. Consequently, they produced
the most detailed and useful work to date on a single shell-and-tube heat exchanger optimization.
The problem with their method however, is that it is restricted to shell-and-tube heat exchangers
fitted with plain tube. Extension to other exchanger types requires new equations. No guidance is
7
given on how to generate these equations. Their results like all other previous authors are only
applicable to only pumped systems. Their method cannot be applied for shell-and-tube heat
exchangers with the specified pressure drops.
Kovarik [7] has formulated the design procedure as the solution of five simultaneous
equations for a cross flow heat exchanger. The analysis of these equations yields general
properties of optimal cross flow heat exchanger. He has developed the optimization function,
which he defines J as the ratio of performance to cost, which is given as below
J
1
Cs  C p  Q
(2.2)
Cs is the cost component related to the heat exchanger size, and Cp is the cost component related
to the pumping power. The position of the maximum J coincides with the minimum of the first
term in the denominator of the right hand side of the equation (2.2), and is independent of the
value of the energy cost factor. Therefore an optimal heat exchanger is optimal for any cost of
energy. A necessary condition for J to reach its maximum is the simultaneous vanishing of its
partial derivative with respect to all free variables. For any variable X i , this means
 Q


TC   TC  Q 
X i
 X i

TC 2  0
(2.3)
where TC is the total coat
TC  C s  C p
(2.4)
As Q and TC are inevitably positive, equation (2.3) implies
Qi 
X i TC 
TC X i
(2.5)
8
Where Qi is the logarithmic derivative of Q with respect to X i :
Qi 
X i Q
QX i
(2.7)
Qi is defined as the sensitivity of output to variable X i . The free variables can be flow lengths
and capacity rates. The model to be analyzed is a section that is rectangular and prismatic in
shape, consisting of passages bordered by heat transfer surfaces of known properties. In a cross
flow heat exchanger, the flow lengths are independent and the optimization scheme can be
applied with greater generality than with parallel flow and counter flow cases like shell-and-tube
heat exchanger.
Polley, Shahi and Nunez [8] have developed the rapid design algorithm for both shelland-tube exchanger and compact heat exchanger. They are based on full use of the allowable
pressure drops of both the streams being contacted. In case of shell-and-tube heat exchanger
algorithm, it is assuming that the best shell side performance can be gained by making baffle
window flow velocities and bundle cross flow velocities equal. This in turn leads to a ‘similarity
concept’ that can be used for the derivation of simple performance equation from of shell side
model. They have not shown theoretically that how much shell side performance is sensitive to
the window/cross flow area ratio. They have developed and shown how simple relationship
between fluid exchanger pressure drop, exchanger area and film heat transfer coefficient can be
used to rapidly design. For the tube side and shell side performance, the following relationships
exist:
PT  K T Ahio3.5
(2.8)
9
PS  K 1 A  K 2 hS2
(2.9)
The constants appearing in the above equations are complex functions involving shell geometry,
ideal friction factors and ideal heat transfer factors and are based on Delaware method. These two
equations are solving together with the basic design equation:
Q  UAFT TLM
(2.10)
1
1
1


 RF
U hS hT
(2.11)
The three simultaneous equations (2.8, 2.9 and 2.10) are then solved to yield exchanger area and
heat transfer coefficient for given pressure drop on both sides of shell-and-tube heat exchanger.
This in turn allows the calculation of velocities and shell diameter and baffle cut. The shell side
friction factor, heat transfer j factor, baffle cut and shell diameter are all set at standard initial
value. This allows the initial estimate of tube count and baffles spacing, and subsequently leakage
and bypass areas and correction factors to be made. From detailed geometry actual friction factors
and j factor are estimated and initial assumption are tested and updated if necessary. However, the
method is restricted. The first restriction is that the pressure drops referred to in the above
equations is that associated with the flow through the exchanger bundle. No account is taken of
any nozzle or header pressure drops. Allowance for these must be made ahead of design and
checked after design. This restriction is not considered here a serious impediment. The second
restriction is the use of the Kern’s correlations, which are generally considered too inaccurate for
use in modern exchanger design. In the derivation of relationship on shell side performance
(equation (2.9)), the assumptions made have not tested in theory.
When designing shell-and-tube heat exchangers, achieving the full use of the allowable
pressure drops from experience can be both difficult and dangerous. There is always the
10
possibility that it is not utilized properly. The allowable pressure drops of a stream will vary from
one system to another since it is dependent on the interaction between the streams. It will also
vary from one economic scenario to another. It is important that the full utilization of allowable
pressure drops be achieved for the streams in a shell-and-tube heat exchanger design as far as
possible. Furthermore, it is also important that once the allowable pressure drops of the stream
have been set, full advantage must be taken of them in order to obtain optimum heat exchanger
area in the design. Jegede and Polley [9] have considered the trade-offs involved in the optimum
design of shell-and-tube heat exchanger. They have shown how full use can be made of the
allowable pressure drops and shown how the optimum heat exchanger size can be determined.
The procedure is based on Kern’s correlations. For the tube side of the exchanger the pressure
drop relationship takes the form given by the equation (2.8). Similarly, for the shell side flow the
relationship takes the form given by
PS  K PS AhS5.1
(2.12)
The constants are given below:
KT  K1t Dti 4V0 Dt l K 2t 
3.5
(2.13)
K1t  0.092 Dti Dti  
(2.14)
K 2t  0.023k Dti  Pr 0.33 Dti  
(2.15)
K PS  K1S K 2 S K 3S
(2.16)
0.2
0.8
1.79 S De 
2 De
3.81
K 1S 
 1.8

K 2 S  4Ltp Ltp  D0   2 D0V0
(2.17)

(2.18)
11
K 3S  0.36k De  Pr
0.33
De  S 0.55
(2.19)
∆PT, ∆PS, Q and ∆TLM are specifying in the design requirements. Three equations (2.8, 2.10, and
2.12) with only three unknowns (hT, hS and A) are solved simultaneously and as such rapid
solution is possible. The procedure is independent of whether the streams involved are pumped
liquids, compressed gases, or a combination of these.
A general procedure for heat exchanger design has been presented in the Heat
exchanger Design Handbook (HEDH), but no precise criteria for determining the baffle spacing
has been offered, and the emphasis is only on its permissible range of application. Saffar-Avval
and Damangir [10] have established the optimization procedure to calculate the optimum baffle
spacing and the number of sealing strips for all types of shell-and-tube heat exchangers. Here the
objective function J is defined as:
J  W1 A  W2W
(2.20)
W1 is the heat transfer area weight factor, W2 is the pumping power weight factor, and W is
power. The weight factors are defined as:
W1 
Cp
Cs
, W2 
Cs  C p
Cs  C p
(2.21)
It is concluded that, non-dimensional value of ReS.PrS.exp(Dr/Dti) for each optimization design is
well correlated with heat transfer area weight factor, W1. These results for each type of exchanger
are presented as follows:

E-Type shell-and-tube heat exchanger:
Re S . PrS .e Dr / Dt   8.89756  12.23475W1  6.24858W1
2
(2.22)
12

Floating head type shell-and-tube heat exchanger:
Re S . PrS .e Dr / Dt   6.48571  23.67138W1  6.08711W1

2
(2.23)
U-tube shell-and-tube heat exchanger:
Re S . PrS .e Dr / Dt   5.98419  28.88928W1  14.13602W1
2
(2.24)
Where the shell-side Reynolds number is
.
M D
Re S  S t
S Sm
(2.25)
Where S m is the cross flow area, given as:


D 
S m  Lbc  Lbb  DS  Lbb  Dt 1  t 
 L 

tp 

Where
Dr  Reference diameter [25.4mm]
DS  Shell diameter
Lbb  Inside shell diameter to bundle clearance
Dt  Tube outside diameter
Lbc  Baffle spacing
Ltp  Tube pitch
.
M  Mass flow rate
(2.26)
13
Once the Reynolds number is obtained, the cross flow area S m is calculated and hence also
optimum baffle spacing. They have studied the effect of baffle spacing on heat transfer area and
pressure drops, and conclude that baffle spacing has a decisive effect on pumping power and
noticeable on required heat transfer area.
Poddar and Polley [11] present a new design heat exchanger through parameter plotting.
It can be used with any existing state-of-the-art exchanger-rating program. Rather than
systematically exploring the whole of the available exchanger sizes (diameters and tube length), it
determines the relationship between duty and tube length, pressure drop and tube length, etc. for a
range of diameters. This information is then used to clearly indicate the full range of geometries
that are suitable for a given duty and given constraints. Most state-of-the-art programs for the
rating of shell-and-tube heat exchangers present a wealth of information on exchanger
performance. Virtually all of these programs will inform the user of the effective mean
temperature difference, the overall heat transfer coefficient, the tube side pressure drop and the
shell side pressure drop for a single baffle space. By running a rating program for a series of shell
diameters with a selected baffle configuration all of the performance information can be related to
shell diameter. The importance of maximum allowable pressure drop can be determined as
follows. First, allowance is made for exchanger nozzles. Normal design practice is to design the
exchanger nozzles such that they absorb just a small percentage of the total allowable value. So,
for each shell diameter studied, the tube side pressure drop is per unit length is determined. By
dividing the allowable tube side pressure drops by this value, the length of shell-and-tube heat
exchanger that coincides with the absorption of the allowable pressure drop is determined. The
relationship between shell diameter and the tube length for maximum pressure drops is shown in
Figure 2.1. Acceptable design lie above and to the left of this line; the design space has now been
14
reduced to EFIJH. The data generated on shell side pressure drop per unit length of exchanger can
be treated in exactly the same way. The result is also incorporated in Figure 2.1
Figure 2.1 Pressure Drop Constraints [11]
Finally, the information on overall heat transfer coefficient and effective mean temperature
difference can be used to determine the area needed for the given duty as a function of shell
diameter. For each diameter, this can be related to tube length necessary for the heat transfer duty.
This relationship can now be placed on the plot. The result could be that shown in Figure 2.2.
Acceptable designs are those that are above and to the right of this line, the design space finally
reduced to MFKN. The procedure is a graphical technique and lays bare the influence of the
‘secondary constraints’ on design. This design procedure suffers from limitation like the one
some of the constraints are not considered (e.g., on shell side velocity). It cannot be readily
considered (e.g., on baffle spacing) in the approach proposed by authors, who plotted shell
diameter versus tube length. In addition, they did not establish any targets for minimum area and
cost.
15
Figure 2.2 Area Requirements [11]
Some designers have a conceptual problem in envisioning the cost of buying a heat
exchanger or the cost of paying the electricity to supply the pressure needed to overcome heat
exchanger pressure drop on the same basis as the lost value of unrecovered thermal energy
represented by the temperature driving force (∆T). To overcome these problems, Steinmeyer [12]
establishes the development of the optimum ∆T and ∆P relationships from a single turbulent
energy dissipation relationship, and the quantitative comparison of the relative “bills” of the three
components of heat exchanger costs. Also unique is the comparison of the conventional shelland-tube relationships to the prediction from energy dissipation. The most remarkable statement
he made in his paper is that at the optimum, the bill for pressure drop for the life of the heat
exchanger is one-third the life time bill for heat transfer area. The statement is known as the “onethird rule”. The one-third rule provides a way of checking for proper allocation of pressure drop.
A thermo economic optimization analysis is presented by Soylemez [13] yielding simple
algebraic formulas for estimating the optimum heat exchanger area. The P1-P2 method is used in
the study, together with the well-known Effectiveness-NTU method, for thermo economic
16
analyses of three different unmixed type heat exchangers. Variable parameters used in
formulating the thermo economical optimum heat exchanger area are listed as: technical life of
the heat exchanger N  , area dependent first cost of the heat exchanger C s  , annual interest
rate d  , present net price rate of the energy i  , annual energy price rate, annual total heat
transfer Q , overall heat transfer coefficient U  , maximum temperature differential Tmax  ,
and annual total operation time t  . First of all for the C = 0 case, the following optimum heat
exchanger area Aopt formula is as:
Aopt
 .

 M Cp 

P2 C s

 min 

ln 

U
UP1C e Tmax t 
(2.27)
The P1 and P2 values are defined by the following:
If i  d
N
 1   1  i  
P1  
 
 1  
 d  i    1  i  
If i  d
P1 
N
1 i
(2.28)
(2.29)
P2  1  P1 M  Rv 1  d 
.
N
(2.30)
If i  d then, the payback period N p is




P2 C s Ad  i 

ln 1 
 C  M. C  T t 
e
p
max



 min


Np 
 1 i 
ln 

1 d 
(2.31)
17
If i  d , then, the payback period N p is:
Np 
P2 1  i C s A

 .

Ce  M C p  Tmax t 1  e NTU C 1

 min

(2.32)
Similarly, the optimum heat exchanger area, Aopt, and the payback period can be
determined by using the same procedure for the parallel flow exchanger as:
Aopt
 .

 M Cp 

P2 C s

 min 

ln 

1  C U
UP1C e Tmax t 
(2.33)
If i  d :




P2 C s Ad  i 


ln 1 
 C  M. C  T t 
e
p
max



 min


Np 
1

i


ln 

1 d 
(2.34)
If i  d :
Np 
1  i C s A1  C 



Ce  mC p  Tmax t 1  e 1C NTU

 min
.

(2.35)
Finally, for countercurrent heat exchanger, C = 1, case, the following are evaluated:
Aopt
 .

 M Cp 

 min

U

P1Ce Tmax tU 
1 

P2 C s


(2.36)
18
If i  d :



C s Ad  i 1  NTU  

ln 1 
 NTUC  m. C  T t 
e
p
max



 min


Np 
 1 i 
ln 

1 d 
(2.37)
If i  d :
Np 
1  i C s Aa  NTU 
(2.38)
.

C e  m C p  Tmax t.NTU

 min
Murlikrishna and Shenoy [14] have proposed a methodology that graphically defines the
space of all feasible designs. Given the large number of geometrical parameters, this space is
quite complex in nature. It is demonstrated that this complex space can be conveniently
represented on a two dimensional plot of shell side versus tubes side pressure drop. Equations are
derived for the various constraints and then plotted on the pressure drop diagram to define the
region of feasible design. The tube side pressure drop is given by:
PT  K T 1
L
DS  a 
2 K T N tp 
n  2 mt 
3 m t
KT1 
 KT 2
1
DS  a 2n
NS  4 M T 
t

T T 
mt
2 m t
2 m t
(2.35)
bDt n 2 m t

5 m t
Dti
(2.36)
19
20N tp  NS  M T bDt 
.
3
KT 2 
2
2n
 T  2 Dti 4
(2.37)
For smooth pipes, the correlations for friction factors are
f T  K T Re T
mt
(2.38)
The shell side pressure drop is given by the following expression:
PS  K S1
K S1 
Rbs
L
42 ms
DS
(2.39)
3ms
2 K S De
ms 1
.
NS  M S 2 ms
 S ms  S 1  Dt Ltp 2 ms
(2.40)
The shell side friction factor correlation is of the form:
f S  K S Re S
ms
(2.41)
where typical values of KS and ms are 0.4475 and –0.19 respectively. In a manner analogous to
that used in deriving equations (2.35 and 2.39), the heat duty equation is rewritten below as
function of tube length, shell diameter and the baffle spacing to shell diameter ratio.
For Re T  2100
 DS 1.1 Rbs 0.55 L1 / 3 DS  a n / 3

LDS  a   K 2 

 K4 
K1
K3


(2.42)
20
For 2100 < Re T  10000


 1.1 0.55

1
 DS Rbs

L  DS  a   K 2 

 K4 
2/3
K1
 D


K6



K 5 1  ti2 / 3 

125
2n / 3



L


D

a

 S



(2.43)
For Re T > 10000
 D S 1.1 Rbs 0.55 DS  a 0.8 n

LD S  a   K 2 

 K4 
K1
K7


(2.44)
Where
0.36k S
1/ 3  D
K1 
PrS  e
De
 S



.
0.55
MS
1  D
t
0.55
Ltp 
0.55
QbDt 
K2 
Dt NS Ft TLM
(2.45)
n
(2.46)
1/ 3
1/ 3
n/3
 . 
 4 M T  N tp  bDt 
1.86kT
1/ 3

K3 
PrT 
Dt
T 1 / 3
K4  Rf 
Dt  Dt 

ln 
2k  Dti 
(2.47)
(2.48)
21
K5 
0.116kT
1/ 3
PrT
Dt
 . 
4MT 

K6  
2/3
(2.49)
N  bD 
2/3
tp
2n / 3
t
(2.50)
Dti  T 2 / 3
0.8
0.8
0.8 n
 . 
 4 M T  N tp  bDt 
0.023kT
1/ 3

K7 
PrT 
Dt
Dti  T 0.8
(2.51)
The tube side pressure drop relationship (equation 2.35), the shell side pressure drop
relationship (equation 2.39) and the heat duty relationship (equations 2.42, 2.43, and 2.44) form
three equations in five variables ( PT , PS , DS , L, and Rbs ). Thus, there are two degrees of
freedom. The shaded region in Figure 2.3 defines the region of all possible design satisfying the
constraints. The methodology presented by them is equation based. If two of the five are
specified, then the remaining can be solved. Although every point in this feasible region
corresponds to a unique design that satisfies all the constraints, the designer may seek optimal
design, i.e., designs that meet certain objectives like minimum area or minimum cost. The
minimum area design will usually require the allowable pressure drops to be utilized to the
maximum extent, and the point can be readily located within the feasible region. The minimum
area design corresponds to minimum capital cost of the heat exchanger; but to minimize the total
annual cost, a simple techno-economic analysis is needed to determine the optimum pressure.
22
Figure 2.3 Region of Feasible Design on the Pressure Drop Diagram [14]
Literature has been reviewed for design of shell-and-tube heat exchangers where pressure
drop is considered as main constraint. All of the methods have some essential limitations, like use
of Kern’s correlation, less use of specified pressure drops. The methods discussed above proceeds
through the examination of the performance of a range of potential geometries. This leads to the
longer execution of program. To reduce the execution time, a quantitative relationship must be
derived to arrive at the initial size of a heat exchanger.
23
Chapter 3
SHELL AND TUBE HEAT EXCHANGER
By far the most common type of heat exchangers to be encountered in the thermal
applications is shell-and-tube heat exchangers. These are available in a variety of configurations
with numerous construction features and with differing materials for specific applications. This
chapter explains the basics of exchanger thermal design, covering such topics as: shell-and-tube
heat exchanger components; classification of shell-and-tube heat exchangers according to
constructions.
3.1 Constructional Details of Shell and Tube Heat Exchanger
It is essential for the designer to have a good knowledge of the mechanical features of
shell-and-tube heat exchangers and how they influence thermal design. The principal components
of shell-and-tube heat exchangers are:

Shell

Shell cover

Tubes

Channel

Channel cover

Tube sheet

Baffles

Nozzles
24
Other components include tie-rods and spacers, pass partition plates, impingement
Plate, longitudinal baffles, sealing strips, supports, and foundation. The Tubular Exchanger
Manufacturer is Association, TEMA, has introduced a standardized nomenclature for shell-andtube heat exchangers. A three-letter code has been used to designate the overall configurations.
The three important elements of any shell-and-tube heat exchangers are front head, the shell and
rear head design respectively. The Standards of Tubular Exchanger Manufacturers Association
(TEMA) [15] describes the various components of various class of shell-and-tube heat exchanger
in detail.
Figure 3.1-Fixed Tube Sheet Shell and Tube Heat Exchanger [15, 16]
25
Type
Type P
Type S
Type T
Type U
Type
L,M,N
Outside
Floating
Pull
U Tube
W
fixed
Packed
Head with
Through
Bundles
Externa
tube
Floating
Backing
Floating
-lly
sheet
Head
Device
Head
Sealed
Floating Tube
sheet
Relative cost
2
4
5
6
1
3
Provision for
Expansi
Floating
Floating
Floating
Individual
Floatin-
Thermal.
on Joint
Head
Head
Head
Tubes Free
g Head
Expansion
in Shell
Bundle Rem-
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Outside
Yes
1=Least cost
to Expand
ovable
Tubes
Replaceable
Tube side
Mechanically
Cleanable
Row Only
Yes
Yes
Yes
Yes
No
Yes
26
Shell side
No
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Possible Tube
Any
Any
Any
Any
Any Even
One or
side Passes
Number
Number
Number
Number
Number
Two
Mechanically
Cleanable
Double Tube
sheet
Possible
Bundle
Replaceable
Internal
Gaskets
Table 3.1 Features of TEMA Type Heat Exchangers [17]
Use of multiple tubes because of that is increasing the heat transfer area. Reason of
increasing heat transfer area is increase the velocity of fluid and lower effective ∆T.
There is different type of shell available, all shell are identified regarding the diameter
.Basically sizes of the shell are 8, 10, 12 inches. We find 2 inches of increment every step start
from 13 inches to 25.From 25 to 39 we find 2 inches increment and after 39 to 72 we find 3
inches increment in shell.
Tube size, which type of materials and array are primary criteria of designing of tube and
shell type of mat exchanger. After done this step hydraulic design will be done on automatically.
27
Small tube gives less cost with good thermal conductivity and Use of multiple tubes because of
that is increasing the heat transfer area. Reason of increasing heat transfer area is increase the
velocity of fluid and lower effective ∆T. It will create less shell area and size. Normally two
arrays are available, triangular array produces the more tube with lower cost for particular heat
transfer unit. We can control the pressure difference in square type of array so it is more
preferable rather than the triangular type of array. When the cleaning require because of
mechanical work, on that time square type of array are preferable. Wide pitch is used in this type
of array and 60o and 90o arrays have a tendency to create a channeled flow. So that way fluid
have a tendency to pass between two row of tube so there si not need to complete the full round
of flow. This is happen in each tube so it is big gain for evaporators and condensers for vapor
distributions.
With the close type of temperature, difference and tube side of pressure difference
generally start to design the heat exchanger with two or more tube passes. The way is to
established lot of heat exchanger with normal way. Front and rear end the pass particles are
installed in the tube side. For the multi-pass tube arrangement the stress are developed at high
joint. With the pressure and temperature difference, high tensile and compressive load located the
tube side.
3.2 Design Methods of Shell and Tube Heat Exchangers
First step in designing of heat exchanger, there is two way to design heat exchanger.
1. LMTD
2. NTU Method.
General equation of heat exchanger is
Q  UA0 FT TLM
(3.1)
28
Where ∆T is the Temperature difference between hot and cold fluid
In terms of energy flow for heat exchanger, we can use this equation for hot fluid,
.
Q   M C p Th
(3.2)
Where ∆T is the Temperature difference between hot fluids
In terms of energy flow for heat exchanger, we can use this equation for cold fluid,
.
Q  M C p Tc
(3.3)
Where ∆T is the Temperature difference between hot fluids
3.3
Log Mean Temperature Difference Method
Heat flows between the hot and cold streams due to the temperature difference across the
tube acting as a driving force. The difference will vary with axial location. Average temperature
or effective temperature difference for either parallel or counter flow may be written as:
TLM  LMTD 
T1  T2
 T
ln  1
 T2



(3.4)
Normal practice is to calculate the LMTD for counter flow and to apply a correction
factor FT, such that
TLM  FT .TLM ,CF
(3.5)
29
The correction factors, FT, can be found theoretically and presented in analytical form. The
equation given below has been shown to be accurate for any arrangement having 2, 4, 6… 2n
tube passes per shell pass.
 R2 1  1 P 

 ln 

 R  1   1  PR 

2 P 1 R  R2 1
ln 

 2 P  1  R  R 2  1 
F1 2
(3.6)
Where the capacity ratio, R, is defined as:
R
T1  T2
t 2  t1
(3.7)
The parameter P may be given by the equation:
P
1  X 1 / N SHELL
R  X 1 / N SHELL
(3.8)
Provided that R  1 in the case that R  1 , the effectiveness is given by:
P
N Shell
P0
 P0 .N Shell  1
(3.9)
P0 
t 2  t1
T1  t1
(3.10)
X 
P0 .R  1
P0  1
(3.11)
Gulyani and Mohanty [18] give alternate equations for the calculation of temperature correction
factors. They have derived linear equations for the same and established that the factor is below
0.5 % error. They are given in Table 3.1.
30
NShell
FT
1
1.208 G + 0.8037
2
0.237 G + 0.961
3
0.1202 G + 0.9835
4
0.0661 G + 0.991
5
0.0429 G + 0.994
Table 3.2 Linear Equations for FT [18]
Note: G  1  P0 1  R 
(3.12)
3.4 Effectiveness-NTU Method
In the thermal analysis of shell-and-tube heat exchangers by the LMTD method, an
equation (3.1) has been used. This equation is simple and can be used when all the terminal
temperatures are known. The difficulty arises if the temperatures of the fluids leaving the
exchanger are not known. In such cases, it is preferably to utilize an altogether different method
known as the effectiveness-NTU method. Effectiveness of shell-and-tube heat exchanger is
defined as:

The group
C S TSi  TSo 
C T  TTi 
 T To
Cmin TSi  TTi  Cmin TSi  TTi 
UA
is called number of transfer units, NTU.
C min
Effectiveness for shell-and-tube heat exchanger can also be expressed as:
(3.13)
31
 UA C

   
, min 
C
 min C max 
Where
(3.14)
Cmin C S CT
(depending upon their relative magnitudes).

or
C max CT
CS
Kays and London [19] have given expressions for shell-and-tube heat exchangers. Some
of their relationships for effectiveness are given below:
For one shell pass, 2, 4, 6 tube passes
2


1  exp  NTU 1  1  C min  



 
2
 1  21  C min  1  C min

2 



1  exp  NTU 1  1  C min  



 
(3.15)
For two shell pass, any multiple of 4 tubes
 1   C
1 min
 2  
1

1

2
  1   C

1 min
  1 
1

1
 

2


  C min 


1
(3.16)
3.5 Calculation of Heat Transfer Coefficient and Pressure Drops
Flow across banks of tubes is, from both constructional and physical considerations, one
of the most effective means of heat transfer. However, it is recognized quite early that ideal tube
bank correlations, if applied to shell-and-tube heat exchangers, needed substantial corrections.
In 1951, Tinker presented what has become a classical paper on flow through the tube
bundles of shell-and-tube heat exchanger. He pointed out that a number of differing paths existed
for flow and argued that the assumption that all of the fluid passed through the whole of the
bundle was false. This was clearly demonstrated by his observations of the performance of
exchangers handling highly viscous oils. He then proceeded to propose a flow model based on
32
variety of flow paths cross flow, bundle bypass, tube-baffle leakage and shell-baffle leakage.
These paths are shown in Figure 3.6 and 3.7. This contribution became watershed in shell-andtube heat exchanger technology. Up until that, simple correlations, similar to those used for tubes,
had been produced and used for shell side performance. Following Tinker’s work researchers
concentrated on developing the sophisticated performance model for heat exchanger, which
recognized the existence of flow paths.
Figure 3.2 Mechanical Clearances in Shell and Tube Heat Exchanger [8]
Figure 3.3 Flow Paths on Shell Side, A Cross Flow; B Window; C Shell-Baffle
Leakage; D Tube-Baffle Leakage; E Bundle Bypass [8]
33
3.6 Heat Transfer Efficient
The Bell’s Delaware method uses ideal tube bank j h and f factors and then corrects
directly the resulting hi and ∆Pi for derivations caused by the various split streams. The ideal tube
bank factor j and f is given as:
 1.33
j h  a1 
L D
 tp t
a3
 10.14 Re a4
 1.33

Re a2 And f  b1 

L D

 tp t
b3
 10.14 Re b4

Re b2


(3.17)
For possible computer applications, a simple set of constants is given in [20] for the curve
fit of the above form.
The ideal heat transfer coefficient on shell side is defined as:
.
hiS  jC p M Pr 2 / 3
(3.18)
The shell side actual heat transfer coefficient is given in equation:
hS  hiS jb jc jl j s j r
(3.19)
jc is the correction factor for baffle cut given by:



DS
DS
 Bc  
 cos 1 
 2 cos 1 
sin

1



D L D
D L D


50  
bb
t
 S
bb
t 
 S
jc  1.27  1.44
 
180
2



 Bc    
1    
 50    




jb is the correction factor for bundle bypass flow is given by:


100 N ss L pp
Lbb  0.5Dt 
1 
jb  exp   1.25

Lbb Ltp,eff  DS  Lbb  Dt Ltp  Dt  
50  Bc

jl is the correction factor for baffle leakage flow is given as:




(3.21)
34
jl  0.441  rs   1  0.441  rs e 2.2 rlm
(3.22)
rs 
S sb
S sb  S tb
(3.23)
rs 
S sb  S tb
Sm
(3.24)
Where S m is the cross flow area at the bundle centerline, is given by


D  Lbb  Dt
Ltp  Dt 
S m  Lbc  Lbb  S
Ltp,eff


(3.25)
S sb is the shell-to-baffle leakage area, given by

 B 
S sb  0.00436 DS Lsb  360  2 cos 1 1  c  
 50  

(3.26)
S tb is the tube-to-baffle hole leakage area, is given by



2
2 
S tb   Dt  Ltb   Dt N tt 1  Fw 
4

(3.27)
j s is the correction factor for variable baffle spacing is presented as:
0.4
L 
L 
N b  1   bi    bo 
 Lbc 
 Lbc 
js 
L
L
N b  1  bi  bo
Lbc Lbc
(3.28)
jr is the correction factor for adverse temperature gradient, which is given as:
For Re S  20
j r   j r r 
1.51
Nc
0.18
(3.29)
35
For 20  Re S  100
 20  Re S 
j r   j r r  
 j r r  1
 80 
(3.30)
For Re S  100
jr  1
(3.31)
Nc is the total number of tube rows crossed in the entire heat exchanger:
N c  N tcc  N tcw N b  1
(3.32)
In addition, the shell side heat transfer coefficient is given by the following Nusselt
number correlation:
hS De
0.55
1/ 3   

 0.36 Re S PrS 
kS

 w
0.14
(3.33)
Equation (3.34) is given Kern and Krauss [21, 22]. Various correction factors for heat transfer
coefficient for shell side flow are calculated as per suggested in the Delaware method. The
correlations for tube side Nusselt number are:
For Re T  2100
hT Dti
D 

 1.86 Re T . PrT . ti 
kT
L 

1/ 3
  


 w 
0.14
(3.34)
For 2100 < Re T  10000
  Dti  2 / 3   
hT Dti
2/3
1/ 3 

 0.116 Re T  125 PrT  1  
 
  L    w 
kT




0.14
(3.35)
For Re T > 10000
hT De
0.8
1/ 3   

 0.023 Re T PrT 
kT
 w 
0.14
(3.36)
36
3.7 Pressure Drop
The shell side pressure drop [20] is calculated as a summation of the pressure drops for
the inlet and exit sections Pe  , the internal cross flow sections Pc  , and the window sections
Pw  . For a shell-and-tube exchanger, the combined pressure drop is given as:
PS  Pc  Pw  Pe
(3.37)
The zonal pressure drops are calculated from ideal pressure drop correlations and
correlation factors, which take account of bundle bypassing and leakage effects. The baffled cross
flow pressure drop is given by:
Pc  N b  1Pci Rb Rl
(3.38)
The end zone pressure drop is given by:

N 
Pe  2Pci Rb 1  tcw 
Nc 

(3.39)
and, the window pressure drop by:
Pw  N b Pwi Rl
(3.40)
The correction factors for shell side pressure drop are given as:

Rl  exp  1.331  rs rlm 
L 
Rs   bc 
 Lbo 
0.151 rs 0.8
2 n
L 
  bc 
 Lbi 

(3.41)
2n
(3.42)
37

S
Rb  exp  3.7 b
Sm


100 N ss L pp
1  3

50  Bc





(3.43)
According to Kern and Krauss [22], the shell side pressure drop is given by the following
expression:
2 f S GS DS N b  1NS 
2
PS 
(3.44)
De  S   w 
0.14
The shell side friction factor correlation is of the form:
f S  0.4475 Re S
0.19
(3.45)
The tube side pressure drop is given by:
2 f T GT LN tp NS  1.25GT N tp NS 
PT 

0.14
T
Dti  T   w 
2
2
(3.46)
The first term is due to friction and the second term is due to return losses. Most of the
pressure drop is due to surface friction inside the exchanger in an attempt to increase the heat
transfer. Therefore, only the straight tube pressure is considered. For smooth pipes, the
correlations for friction factor are of the form:
f T  K T Re T
 mt
(3.47)
Note that K T  16, mt  = -1 for Re T  2100 , whereas K T  0.046, mt  -0.2 for
Re T  2100
The overall heat transfer coefficient (U) is related to individual heat transfer coefficient as:
D 
D
1
1
1 Dt


 t ln  t   R f
U hS hT Dti 2kT  Dti 
(3.48)
38
It is essential that the designer of shell-and-tube heat exchangers becomes familiar with
the principles of the various correlations and methods in numerous publications, their advantages
and disadvantages, limitations and degrees of sophistication versus probable accuracy and other
related aspects. All the published methods can be logically divided into several groups:
1. The early developments based on flow over ideal tube banks or even single tubes.
2. The “integral” approach, which recognizes baffled cross flow modified by the presence
of window, but treats the problem on an overall basis without considerations of the
modified effects of leakage and bypass.
3. The “analytical” approach based on Tinker’s multistream model and his simplified
method.
4. The “stream analysis method”, which utilizes a rigorous reiterative approach based on
Tinker’s model.
5. The Delaware method, which uses the principles of the Tinker’s model but interprets
them on an overall basis, that is, without reiterations.
6. Numerical prediction methods.
All of the methods suffer from essential drawbacks, which are given below:
1. All the “integral” methods such as Donohue and Kern cannot be recommended, as the
resulting errors are potentially high.
2. Although Tinker’s flow model is accepted as a valid basis, its full usefulness is idealized
in the rigorous iterative form. Even so, the crucial correlations of the flow resistance
values are not in the public domain.
3. Although the numerical method has promising future, it is difficult to apply to complex
cases and, for design purpose; it is not yet a substitute for the other methods listed.
39
4. The Delaware method appears to be the best available and the most suitable for design of
shell-and-tube exchangers. This method has a limitation that it does not allow for
interaction between the effects of the various parasitic streams.
In selecting the recommended method for the design of exchanger, the considerations
summarized above indicated that, of all the methods surveyed, the Delaware method is in
principle the most suitable on at the present. The method based on the principles of the Tinker’s
flow distribution model, and thus is more superior to “integral” methods. It should be clear,
however, that this no reiterative method cannot compete for accuracy with the complex stream
analysis-type methods.. Nevertheless, for a well-designed exchanger without any extremes, the
results are within respectable limits of accuracy. In this project, the Delaware method is used for
the forward calculations of heat transfer coefficients and pressure drops. This method has
distinctive advantages on all other method.
40
Chapter 4
DESIGN OF SHELL AND TUBE HEAT EXCHANGER USING SPECIFIED
PRESSURE DROP
The classical approach to shell-and-tube heat exchanger design involves a significant
amount of trial-and-error because an acceptable design needs to satisfy a number of constraints.
Typically, a designer chooses various geometrical parameters such as tube length, shell diameter
and baffle spacing based on experience to arrive at a possible design. If the design does not
satisfy the constraints, a new set of geometrical parameters must be chosen. Even if the
constraints are satisfied, the design may not be optimal. In this project, a methodology is
proposed that calculates the approximate free flow areas on tube and shell side for specified
pressure drops. Once these are obtained, geometrical dimensions can be tried to satisfy heat
transfer requirements.
4.1 Input Data
The inputs specified for the design of heat exchangers consists of:

Process Data
Type of fluids on both sides
Mass flow rate of hot fluid and cold fluid
Tube side ∆P
Inlet pressure of tube side
Shell side ∆P
Inlet pressure of shell side
Inlet and outlet temperatures
Fouling resistances
41

Physical properties
Viscosity
Heat capacity
Thermal conductivity
Densities
4.2 Formulation of Design Procedure
In this project, the problem of shell-and-tube heat exchanger is considered in which
pressure drops of the streams is specified. Utilization of pressure drop gives the heat exchanger
having minimum shell diameter. The pressure drop of one of the streams is given as:
G 2 fL
P 
2 D
(4.1)
The characteristic length of heat exchanger is given as:
rh 
Acc
L
A
(4.2)
In alternate form, the characteristic length of heat exchanger may be defined as:
rh 
D
4
(4.3)
Combining equations (4.2 and 4.3), pressure drop of stream of heat exchanger becomes:
P 
G 2 fA
8 Acc
(4.4)
Mass flow velocity of stream is defined as:
G  V
(4.5)
42
.
M
G
Acc
Or
(4.6)
Using equation (4.6) in equation (4.4), and rearranging:
 V 2  P 1 Acc

 
 2   4f A
(4.7)
The number of transfer units of stream is defined as:
NTU 
0 Ah
C
(4.8)
Stanton number is given as:
St 
h
GC p
(4.9)
Combining equations (4.2, 4.5, and 4.9), equation for number of transfer units of streams
becomes:
NTU 
 0 A.St
Acc
(4.10)
Using equation (4.9) in equation (4.6), velocity of stream is given by the formula:
V  2 0
P St 1
 4 f NTU
(4.11)
Alternatively, Stanton number is defined as
St  jh Pr 
2 / 3
Putting equation (4.11) in equation (4.10), velocity of stream is then given by:
(4.12)
43
V  2 0
P j h
1
1
2 / 3
 4 f Pr 
NTU
(4.13)
In equation (4.13), NTU denotes the number of transfer units of the stream. The total number of
transfer unit of shell-and-tube heat exchanger is calculated from equation (3.15 or 3.16).
Equations (3.15 and 3.16) are complex function of minimum heat capacity, effectiveness and total
number of transfer units NTU. Hence, NTU is calculated by using any root solving methods like
bisection method, false position method etc. Once total number of transfer units is available, the
NTU on shell side and tube side is calculated by distributing total number of transfer units in
fractions. To do this, equation (4.13) is used.
1

NTU
1
C
NTU Shell Shell
C min
To calculate the velocity of fluid stream, value of

1
C
NTU Tube Tube
C min
(4.14)
jh
should be available from chart or from
f
correlations.
4.3 Shell Side Procedure
To determine the velocity and free flow area on shell side, the term
Acc
has to be
A
replaced as follows:
The NTU on shell side is expressed as:
NTU Shell 
 0 AhS
.
M Cp
(4.15)
44
The heat transfer coefficient of shell side is given by equation (3.34). Rearranging equation
(3.34), the heat transfer coefficient can be given as:
C
2 / 3   

hS 
. S Pr  
0.45
Acc
Re S
 w 
0.36
0.14
(4.16)
Putting equation (4.15) in equation (4.14), and rearranging, the number of transfer units on shell
side becomes:
NTU Shell 
0.36
Re S
0.45


A
Pr 2 / 3   
Acc
 w 
0.14
(4.17)
Or
Acc
1
  0 j h Pr  2 / 3
A
NTU Shell
Where
jh 
0.36
Re S
0.45
  


 w 
0.14
(4.18)
(4.19)
Equations (3.45, 4.14 4.18, and 4.19) are used in equation (4.13) to determine the shell side
velocity. Once shell side velocity is available, the free flow area is computed. The free flow area
on shell side is given as:
Ds C ' Lbs
A fS 
Ltp
(4.20)
45
The shell diameter is calculated from equation (4.20) for a standard tube diameter, baffle
spacing, tube pitch, baffle cut and clearances and assumed
jh
and Reynolds number. Tube count
f
is determined according to the formula given in HEDH. Alternatively, the value of
Reynolds number for shell side is taken from Figure 4.1.
Re S
Figure 3.4
jh
versus Re for Shell Side Flow
f
jh
versus
f
46
4.4 Tube Side Procedure
To determine the velocity and free flow area on tube side, the term
Acc
has to be
A
replaced as follows:
For laminar flow, Reynolds number < 2100, (from equation (3.35)),
 L 

j h  1.86
D
 ti 
1/ 3
Re 1 / 3
(4.21)
For the transition region, Reynolds number from 2100 to 10000, (from equation (3.36)),
j h  0.166Re
2/3
  L 2 / 3 
 1251    
  D 


(4.22)
For turbulent flow, Reynolds number > 10000, (from equation (3.37)),
j h  0.023 Re 0.8
(4.23)
The Colburn type of equation for tube side heat transfer coefficient is as:
GC p  C p

hT  j h
Re  k




2 / 3
 

 w



0.14
(4.24)
.
M
Replacing G by
in equation (4.23), heat transfer coefficient on tube side is given as:
Acc
.
M C p  C p 


hT  j h
Acc Re  k 
2 / 3
  



 w
0.14
(4.25)
The total number of transfer units, NTU on tube side is given as:
NTU Tube 
 0 AhT
.
M Cp
(4.26)
47
Using equation (4.25) in equation (4.26), the total number of transfer units, NTU on tube side is
given as:


j
A
Pr 2 / 3   
 0 h
Re T Acc
 w 
NTU Tube
0.14
(4.27)
or
Acc
Pr 2 / 3
1
 0 jh
 r
A
Re NTU Tube
(4.28)
Equations (3.47, 4.14 4.28, and 4.21 or 4.22 or 4.23) are used in equation (4.13) to determine the
tube side velocity. Once tube side velocity is available, the free flow area is computed. The free
flow area on tube side is given as:
.
A fT
M
 2

 Dti NTPNS N tt 
 tVt 4
The second and third terms in equation (4.29) should be equal.
jh
and Re is changed until these
f
terms become equal with accuracy of 2 to 5 %. Alternatively, The value of
number for shell side is taken from Figure 4.2
(4.29)
jh
versus Reynolds
f
48
Re T
Figure 3.5
jh
versus Re for Tube Side Flow
f
4.5 Optimization of Shell and Tube Heat Exchanger
The prediction about heat transfer and pressure drop optimization can be very complex –
with two layers of refinements and distinctions, often buried in complex code and sometimes
grossly misapplied. Several papers are present on the optimization heat exchanger. All authors are
succeeded in finding out the optimum pressure drops. In this case, the pressure drop is fixed.
Hence the costs due to process parameters are fixed. The cost associated with the surface is to be
minimized. For such situation, the minimum heat transfer area is the objective function of
optimization model.
49
The objective function is defined as:
F  Cs A  Cs
Q
U 0 FT TLM
(4.30)
Expressing objective function in the design parameters, the objective function becomes
F  Cs
Q
FT TLM
 Lbc Lbb Ltp,eff  DS  Lbb  Dt Ltp  Dt 
45.058Dt  0.8
Ltw 




2 / 3
Prt 1 / 3 M T 0.8 Dt  2Ltw 0.2 k tw 
ji C pS M S Ltp,eff PrS 
j c jb jl j s j r

The optimization on a shell-and-tube heat exchanger consists of the structure size
optimization, and operating parameter optimization. For the former, the vector of the strategic
variable can be expressed by
X 1  x1
Where
x2
x5
x6   Lto
T
Bc
DS
Lbc
Nb
N tt 
T
x3
x4
Bc 
Lbch
DS
(4.33)
Nb 
Lto  2 Lts  Lbi  Lbo
1
Lbc
(4.34)
Lbb  0.020  0.01675DS
(4.32)
(4.35)
Tube diameter is not included as an optimization variable because its value is generally
fixed ahead of actual design. Again, the tube pitch is not usually a design variable since it can be
fixed. Its common values range between 19.75 mm and 31.75 mm depending on the tube size.
For the latter, the vector of the strategic variable is expressed by
50

X2  x
'
1
'
x2
'
x3

T

 N


M

.
P
T
(4.36)
.
Where N , P, M are the rotary speed of power machinery, discharge pressure, and the flow
quantity of fluid respectively. The operating parameters are fixed for a fixed pressure drops.
The constrained condition for optimization structure size of a shell-and-tube heat
exchanger:
For the inequality constraints
gi X 1   0
g1 
Lto
 2.5
Ds
g2 
Z oo
 1.0
Ds
g3 
DS
 1.0
40
DS
Dt
g5 
38.1
 1.0
Dt
g6 
DS
1
Lbc
g8 
0.5
 1.0
Bc
g9 
Bc
1
0.10
g12 
PT max
 1.0
PT
g 4  15 
g7 
(4.37)
Lbc
 0.20
DS
2
0.78Dotl
N
g10 
 N tt g11  tt  1.0
C1 Ltp
7
g13 
PS max
 1.0
PS
g14 
Q
 1 .0
Qmin
g15 
Lbb
 1.0
0.022
g16 
0.075
 1 .0
Lbb
g17 
jc
 1.0
0.5
g18 
1.3
 1.0
jc
g19 
jb
 1.0
0.3
g 20 
1.3
 1.0
jb
g 21 
js
 1.0
0.5
51
g 22 
1.3
 1.0
js
g 23 
jl
 1.0
0.7
g 24 
0 .8
 1 .0
jl
For the equality constraints
h j X 1   0
h1  N b 
(4.38)
Lto  2 Lts  Lbi  Lbo
Lbc
Equations (3.20, 3.21, 3.22, 3.28, 3.29 or 3.30 or 3.31) are used for the calculation of
correction factors. Pressure drop in shell side is calculated as per equation (3.37) and pressure
drop in tube side is calculated as per equation (3.46). From the above equations, it is vivid that the
objective function is a minimum of multivariable design parameters, subjected to nonlinear
inequality and equality constraints. Hence, a multivariable search method is used for the
minimum area objective function. When the optimizing systems, where components are available
in finite steps of sizes, as in shell-and-tube heat exchangers, search methods are often superior to
calculus methods, which assumes infinite gradation of sizes.
4.6 Mechanical Design of Shell and Tube Heat Exchanger
Designers and fabricators of heat exchanger often treat thermal design and mechanical
design as two discrete and separable functions. The interaction between these two is essential in
some cases like thermal stresses in multiple passes fixed tube heat exchanger, effect of flexing of
tube sheets. Therefore, a designer alert to the mutual influence of these two designs and hence
hydro-mechanical design is also done here.
52
4.7 Tube Sheet
In this report the thickness of tube sheet is calculated as per the TEMA [15]. Subjected to
requirements of the Code, the formulas and design criteria contained below are applicable with
limitations noted, when the following normal design conditions are met; size and pressure are
within the scope of the TEMA Mechanical Standards.
Effective tube sheet thickness is calculated as:
For bending
T
For shear
T 
FG P
2 S
0.31DL  P 
 

 S 
D
t
1 



L
tp


(4.39)
(4.40)
Where T = effective tube sheet thickness
DL =
4A
= equivalent diameter of tube center limit perimeter
C
C = perimeter of tube layout measured stepwise in increments of one tube pitch from center to
center of the outer most tubes.
A = total area enclosed by perimeter C,
P = effective design pressure as per TEMA
S = code allowable tensile stress
F and G are tube sheet constants
53
4.8 Channel Cover
The effective thickness of flat channel covers shall be the thickness measured at the
bottom of the pass partition groove minus tube side corrosion allowance in excess of the groove
depth. The required value shall be either that determined from the appropriate code formula or
from the following section, whichever is greater:
4

h A
 G 
T  5.7 P
 2 G B
dB
 100 

 G 


 100 
1/ 3
(4.41)
G = mean gasket diameter
dB = nominal bolt diameter
hG = radial distance between mean gasket diameter and bolt circle
AB = actual total cross sectional area of bolts
4.9 End Flanges and Bolting
Flanges and bolting for external joints shall be in accordance with design rules subjected
to the following limitations. The minimum permissible bolt diameter shall be 1.27 cm for
exchangers with shell diameter of 30.48 cm or less, and 1.58 cm for all other sizes. Maximum
recommended bolt spacing for channel is given by:
Bmax 
2 Dbo  6t cc
0.6
(4.42)
4.10 Baffle Design
The segmental baffle and tube support plate are standard parts. Baffle has holes for tubes
of sizes depending upon the tube outer diameter and length of the tube as described in Table.
54
Similarly, baffle diameter and thickness are dependent on length and outer tube diameter and
internal shell diameter. They are selected using the Tables 4.1, 4.2 and 4.3.
Internal shell diameter, m
Baffle diameter, m
DSi < 0.330
DSi – 0.0508
0.330 < DSi < 0.431
DSi – 0.0508
0.431 < DSi < 0.584
DSi – 0.0508
0.584 < DSi < 0.990
DSi – 0.0508
0.990 < DSi < 1.371
DSi – 0.1143
DSi > 1.371
DSi – 0.1524
Table 4.1 Baffle Diameter [15]
Tube length, m
Internal shell diameter, m
Baffle thickness, m
L < 0.305
DSi < 0.356
1.58
0.356 < DSi < 0.711
3.17
0.711 < DSi < 0.965
4.76
DSi < 0.356
3.17
0.356 < DSi < 0.711
4.76
0.711 < DSi < 0.965
6.10
0.965 < DSi < 1.524
6.10
DSi < 0.356
4.76
0.356 < DSi < 0.711
6.10
0.305 < L < 0.606
0.606 < L < 0.914
55
0.914 < L < 1.219
0.711 < DSi < 0.965
7.93
0.965 < DSi < 1.524
9.52
DSi < 0.356
6.10
0.356 < DSi < 0.711
9.52
0.711 < DSi < 0.965
9.52
0.965 < DSi < 1.524
12.70
DSi < 0.356
9.52
0.356 < DSi < 0.711
9.52
0.711 < DSi < 0.965
12.70
0.965 < DSi < 1.524
15.87
DSi < 0.356
9.52
0.356 < DSi < 0.711
12.70
0.711 < DSi < 0.965
15.87
0.965 < DSi < 1.524
15.87
1.219 < L < 1.524
L > 1.524
Table 4.2 Baffle Thickness [15]
Tube length, m
Outer tube diameter, cm
Diameter of hole, mm
L < 0.914
Dto > 3.175
Dto + 0.7937
Dto < 3.175
Dto + 0.3968
Dto > 3.175
Dto + 0.3968
Dto < 3.175
Dto + 0.7937
L > 0.914
Table 4.3 Diameters of Holes in Baffle Plate [15]
56
4.11 Costing of Shell and Tube Heat Exchanger
Pricing of tube and shell heat exchanger is clearly not a precise matter. It depends, in part
on the costs of constructing the unit, but other factors may dominate. Prices will vary depending
on the average production backlog and general marketing conditions. However, statistical studies
are regularly done and reported in the engineering magazines. In the present project the costs are
taken as given by Crane [17]. Typical articles indicate that the price may be estimated using
techniques similar to those below.
4.12 Shell Cost
The data included in this study-included carbon shells under 30 inches outside diameter.
In the absence of data for larger shell, these equations may be extrapolated to larger sizes. For
expansion joints it is recommended that the shell be priced as if an additional 5 Ft were added to
the length of the shell.
For 0 < P < 27.59 bar
Cost = 4.76 L DS0.93
(4.43)
For 27.59 < P < 41.36 bar
Cost = 6.72 L DS0.93
(4.44)
4.13 Tube Costs
Tube costs are based on (a) the cost of the tubing itself, usually reported on a cost per
square foot of heat exchanger surface, and (b) the cost associated with preparing the tube sheets,
installing and rolling the tubes. These two factors may be estimated using the data below:
57
Tube OD, mm
Rated pressure, bar
Straight Tubes, $ / ft-Tubes
U-Tubes, $ / ft-Tubes
<= 19.75
10.34
1.15
3.85
<= 19.75
20.68
1.30
4.15
<=19.75
27.59
1.40
4.50
> = 25.4
10.34
1.30
4.14
>= 25.4
20.68
1.45
4.50
>= 25.4
27.59
1.75
4.60
Table 4.4 Preparation Cost [17]
Note: This is an unusual procedure required only when fluids must absolute not leak. Normal cost
is taken as $4.72 / Tubes.
Material
Cost, $/inch3
Alum / Brass
1.38
Admiral Brass
1.36
304 SS
2.56
316 SS
7.74
321 SS
3.57
70 / 30 CuNi
2.76
90 / 10 CuNi
2.39
A3003
0.79
330 Brass
1.79
Half – hard Copper
2.34
58
Copper
2.02
Carbon Steel
1.71
Table 4.5 Material Cost [17]
4.14 Installed Nozzle Cost
The total cost of preparing the opening, purchasing and welding the nozzles in place may
be estimated from the following equations. The data from which these fits were obtained were for
nozzles ranging between 3 and 12”.
For 0 < P < 10.34 bar
Cost = 118 – 4.33D + 2.46D2
(4.45)
For 10.34 < P < 20.68 bar
Cost = 140 – 10D + 3.33D2
(4.46)
For 20.68 < P < 41.36 bar
Cost = 119 – 2.5D + 3.75D2
(4.47)
4.15 Front and Rear Head Cost
The following equation has been fitted to estimate the costs of the front and rear end heads
based on various TEMA categories:
Costs = C DS1.037
(4.50)
Where C is given from Table 4.6 below as a function of pressure
Construction
10.34, bar
20.68, bar
27.59, bar
41.36, bar
AEU
201
230
258
276
AEM
306
351
391
421
AEN
337
387
432
463
59
AEL
387
441
494
532
AEW
423
484
541
582
AEP
460
526
587
632
AES
496
569
634
682
AET
639
733
817
878
BEU
120
140
155
165
BEM
225
261
288
309
BEN
256
297
329
352
BEL
306
351
391
421
BEW
326
368
403
439
BEP
345
385
414
457
BES
365
402
426
475
BET
558
642
698
810
CEU
175
202
226
241
CEM
288
324
360
396
CEN
306
348
387
421
CEN
337
387
432
463
CEW
369
425
473
507
Table 4.6 Shell Cost Factors for Selected Shell Constructions [17]
60
4.16 Miscellaneous Cost
Delivery cost may be taken as 3 % of total construction cost.
Engineering, purchasing and administrative cost may be taken as 16 % of total
construction costs.
The equations derived for shell-and-tube heat exchanger for given pressure drops are
used for thermal evaluation purposes. All the equations are used in design and optimization
algorithm in which heat exchanger geometrical dimensions are obtained from performance
specifications. Various cost equations are derived with the assumption that the market price of the
components is not changing with time.
61
Chapter 5
DEVELOPMENT OF ALGORITHM AND OPTIMIZATION
FOR DESIN OF SHELL AND TUBE HEAT EXCHANGER
Based on the design and optimization procedure formulated in chapter 4, design and optimization
algorithm is developed for shell-and-tube heat exchanger. A solution of core velocity equation is
a heart of such an algorithm.
The design process of shell-and-tube heat exchanger proceeds through the following
steps:

Process conditions (stream compositions, flow rates, temperatures, and pressures) must
be specified.

Required physical properties over the temperature and pressure ranges of interest must be
obtained.

The type of heat exchanger to be employed is chosen.

A preliminary estimate of the size of the exchanger is made, using a heat transfer
coefficient appropriate to the fluids, the process, and the equipment.

A first design is chosen; complete in all details necessary to carry out the design
calculations.

The design chosen is now evaluated or rated, as to its ability to meet the process
specifications with respect to both heat duty and pressure drop. To do this, heat transfer
rate in shell-and-tube heat exchanger is calculated using equation (3.2 or 3.3). The
temperature correction factor is determined using equations (3.6). The calculated
temperature correction factor should not be less than 0.75. If it is less than 0.75, the
62
number shell passes and tube passes are increased by 1 and 2 respectively. Effectiveness
of shell-and-tube heat exchanger is obtained by using equation (3.13). Once effectiveness
is available, overall number of transfer units NTU is calculated from equations (3.15 or
3.16). Equations (3.15 and 3.16) are complex functions of minimum thermal heat
capacity and NTU. So, bisection method is used for the computation of NTU. The shell
side friction factor, heat transfer j factor and baffle cut are all set at standard initial
values. The core velocity equation (4.13) is used to find out the velocity on the shell side.
This shell side velocity is then used to compute free flow area. Once free flow area is
known, the shell diameter is known. The tube count gets fixed for a determined shell
diameter. The free flow area on tube side is also determined from core velocity equation.
This can be obtained by also tube count. These two free flow areas are matched. Once
this is achieved, the heat exchanger area, heat transfer coefficient on tube and shell side is
calculated. From the detailed geometry actual friction factor f and j h - factors are
estimated and the initial assumptions are tested and updated if necessary. Once initial
assumptions and detailed geometry coincide, the design has been successfully
accomplished.

Based on this result a new configuration is chosen if necessary and the above step is
repeated. If the first design was inadequate to meet the required heat load, it is usually
necessary to increase the size of the exchanger, while still remaining within specified
pressure drops, tube length, shell diameter, etc. This will sometimes mean going to
multiple exchanger configurations. If the first design more than meets heat load
requirements or does not use the entire allowable pressure drop, a less expensive
exchanger can usually be designed to fulfill process requirements.
63
Chapter 6
RESULT, DISCUSSION, CONCLUSION AND FUTURE SCOPE OF WORK
The pressure drop relationship, (equation 4.13), has been applied to develop a specific
relationship for a shell-and-tube heat exchanger based on the effectiveness-NTU approach. The
Bell’s Delaware design method is used for estimating various parameters. The actual heat transfer
coefficient is estimated and pressure drops are checked according to the HEDH method.
The flow rates, temperatures, allowable pressure drops, and physical properties of streams are
fixed. It is required to determine the optimum area and optimum cost of shell-and-tube heat
exchanger. A full specification of the design problem is given in Table 6.1 and Table 6.2.
Physical Properties
Shell side
Tube side
Fluid
Oil
Water
Flow rate (kg/s)
22.4
77.96
Fluid density (kg/m3)
740
1000
Heat capacity (J/kg. K)
2407
4187
Viscosity (cps)
0.494
1.000
Thermal conductivity (W/m. K)
0.105
0.61
Inlet temp. (deg C)
100
7.1
Outlet temp (deg C)
42.5
16.6
Allowable P (kPa)
13.7
11.6
Dirt factor (K m2/W)
0.000
0.000
C32100
SS 316
Material
64
Wall resistance (K m2/W)
0.00003
Heat Duty (kW)
3100
Table 6.1 Shell and Tube Exchanger Design Problem [8] – Physical Properties
Geometry
Values
Tube OD (mm)
16
Tube ID (mm)
13.5
Tube layout (deg)
30
Tube pitch (mm)
20.8
Baffle-to-shell clearance (mm)
5.5
Tube-to-baffle clearance (mm)
0.5
Bundle-to-shell clearance (mm)
10
Table 6.2 Shell and Tube Exchanger Design Problem [8] – Geometry
The example used here is an adaptation of the one used by Polley, Panjeh Shahi and Nunez
[8] to demonstrate the inverse design methodology. The original example involved water on the
tube side of the exchanger with an assumed film heat transfer coefficient of 6000 W/m2 K. The
fluid on shell side is viscous oil. The tube side and shell side pressure drops for this situation are
11.66 kPa and 13.7 kPa. These are the allowable P subsequently used in our design.
65
The design process of shell-and-tube heat exchanger proceeds through the following
steps:

Process conditions (stream compositions, flow rates, temperatures, and pressures) must
be specified.

Required physical properties over the temperature and pressure ranges of interest must be
obtained.

The type of heat exchanger to be employed is chosen.

A preliminary estimate of the size of the exchanger is made, using a heat transfer
coefficient appropriate to the fluids, the process, and the equipment.

A first design is chosen; complete in all details necessary to carry out the design
calculations.

The design chosen is now evaluated or rated, as to its ability to meet the process
specifications with respect to both heat duty and pressure drop. To do this, heat transfer
rate in shell-and-tube heat exchanger is calculated using equation (3.2 or 3.3). The

Temperature correction factor is determined using equations (3.6). The calculated
temperature correction factor should not be less than 0.75. If it is less than 0.75, the
number shell passes and 1 and 2 increases tube passes respectively. Effectiveness of
shell-and-tube heat exchanger is obtained by using equation (3.13). Once effectiveness is
available, overall number of transfer units NTU is calculated from equations (3.15 or
3.16). Equations (3.15 and 3.16) are complex functions of minimum thermal heat
capacity and NTU. So, bisection method is used for the computation of NTU. The shell
side friction factor, heat transfer j factor and baffle cut are all set at standard initial
values. The core velocity equation (4.13) is used to find out the velocity on the shell side.
66
This shell side velocity is then used to compute free flow area. Once free flow area is
known, the shell diameter is known. The tube count gets fixed for a determined shell
diameter. The free flow area on tube side is also determined from core velocity equation.
This can be obtained by also tube count. These two free flow areas are matched. Once
this is achieved, the heat exchanger area, heat transfer coefficient on tube and shell side is
calculated. From the detailed geometry actual friction factor f and j h - factors are
estimated and the initial assumptions are tested and updated if necessary. Once initial
assumptions and detailed geometry coincide, the design has been successfully
accomplished.

Based on this result a new configuration is chosen if necessary and the above step is
repeated. If the first design was inadequate to meet the required heat load, it is usually
necessary to increase the size of the exchanger, while still remaining within specified
pressure drops, tube length, shell diameter, etc. This will sometimes mean going to
multiple exchanger configurations. If the first design more than meets heat load
requirements or does not use the entire allowable pressure drop, a less expensive
exchanger can usually be designed to fulfill process requirements.

The final design should meet process requirements (within the allowable error limits) at
lowest cost. The lowest cost should include operation and maintenance costs and credit
for ability to meet long-term process changes as well as installed (capital) cost.
Exchangers should not be selected entirely on a lowest first cost basis, which frequently
results in future penalties.
67
6.1 Area Targeting
The optimized heat exchanger design derived using the new algorithm is compared with
the original one in Table 6.3 and Table 6.4.
Geometry
New algorithm
Polley, Shahi, and Nunez
Shell diameter (mm)
520
563
Tube length (mm)
1728
1815
Baffle cut (%)
26.8
29.3
Baffle spacing (mm)
228
253
No. of baffles
5
6
No. of tubes
548
574
No. of tube passes
2
2
Required area (m2)
49.39
52.3
Installed area (m2)
49.39
52.3
Table 6.3 Comparison of Shell and Tube Heat Exchanger Designs – Geometry
Performances
New algorithm
Polley, Shahi, and Nunez
Shell side Re
27926
21398
Shell side P (kPa)
13.493
13.7
Tube side P (kPa)
11.61
11.69
Shell side coeff. (W/m2. K)
1471
1406
Tube side coeff. (W/m2. K)
6750
6641
O.H.T.C. (W/m2. K)
1149
1088
Table 6.4 Comparison of Shell and Tube Heat Exchanger Designs – Performances
68
The new algorithm makes the full utilization of the available pressure drop and achieves
an overall heat transfer coefficient of 1149 W/m2 K and the required area 49.39 m2 when 90 % of
total NTU is distributed between shell and 10 % of total NTU between tube sides. The original
design has an overall heat transfer coefficient of 971 W/m2 K with a required area 58.9 m2. Their
design procedure yields an overall heat transfer coefficient of 1088 W/m2 K and a required area of
52.3 m2. Because of the way in which problem is set up, all the design makes full use of pressure
drop.
6.2 Optimized Results of Components of Shell and Tube Heat Exchanger
Program is run to evaluate the thickness of exchanger parts like tube sheet, baffle, shell
and tube. It is also possible to calculate the diameter and number of tie rods. Table 6.3 shows the
optimized results for mechanical design of a given shell-and-tube heat exchanger
Tube thickness
1.25 mm
Shell thickness
7.937 mm
Tube sheet thickness
13.54
Baffle thickness
12.7 mm
Diameter of tie rods
12.7 mm
No. of tie rods
6
Table 6.5 Optimized Results of Mechanical Design
69
6.3 Cost Analysis
Area targeting in the previous section ensures exchanger of the smallest size with
minimum capital cost. However, the power cost and capital cost with pumping liquids and/or
compressing gases through an exchange often constitute a significant factor. However, in this
thesis, the problem is set up such that the cost associated with power and capital cost of
pumps/compressor is fixed. The only cost we look for here is the cost associated with the surface
area. The costs of various parts of exchanger for the outputs of the above problem are given
below in Table 6.4.
Parts list
Cost (in $)
Shell
3463
Installed nozzles
1330
Baffles
272
Saddle
50.06
Tubes (preparation)
3106
Tube (material)
7893
Front and rear end heads
3205
Table 6.6 Cost Analysis
70
From cost analysis, the total cost of heat exchanger is $ 19319. This is the minimum
initial surface cost of a shell-and-tube heat exchanger. The minimum cost is found for the BEU
type construction, U-tube material SS 316.
6.4 Conclusion
1. Based on the effectiveness-NTU, a novel methodology is developed for a shell-and-tube
heat exchanger with a given pressure drops and provides targets for minimum area and
cost. In contrast to earlier approach, the methodology accounts for full use of given
pressure drops on both sides of exchanger to yield the smallest exchanger for a given
duty. For this, a quantitative relationship is developed that relates the pressure drop,
velocity, friction factor and heat transfer factor and NTU.
2. The methodology as presented in this work is based on Delaware method, which provides
good predictions for shell side flow. It has been shown that how the basic algorithm can
be applied using Delaware method.
3. It must be emphasized heat exchanger had the potential danger of accepting a design that
satisfies the dirt factor and pressure drop constraints without thoroughly investigating
other options that may prove to be more promising. In contrast, in this work a rapid
algorithm is developed which takes care of all constraints.
4. Targeting for area and cost is vital and well-established step in the design of heat
exchanger networks by pinch technology. Targets present what is the best performance
that can be possibly achieved, before actually attempting to achieve it. The targets
proposed in this work allow the designer to determine the minimum area and cost (along
with tube length, shell diameter and baffle spacing etc.).
71
6.5 Feature Scope of Work
With shell-and-tube heat exchangers, the design and optimization methodology is
restricted to applications involving single-phase turbulent flows with compressible fluids.
This is because vaporization and condensation processes in this type of heat exchangers are
often. However, the design method can also be used for two-phase heat transfer exchangers
like compact heat exchangers with some little modifications in core velocity equation.
Further research is needed before the approach can be extended to cover non-isothermal
phase changes.
72
REFERENCES
1. Mcadams, W.H., Heat Transmission, (McGraw-Hill, New York), pp 430-441, 1954
2. Jenssen, S.K., Heat exchanger optimization, Chemical Eng. Progress, 65(7), pp 59, 1969
3. Sidney, K., and Jones, P.R., Programs for the price optimum design of heat exchangers,
British Chemical Engineering, April,pp 195-198, 1970
4. Steinmeyer, D.E., Energy price impacts design, Hydrocarbon Process, November, pp
205, 1976.
5. Steinmeyer, D.E., Take your pick – capital or energy, CHEMTECH, March, 1982
6. Peter, M.S. and Timmerhaus, K.D., Plant design and economics for chemical engineers,
pp 678-696 3rd Ed., McGraw-Hill, New York, 1981
7. Kovarik, M., Optimal heat exchanger, Journal of Heat Transfer, Vol. 111, May, pp 287293, 1989
8. Polley, G.T., Panjeh Shahi, M.H. and Nunez, M.P., Rapid design algorithms for shelland-tube and compact heat exchangers, Trans IChemE, Vol. 69(A), November,pp 435444, 1991
9. Jegede, F.O. and Polley, G.T., Optimum heat exchanger design, Trans IChemE, Vol.
70(A), March, pp 133-141, 1992
10. Saffar-Avval, M. and Damangir, E., A general correlation for determining optimum
baffle spacing for all types of shell-and-tube heat exchangers, International Journal of
Heat and Mass Transfer, Vol. 38 (13), pp 2501-2506, 1995
11. Poddar, T.K. and Polley, G.T., Heat exchanger design through parameter plotting, Trans
IChemE, Vol. 74(A), November, pp 849-852, 1996
73
12. Steinmeyer, D.E., Understanding ∆P and ∆T in turbulent flow heat exchangers, Chemical
Engineering Progress, June,pp 49-55, 1996
13. Soylemez, M.S., On the optimum heat exchanger sizing for heat recovery, Energy
Conversion and Management, 41, pp1419-1427, 2000
14. Murlikrishna, K. and Shenoy, U.V., Heat exchanger design targets for minimum area and
cost, Trans IChemE, Vol. 78(A), March, pp 161-167, 2000
15. Bevevino, J.W., ET. al., Standards of tubular exchanger manufacturing association,
TEMA, New York, 6th Edition, 1988
16. Mukherjee, R., Effectively design shell-and-tube heat exchangers, Chemical Engineering
Progress, February, pp 21-37, 1998
17. Crane, R.A., Thermal Aspects of Heat Exchanger Design, University of South Florida,
Department of Mechanical Engineering
18. Gulyani, B.B. and Mohanty, B., Estimating log mean temperature difference, Chemical
Engineering, November, pp127-130, 2001
19. Sukhatme, S.P., Heat exchangers, A Text Book on Heat Transfer, University Press India
Limited, pp 201-226 1996
20. Taborek, J., Shell-and-tube heat exchangers, Heat Exchanger Data Handbook,
Hemisphere, 1983
21. Poddar, T.K. and Polley, G.T., Optimize shell-and-tube heat exchangers design,
Chemical Engineering Progress, September,pp 41- 46, 2000