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ABSTRACT

SENSITIVITY STUDY OF PLATE HEAT EXCHANGERS

By

Stephen Frederick DeBoer

An algorithm for the simulation of heat transfer in
plate heat exchangers was developed. The simulated results
compared well with data of Buonopane (1963). The importance
of various design parameters was investigated by a sensitiv-
ity study using the computer simulation model. Flow rates,
channel thickness and plate thickness were found to be the
main parameters effecting the plate heat exchanger perform-

8.1106.

Approved4fl€Z/:2%%égég:-éégégggp

Major Professor/Zaijjza

Approved W
Depar men Chairman

 

SENSITIVITY STUDY OF PLATE HEAT EXCHANGERS

by

Stephen Frederick DeBoer

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

(1973)

<33“ 7 C675);

ACKNOWLEDGEMENTS

The author gratefully acknowledges the encouragement
and understanding of Dr. F. W. Bakker-Arkema.

The financial support of the Anderson's Agricultural
Research Fund. Maumee, Ohio, was much appreciated. The use
of heat exchangers as an energy conserving device in re-
cycling air prompted this study.

A note of thanks is also due to Julie West for her

help in keypunching and the preparation of the manuscript.

ii

TABLE OF CONTENTS

Page

I. INTRODUCTION. . . . . . . . . . . . . . . . . . 1
II. REVIEW OF LITERATURE. . . . . . . . . . . . . . 7
A. Conclusions . . . . . . . . . . . . . . . . 1h

III. THEORETICAL ANALYSIS. . . . . . . . . . . . . . 15
IV. NUMERICAL SOLUTION. . . . . . . . . . . . . . . 2h
V. EXPERIMENTAL VERSUS SIMULATED RESULTS . . . . . 27
VI. SENSITIVITY STUDY . . . . . . . . . . . . . . . 29
A. Standard conditions and results . . . . . . 30

B. Effect of fluid properties. . . . . . . . . 33

C. Effect of changing inlet temperature of
flUidSoo0.00000000000000033

D. Effect of fluid flow rate . . . . . . . . . 3U
. Effect of heat transfer area. . . . . . . . 38
F. Effect of plate thickness . . . . . . . . . “O
. Effect of channel thickness . . . . . . . . 40

H. Effect of plate thermal conductivity. . . . “2
VII. SUMMARY AND CONCLUSIONS . . . o . o o . . o o . nu
VIII. SUGGESTIONS FOR FURTHER STUDY . . o . . . o o . “5

APPENDIX - Typical fouling factors . . . . . . . . . . 49

iii

LIST OF FIGURES

Figure Page

1. Schematic Representation of Concurrent and
Counterflow Plate Heat Exchangers . . . . . U

2. Schematic Representation of Series and Parallel
Flow Configurations . . . . . . . . . . . . 5

3. Control Volume Used to Derive the Energy
Equation. 0 o o o o o o o o o o o o o o o o 18

a. Mechanism of Heat Transfer Across a Plate. . . . 20

5. Schematic Representation of Plate Heat Exchanger
Used to Develop Differential Equations. . . 22

6. Simplified Flow Chart for Plate Heat Exchanger
SiNUlation Program. 0 o o o c o o o o o o o 26

7. Temperature Profiles for Standard Conditions . . 32

8. Variation of Hot Fluid Outlet Temperature as a
Function of Hot Fluid Inlet Temperature . . 35

9. Hot Fluid Outlet Temperature as a Function of
Cold Fluid Inlet Temperature. . . . . . . . 36

10. Variation of Heat Transfer Effectiveness due to
Changes in the Hot Fluid Flow Rate. . . . . 37

11. Variation of Heat Transfer Effectiveness as a
Function of Heat Transfer Area. . . . . . . 39

12. Variation of Heat Transfer Effectiveness due to
Changes in the Thickness of the Plate . . . #1

13. Effect of Channel Thickness on Heat Transfer
EffeCtiVeness o o o o o o o o o o o o o o o “3

iv

LIST OF TABLES

Table Page
1. Comparison of Experimental and Simulated Results. 28

2. Results of Parameter Studies. . . . . . . . . . . 31

NOMENCLATURE

a = plate thickness, ft

b = channel thickness. ft

c = specific heat, Btu/1b F

C = heat capacity of fluid stream, Btu/hr F

D9 = equivalent diameter. ft

E = heat transfer effectiveness. Equation (18), dimension-
less

a = acceleration of gravity. ft/sec2

h = individual convective heat transfer coefficient,
Btu/hr sq ft F

hf = fouling factor, Btu/hr sq ft F

i = enthalpy, Btu/1b

k = thermal conductivity. Btu/hr ft F

L = channel length. ft

p.q,r,s = constants

Q = heat, Btu/lb

T = temperature, F

U = overall heat transfer coefficient, Btu/hr sq ft F

v a fluid velocity, ft/hr

w = work. ft lbf

W = mass flow rate, lb/hr

X = distance, ft

Y == height above a given reference. ft

vi

M,

/’

channel width (between gaskets), ft

dynamic viscosity, lb ft/hr

density. lb/cu ft

Dimensionless Groups

Nu = hDe Nusselt Number
—F_

Pr = 0‘“ Prandtl Number

Re = :22 Reynolds Number
AL.

Subscripts

in = inlet condition

max = maximum

min = minimum

n = channel number

out = outlet condition

p = primary

s = Iecondary

vii

INTRODUCTION

Heat transfer is one of the principle unit operations
in the food industry. The importance of the heat exchanger,
the piece of equipment used for most heat transfer. is illus-
trated by the fact that about 10% of the total expense for
capital equipment in the food processing industry is for
heat exchangers (Kroehle. 1967). The search for greater
economy and efficiency has led to the deve10pment of many
types of exchangers including: shell and tube. plate, screw,
scraped surface. double pipe and spiral types. The plate
heat exchanger has been one of the most successful in
meeting the strict sanitary and efficiency requirements of
the food industry. The earliest known patent on such an
exchanger was obtained in Germany in 1878; however. it was
not until the 30's (when the present design was introduced)
before it began to meet the needs of the dairy industry.

The plate heat exchanger consists of a frame and a
pressure plate between which are mounted corrugated metal
plates. The plates are separated by gaskets and are
arranged face to face with the hot and cold fluids flowing
on opposite sides of the plates. The width of the channel
between plates is determined by the gasket thickness and

the amount of force with which the plates are compressed

together in the frame. The exact flow pattern within the
exchanger, series, parallel, or looped, is determined by the
gasket and port design. Connector plates are used to facil-
itate several stages of heat transfer within one frame.

The efficiency of heat transfer of the plate heat
exchanger is considerably higher than with the conventional
shell and tube exchanger. This is due to the relatively thin
films of fluids being heated and cooled and the corrugations
on the plate surfaces. These factors combine to give turbu-
lent flow at low fluid velocity due to the narrow stream
changing direction rapidly. The turbulent flow increases
the heat transfer coefficient and reduces the temperature
gradient within the channel. The advantage of high heat
transfer efficiency must be balanced against the disadvan-
tage of the increased pressure drOp due to the narrow streams
and many changes in direction when comparing the plate heat
exchanger with other types.

An additional advantage of the plate heat exchanger is
its ease of cleaning. Simply by releasing the force which
compresses the plates together, the whole unit can be pulled
apart and each plate individually cleaned. The units can
also be cleaned in place.

Various flow patterns can exist in the plate heat ex-
changer. While it is impractical to develop nomenclature
for all possible flow patterns, it is useful to define a
few of the more common terms. A plate heat exchanger can be

either concurrent or counterflow in design. A concurrent

exchanger is one in which both fluids enter on the same side
of the exchanger. flow through the exchanger in the same
general direction, and exit on the same side of the exchanger.
A counterflow exchanger is one in which the fluids enter at
Opposite sides of the exchanger, flow in opposite general
directions, and exit at opposite sides of the exchanger.
Figure 1 illustrates the idea of concurrent and counterflow
heat exchangers.

Series, parallel, and looped flow apply to the flow
pattern within the exchanger itself. In series flow the
fluid travels through alternate channels throughout the
exchanger. In parallel flow a stream may divide at a loca-
tion with part of the flow going through one channel with
the remaining fluid going through another channel. An ex—
changer has looped flow when both fluid streams have paral-
lel flow. The various flow configurations are illustrated
in Figure 2.

The end plates, although not transferring heat, will be
considered when Specifying the number of plates an exchanger
has. The number of channels is one less than the number of
plates.

The wide use and great flexibility of the plate heat
exchanger requires an adequate method for design of new
exchangers and evaluation of operating characteristics of
existing ones. Review of the literature shows several

attempts at describing the performance of a particular plate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Flow

Parallel

Schematic Representation of Series and Parallel

Flow Configurations

Figure 2:

heat exchanger. Analytical methods and the techniques of
log-mean temperature differences and efficiency—number of
transfer units have been used to predict the performance of
plate exchangers under limited conditions. However, no
method has yet been deve10ped for design which takes into
account all the conditions which can be encountered. There-
fore, the purpose of this study is the deve10pment of a com-
puter simulation model to accurately predict the performance.
of plate heat exchangers. This model is to be used for a
sensitivity study of the various factors affecting heat

exchanger design and performance.

The plate heat
pieces of equipment
The major deterrent
changer use in this

mation. The review

REVIEW OF LITERATURE

exchanger is one of the most widely used
for heat transfer in the food industry.
to the development of future plate ex-
field is the lack of basic design infor-

presented here consists of those papers

which have contributed significantly to the present state of

the art in plate heat exchanger design.

The literature

is dominated by two

describing the design of heat exchangers

basic approaches. The log-mean tempera-

ture difference (LMTD) method invlolves the logarithm of the

ratio of the temperature differences at the two ends of the

heat exchanger (Fraas and Ozisik, 1965). Once the LMTD has

been determined the
calculated from the

equation.

heat transfer rate for the exchanger is

standard convective heat transfer

The efficiency-number of transfer units (E-NTU) tech-

nique is also used extensively for heat exchanger design.

While the method dates back several decades, little use was

made of this method until Giedt (1957) and Kays and London

(1958) published their thorough reviews of the method.

Basically the method involves expressing the efficiency in

terms of the thermal capacity of the fluids and a dimension-
less term, the number of transfer units. Charts are prepared,
either from experimental or analytical data for each heat
exchanger type and configuration of interest.

The early attempts at evaluating the performance of
plate type heat exchangers wascione by researchers studying
high temperature - short time pasteurizers. Ball (19h3) and
Fay and Fraser (l9h3) investigated the plate heat exchanger
as a piece of equipment for pasteurizing milk. Perry (1951)
discussed various factors which influence the performance of
HTST pasteurizers. and presented equations for calculating
the pressure drop through commercial units.

Watson (1955) used motion pictures and electrical
conductivity tests to determine velocity patterns, residence
times and pressure drops in single and multipass plate heat
exchangers. Equations were presented to predict the pressure
drop as a function of fluid velocity in various plate type
exchangers.

Lawry (1959) presented one design approach which employs
a correction factor applied to the overall heat transfer
coefficient used in the LMTD method. The correction factor
is required because the particular plate heat exchanger
modeled deviates from true counterflow conditions thereby
invalidating the straightforward use of the LMTD method.

The correction factor must be experimentally determined for

each particular plate and exchanger configuration. Cary

(1959) reviewed the E-NTU method for counterflow and concurs
rent flow exchangers and extended the method for use with
plate heat exchangers in series. The variation of the over-
all heat transfer coefficient as a function of temperature
was compensated for by the use of an additional chart.

McKi110p and Dunkley (1960) developed an excellent
theoretical analysis of heat transfer in a plate heat ex-
changer. The solution requires the solving of a system of
n linear first order differential equations for n+1 plates.
The boundary conditions required to solve the system of
equations are in general not known. The study did not con-
sider the effect of the Prandtl number and therefore is
limited to non-viscious fluids.

Buonopane (1963) presented plots of experimentally
determined LMTD correction factors for design of exchangers
with similar channel geometry and flow rates to the one
tested. A design method based on this correction factor is
illustrated in a step by step procedure. The information
needed for design are the flow rates, inlet and outlet
temperatures and physical characteristics of the plate being
used.

Jackson and Troupe (1964) outlined a method for finding
E-NTU relationships using either an analog or digital com-
puter to solve the system of equations deve10ped by McKillop
and Dunkley (1960) with the additional assumption of a

constant heat transfer coefficient. The E-NTU relationships

10

for a given plate configuration could be obtained from the
computer program. These relationships can be used to pre-
dict the operating characteristics of an exchanger.

Lohrisch (196k) addressed himself to a fundamental
problem in plate heat exchanger design. Increasing the fluid
velocity increases the heat transfer coefficient but at the
same time increases the pressure drop. This results in an
economic trade off between heat transfer efficiency and power
required for operation. Lohrisch combined these factors into
a single equation which permits rapid determination of Opti-
mal pressure drop for each fluid for lowest operating cost.
Although designed for the shell and tube exchangers. the
method also applies to plate heat exchangers.

Wolf (196M) derived a general solution to the system of
differential equations describing the temperature distribu-
tion in fluids within the exchanger channels. The solutions
are given in a form which allows the introduction of boundary
conditions to modify the general case to conform to the par-
ticular exchanger of interest. Although elegant mathemat-
ically, the solution requires extensive matrix manipulations
before a particular solution is obtained. Settari (1972)
analyzed Wolf's mathematical model and concluded that one
of Wolf's basic assumptions is incorrect.

Crozier et al. (1969) extended Buonopane's method of
LMTD correction factors to viscous single phase liquids. A

viscous polymer solution was used in an experimental appara-

11

tus for determining the apprOpriate LMTD correction factor.
Results showed that equations presented by Metzner and Gluck
(1960) adequately predict individual heat transfer coeffi-
cients for viscous polymers and that a capillary rheogram

is useful in predicting pressure drop in the plate heat ex-
changer.

Jackson and Troupe (1964) found that under many condi-
tions, partibularly with viscous fluids, that laminar flow
exists in the exchanger channels. Using water and corn
syrup a laminar flow correction factor was determined to
allow the use of the LMTD method to evaluate heat exchanger
performance. It is necessary to experimentally determine
the correction factor for each flow configuration and fluid.

Flack (1964) described the general operating character-
istics of plate heat exchangers. In a comparison between
plate and shell and tube exchangers he concluded that in
places where expensive materials of construction are requir-
ed due to sanitary or corrosion requirements, the plate heat
exchanger is in general more economical. Smith (196h)
constructed a plastic prototype of a commercial model ex-
changer to study pressure drop characteristics. Entrance.
exit, crossover. and ribbed section pressure drops were
combined in an expression for overall pressure drop as a
function of fluid velocity for an exchanger with any number
0f plates and any fluids. Equations were developed for both

loop and series flow.

12

Nunge and Gill (1965) and Stein (1966) independently
obtained an analytical solution for laminar flow in counter-
flow plate heat exchangers. The solution required a gener-
alization of the Graetz solution for a single stream to the
case of two streams. The analysis requires knowledge of the
fluid velocity profile. Each author presented a different
method for evaluating the matrix of expansion coefficients
required for solution. Both methods, however, result in
similar solutions.

Pertsev (1968) considered the physical construction of
an exchanger. By analyzing the forces and deformations in
the plates and gaskets, a design procedure for the required
physical strength of an exchanger was developed. Tien and
Srinivason (1969) presented an approximate method to the
solution of counterflow plate heat exchangers. The approach
consists of using an integral approximation which reduces
the energy equations to a pair of first order differential
equations. While much simpler numerically than the Nunge
and Gill technique, it still requires the velocity distrib-
ution for solution of the problem. It therefore only ap-
plies to laminar flow situations.

Cocks (1969) described a computer program used by the
A.P.V. Company for selecting and designing a heat exchanger
for a particular situation. The program calculates the
minimum number of plates required to achieve a specified

performance and selects the flow arrangement for minimum

13

pressure drop. The selection of particular components is
made from standard stock sizes available. The total cost
of the unit is calculated by the computer program. No 0p-
erating costs are considered.

Settari and Venart (1970) proposed an approximate
solution to the system of linear first order differential
equations describing heat transfer in multi-channel parallel
and mixed flow plate heat exchangers by using second and
third degree polynomial approximations for the temperatures
in each stream. The method agrees with the analytical so-
lution for situations involving fluid and exchanger proper-
ties independent of temperature.

Marriott (1971) summarized all the important consider-
ations in the design of a plate heat exchanger. Operating
characteristics, pressure drop, pumping costs and fouling
problems are considered. Beverloo et al. (1972) investi-
gated the heat transfer rate and pressure drop in various
plate heat exchangers. The study determined the critical
velocity at which turbulent flow begins for each plate
design. Cattell (1972) applied laminar flow theory to
plate heat exchangers and the problems involved in the
analysis of the complicated flow patterns found in a plate
heat exchanger. Existing correlations for Newtonian flow
are presented and the implications of correction factors to

non-Newtonian fluids are considered.

1U

Conclusions

Although many investigations have been made on pre-
dicting the performance of particular design of plate heat
exhcangers. there does not exist a general simulation model
for the plate type heat exchanger. No sensitivity studies
have been made of the relative importance of the individual

design parameters.

THEORETICAL ANALYSIS

The heat transfer in a plate heat exchanger will be
analyzed making the following assumptions:
1. Steady state conditions exist within the exchanger

2. Heat is not conducted in the direction of fluid
flow by the plates or the fluid

3. Heat losses to the surroundings are negligible

h. Fluids exist only in liquid phase within the
exchanger '

5. No air pockets exist in the exchanger channels

6. The temperature and flow rate are uniform across
the channel width

The plate heat exchanger comes close to satisfying all the
conditions.

Several researchers (BuonOpane. 1963; McKillop and
Dunkley, 1960) have verified that steady state conditions
exist within an exchanger when the inlet fluid streams are
constant in temperature and flow rate. Constant monitoring
of fluid temperatures at several locations during test runs
verified that steady state conditions existed.

It is possible to treat heat transfer in the plate heat
exchanger as a one dimensional problem. The conduction heat
transfer through the fluid in the direction of flow is very
small. In most cases the thermal conductivity of the fluid

is low compared to the conductivity of the metal plates.

15

16

This low conductivity coupled with a small temperature
gradient in the direction of flow allows heat transfer
through the fluid in the direction of flow to be neglected.
Heat transfer through the plates in the direction of fluid
flow can also be neglected due to the small temperature
gradients in that direction.

The heat loss to the surroundings from the exchanger
are very small. The end plates of the exchanger are exposed
to dead air space at nearly the same temperature as the
fluids within the exchanger. The low convective heat trans-
fer coefficient of still air and the small difference in
temperatures result in small heat losses to the surrounding
environment from the end plates. In general. gaskets with
a low thermal conductivity, make up most of the exposed
surface of the side of a plate heat exchanger. The low
conductivity guarantees little heat will be lost from the
sides of the exchanger.

The fourth assumption could be relaxed if energy re-
quired for change of phase is included in the energy bal-
ances. In most cases, however, the plate heat exchanger is
not used for change of state processes because the narrow
plate gaps (and induced turbulence) results in appreciable
pressure drOps on the vapor side (Usher. 1970). Extremely
large ports are required to handle the large flow rates
required for vapor condensation.

Watson (1955) studied flow characteristics in a

Plexiglas model of a single channel heat exchanger. At low

1?

flow rates he occasionally found air pockets on the downflow
channel. The volume of the pocket was inversely prOportional
to the flow rate of the fluid. In general, no air pockets
are found in plate heat exchangers at normal operating con-
ditions.

The weakest assumption made in the analysis is the
uniformity of the temperature and velocity profiles across
the width of the channel. Watson (1955) found a channeling
effect around the edges of the plates. Although the short
circuiting fluid has a velocity higher and a temperature
lower than those of the mainstream, the volume of fluid and
the temperature and velocity difference involved are negli-
gible in relation to the total flow and heat transfer.

Applying the First Law of Thermodynamics to the control

volume shown in Figure 3 results in an equation of the form:

2
- = ' V
dQ dW ( 1 + 1? + gy ) (1)

No work is done on the control volume so dW = O. The veloc-
ity in any cross-section is assumed constant and the poten-
tial energy due to height differential is small in comparison
to the change in enthalpy. Equation (1) then reduces to:

do = di (2)
The only heat added to the control volume comes from the

fluids in adjacent channels. This may be expressed as:

dQ = Un-l ( Tn - Tn-i ) z dx + Un ( T - Tn+1 ) 2 dx (3)

n

18

n-2 n-1 n n+1

 

A—-—‘p-—-7q

_{

dx

L // Tn ’/
Tn-l ! ----- up «I- dr / Tn+1
/

\
I
l\
l
V.
j,

 

 

 

 

n-l wn wn+1

 

 

 

 

 

 

 

 

_L__. d J ..J
a) a b—_—‘l

 

Figure 3: Control Volume Used to Derive the Energy Equation

 

19

For an incompressible fluid the change in enthalpy is ex-
pressed as:

d1 = cnwndTn (h)
Substituting Equations (3) and (h) in Equation (2) and re-
arranging results in the differential equation describing

heat transfer in one channel:

dTn_ z
fif-W(Un-1(Tn-Tn-1)+Un(Tn-T

)) (5)

n+1
Application of Equation (5) to a plate heat exchanger results
in a system of n simultanious equations when there are n+1
plates in the exchanger.
Denote the fluid flowing in the channel between plates
n and n-1 as the primary fluid and the fluid flowing in the
channels between plates n-1 and n-2 and plates n+1 and n as
the secondary fluid. The distinction between fluids is nec-
essary when considering the overall heat transfer coefficient.
The overall heat transfer coefficient for plate n can be

expressed as:

l. = l. .1. E _l_. l.
U h+h +k+h +h (6)
n 8 fs f0 p

A pictorial representation of the heat transfer across a
plate as reflected by Equation (6) is shown in Figure h.
For turbulent flow the convective heat transfer coefficients
are correlated by:
Nu = p Req Prr (<fifl2m)s (7)
Icahn”

Typical values for the constants for various plate designs

are (Marriott, 1971):

20

x

 

L

hs

Secondary

Primary
Fluid

Fluid

 

 

-—-----—-—-—-

23‘

L— Foul ing —J
h

f8 hfp

Figure U: Mechanism of Heat Transfer Across a Plate

21

p = .15 to .40
q = .65 to .85
r = .30 to obs

s = .05 to .20

For most fluids the change in viscosity due to the
temperature difference between the wall and the center of
the channel is fairly small. Equation (7) can than be

written as:

%=P‘%>“<%’r ‘8’

The equivalent diameter. D in Equation (8) is defined as

e.
twice the width between plates. Troupe et al. (1959) ar—
rived at this expression based on the fact that channel width
is very much smaller than plate width (b z). Using this

relationship and solving Equation (8) for h results in:
= k 2wb CA2.
Combining Equations (6) and (9) gives the overall heat trans-

fer coefficient. Typical values for h are given in Appen-

f
dix A.
Applying Equations (5), (6) and (9) to the exchanger

shown in Figure 5 results in the following system of

 

 

equations:
dT
__l = z ( U ( T - T ) ) (10)
dx c w 1 1 2
1 1
a}. _ 01 2 - 1 ) + u2 ( T2 - T3 ) ) (11)

°2w2

22

Figure 5: Schematic Representation of Plate Heat Exchanger
Used to Develop Differential Equations

 

 

 

 

 

 

 

 

 

"""""‘1
Semis” H I 1 +
I I I l x=L
I I
I I
I I
I I
T Y I +
T1 T2: T3 Tu:
I I
I I
I I .
I ' x=0
_: I

+
I
I
I
I

c... _. 4 Primary Fluid

23

 

 

dT

3;} = - czw ( U2 ( T3 - T2 ) + U3 - Tu ) ) (12)
3 3

dTu _ z

3;. - - Cuwu ( U3 ( '1‘,+ - T3 ) ) (13)

where 01' U2,

boundary conditions are:

and U3 are defined by Equation (6). The

At x = 0

T1=T3

Tu is given
At x = L

T2=Tu

T1 is given
The main difference of the above system of equations

and those deve10ped by McKillop and Dunkley (1960) is the
latter researchers assumed an average overall heat transfer
coefficient. This implies that all fluid prOperties are
independent of temperature. In actuality, great variation
from the average overall coefficient occurs in the plate

heat exchanger with series type flow patterns at equal flow

rates of both fluids (BuonOpane. 1963).

NUMERICAL SOLUTION

Standard numerical techniques such as Runge-Kutta or
predictor-corrector methods can be used to solve differen-
tial equations. These methods require transforming the
problem into an initial value problem since only the inlet
temperatures of the primary and secondary streams are known.
Difficulties soon arise since not all initial conditions
associated with the return streams are known.

Optimization techniques, entailing an appropriate ob-
jective function, provide an efficient method for deter-
mining the initial conditions. Aoki (1967) and Gue and
Thomas (1968) presented several algorithms for finding the
minimum of a function. The minimization of an objective
function. which reflects the difference in temperatures in
alternate channels and the difference between temperatures
at the ports and inlet temperatures, yields the initial
conditions for a system of simultanious differential
equations representing the plate heat exchanger.

A Fortran IV computer program has been written to model
the exchanger. The program can be used to compute the temp-
erature profiles for exchangers of any number of plates for
either concurrent or counterflow flow patterns. Fluid

properties as a function of temperature can be included for

2h

25

any fluid of interest, including non-Newtonian. Experi-
mentally determined equations for the convective heat
transfer coefficient can be included for each particular
plate design. A flow diagram of the program is shown in
Figure 6.

The Operation of the computer program requires the
following data:

1. Number, length, width, thickness and thermal
conductivity of plate

2. Channel thickness

3. Inlet temperatures and flow rates of fluids

4. Locations of entrance and exit ports

5. Fouling factors.
Given the data, the program searches for the initial condi—
tions required to minimize the objective function. The
speed of the program is highly dependent on the search
algorithm and the objective function used. Once a solution
has been reached the temperature profile of each channel as

a function of distance along the plate in the direction of

flow is printed out.

26

Figure 6:
Simulation Program

 

 

’Read and Print Input Data]

 

 

 

 

Determine flow direction in each
channel based on
location of parts

 

 

 

 

 

Set up initial estimated temper-
ature distribution at
x=0 in the exchanger

 

 

Simplified Flow Chart for

Plate Heat Exchanger

 

 

 

 

 

Calculate temperature in each
channel at every location
Adams-Moulton method

 

 

 

 

 

Evaluate objective function

a. Temperatures at inlet ports
equal to inlet temperatures

b. Temperatures in alternate
channels must have equal
temperatures

 

 

 
 

 
 
   
 

 
 

Is objective
function within desired
accuracy?

 

No

Yes

 

 

Print temperature distribution
within channels at
desired locations

 

 

 

Replace initial temper-
atures with the pro-
posed new values

 

 

 

 

Search for new initial
temperatures to mini-
mize objective
function

 

 

 

 

 

EXPERIMENTAL VERSUS SIMULATED RESULTS

The theoretical model was compared to experimental
results of Buonopane (1963). The characteristics of the
plate heat exchanger used in the experiments of Buonopane

were the followings

Plate material 316 SS
Plate thickness .0033 ft
Width (between gaskets) .588 ft
Channel width .0117 ft
Heat transfer area 1.53 ft2
Heat exchange media water-water

The experimental and simulated outlet fluid temperatures are
compared in Table 1.

The agreement between the experimental and the simulated
results is good. The maximum percentage error is 2.“. It
appears that the theoretical model overestimates the amount
of heat transfer. This indicated that the overall heat
transfer coefficient was too high. The simulated results
were determined assuming no fouling occurred. Neglecting
the fouling and the uncertainty of the thermal conductivity
of the plates accounts for the high heat transfer coeffi-

cient.

2?

28

 

Table 1: Comparison of Experimental and Simulated Results

Simulated

Experimental Temperatures Temperatures

Number Flow Rate Hot Cold Hot Cold
of Plates 459;, Cold In Out In Out Out Out

7 6801 2995 184.8 138.3 56.5 160.1 136.4 163.5

9 3429 3367 187.5 98.4 56.8 146.9 95.7 148.3

9 6083 3061 180.9 125.9 54.6 163.5 127.1 165.9

11 5294 2608 181.5 124.5 57.0 171.6 123.3 174.2

13 3054 3007 173.5 83.3 57.1 147.5 81.2 151.2

15 4535 2247 175.5 117.5 56.3 171.6 117.4 173.5

19 2682 2617 179.3 77.5 58.0 161.1 75.9 164.5

19 2961 1896 185.3 107.4 59.0 181.4 106.2 182.9

 

 

 

SENSITIVITY STUDY

To illustrate a practical application of the plate heat
exchanger computer program, a set of typical operating condi-
tions was chosen and the sensitivity of exchanger performance
to variations in these parameters was explored. A method for
comparing the performance of various heat exchangers develop-
ed by Kays and London (1958) was employed.

The thermal capacity of a fluid, C, is defined as the
fluid flow rate times the specific heat of the fluid (C = we).
It gives an indication of how much heat a fluid stream can
absorb under certain conditions. Two possible limiting
cases of performance exist for all heat exchangers: (1) the
thermal capacity of the hot fluid is greater than that of
the cold fluid, and (2) the thermal capacity of the cold
fluid is greater than that of the hot fluid. In an exchanger
the temperature of the fluid with the smaller capacity will
asymptotically approach the temperature of the fluid with
the greater thermal capacity. The maximum temperature rise
reflects the maximum heat transfer. The theoretical limit

on heat transfer is given by:

Qmax = Cmin ( Thot in ' Tcold in ) (1“)

where Cmin is the smaller of the thermal capacities of the

two fluids.

29

30

A measure of performance of a heat exchanger is the
ratio of actual heat transfer to the theoretical maximum
heat transfer that could occur. This ratio, as shown in
Equation (18), is called the heat transfer effectiveness.

C T , T
E = hot hot in - hot out 1 (18)

I

min ( Thot in ‘ Tcold in )
The f01lowing sections use the heat transfer effective-

ness as a means of evaluating the effect on performance due
to changing a particular design parameter. Table 2 summa-

rizes the results of the parameter study.
Standard Conditions and Results

Conditions similar to those used by Buonopane (1963) in
his experimental studies were selected as standard conditions.
The standard exchanger characteristics and fluid inlet condi-

tions were as follows:

Number of plates ‘ 11

Heat transfer area 1.5 ft2

Plate thickness .0033 ft

Channel thickness .0117 ft

Thermal conductivity of plate 10 Btu/hr ft F

Hot fluid inlet temperature 180 F

Cold fluid inlet temperature 60 F

Hot fluid flow rate uooo lb/hr

Cold fluid flow rate #000 lb/hr

Type of flow counterflow, series

Type of heat exchanger water-water

31.

 

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shah ac:

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32

 

Hot Inlet
\
175 - \
\
\
\
\
\
\
ltk ‘
\ ‘———-----———
\
\ \
CI: \ \
. \ \
——"""' \
g \ \
3 125 ' \ \
a \
n \ \
° \
p. \
S \ \
o \ ————-0—--__
B \
‘ \
100 - \ \
\
\
x -—>
\
\
\
75 b \
\
\ Cold Inlet
50 L 1 1 _4, 1 1 1 I 4 1
1 2 3 b 5 6 7 8 9 10
Channel
Figure 7: Temperature Profiles for Standard Conditions

 

32

 

Hot Inlet
\
175 - \
\
\
\
\
\
\
ltk \
\ ‘——----————
\
\ \
fi‘ \
o. ________________ \
\
E \ \
3 125 » \ \
a \ \
“ \
3. ‘ \
s \ \
0 \ ____._..-..___._
e: \
‘ \
100 - \ \
\
\
. —+
\
\
\
75 - \
\
\ Cold Inlet
50 n 1 1 } l I l I 1 L
1 2 3 b 5 6 7 8 9 10
Channel
Figure 7: Temperature Profiles for Standard Conditions

33

In Figure 7 the fluid temperatures as a function of
location are plotted for the standard conditions. The heat
transfer effectiveness of .765 for the standard conditions

represents a typical value for plate heat exchangers.

Effect of fluid properties

 

Treating fluid prOperties as independent of temperature
does not significantly affect the results of the model.
Identical exchangers were simulated, in one case with fluid
density, conductivity, viscosity and Specific heat as func-
tions of temperature and again with prOperties at constant
values determined by the mean of the hot and cOld stream
inlet temperatures. In all cases studied the outlet temp-
eratures agreed within 1.35 F. The remaining runs for the
sensitivity study assumed constant fluid properties. The
validity of this approach for fluids other than water has

not been proved.

Effect of changing inlet temperature of fluids

The fluid properties can be considered independent of
temperature: therefore. the convective heat transfer coeffi-
cient is a function only of fluid velocity. Thus, the over-
all heat transfer coefficient is constant (independent of
temperature). This implies that the effectiveness is not
dependent on the absolute values but on the difference be-

tween the hot and cold fluid inlet temperatures. Therefore

34

a 20 F change in inlet temperature will result in a 4.70 F
change (.765 effectiveness) in the outlet temperature.
Figure 8 illustrates the linear relationship between inlet
and outlet hot fluid temperatures. Figure 9 shows that a
decrease in the cold stream inlet temperature also produces

a linear change in the cold stream outlet temperature.
Effect of fluid flow rate

Equal flow rates for the hot and cold fluids are the
most ineffective from a heat transfer standpoint. The
effect on exchanger effectiveness of changing the hot fluid
flow rate above and below the cold fluid flow rate is illus-
trated in Figure 10. The highest effectiveness is obtained
when the hot fluid flow rate is either much higher or much
lower than the cold fluid flow rate. Although the heat
transfer effectivenss might be high in both cases, the
actual heat exchanger performance is much different.

A .900 effectiveness obtained with a high hot fluid
flow rate will cool the hot fluid from 180 F to 125 F. The
high effectiveness is reflected in the fact that most of the
cooling capacity of the cold fluid has been utilized. Using
a low hot fluid flow rate can also result in a .900 effect-
iveness. The outlet temperature of the hot fluid is 75 F,
50 F cooler than in the other exchanger with the same ef-
fectiveness. The high effectiveness at the low hot fluid
flow rate is due to the fact that most of the available heat

from the hot fluid is removed. Heat transfer effectiveness.

35

100 '-

95r

85..

Outlet Temperature, Hot Fluid, F

 

75 1 l 1 l L
120 140 160 180 200 220

Inlet Temperature, Hot Fluid, F

Figure 8: Variation of Hot Fluid Outlet Temperature as a
Function of Hot Fluid Inlet Temperature

120

110

Hot Fluid Outlet Temperature, F

Figure 9:

100

90

80

70

60

36

 

l 1 L

I
20 40 60 80 100

 

Cold Fluid Inlet Temperature, F

Hot Fluid Outlet Temperature as a Function of Cold
Fluid Inlet Temperature

37

 

 

1.00 -
e 95 1'
m
0)
g 090 '
0
>
«H
4.)
0
0
2:
m .85 1-
$4
0
L:
U)
I:
d
e‘.‘
.80 .
.p
d
0
£1:
.75 -
070 | l I __L__
0 2000 (+000 6000 8000

Hot Fluid Flow Rate, lb/hr

Figure 10: Variation of Heat Transfer Effectiveness as a
Function of Hot Fluid Flow Rate

38

therefore, is a measure of the efficiency of an exchanger
but not a measure of the ability of an exchanger to do a
Specified job.

Changing the flow rates of the cold fluid while holding
the hot fluid flow rate constant showed similar results with

the most inefficient operation at equal flow rates.
Effect of heat transfer area

The effect of the surface area of the plates on the heat
transfer effectiveness is very difficult to determine due to
the many factors involved. In reality a change in the size
of the plates also requires a change in the thickness of the
plate. It would also require a study of the proper width to
height ratio. In this study the effect of changing the plate
surface area with a constant width to height ratio of .23 and
a constant plate thickness was evaluated.

A slight increase in effectivenss as illustrated in
Figure 11 was shown by increasing the heat transfer area from
.5 to 2.5 ft2 per plate. The increase in effectiveness was
due to the increased area for heat transfer. The increase
‘was damped, however, by the lower fluid velocities resulting
in a lower convective heat transfer coefficient. This ac-
counts for the non-linear increase in effectiveness and
illustrates the fact that doubling the heat transfer area

does not double the heat transfer.

39

.78

e

\7

O\
I

Heat Transfer Effectiveness
i:
4:-

.71

 

0.0 0.5 100 105 200 205

Heat Transfer Area, ft 2

Figure 11: Variation of Heat Transfer Effectiveness as a
Function of Heat Transfer Area

40

ffect of plate thickness

Plate thickness is a relatively important parameter in
plate heat exchanger design.

Variation of plate thickness within practical limits
can change heat transfer effectiveness from less than .700
to almost .780 as shown in Figure 12.

Although it appears from the figure that there exists a
linear relationship between effectiveness and plate thick-
ness, the effectiveness should increase at a faster rate as
the plate thickness decreases due to the nonlinear relation-
ship between the overall heat transfer coefficient and plate
thickness. The apparent linearity is due to the search
routine in the computer program reaching slightly different
ending criteria and the extremely small deviation from lin-
earity. This change is due to the resistance of the plate
to conductive heat transfer. A thicker plate is required
when large pressure differentials across the plates exist.
Determining the optimum plate thickness represents a trade-

off between heat transfer effectiveness and plate strength.
Effect of chagpel thickness

In a plate heat exchanger the channel thickness is
determined by the gasket size and the amount of pressure
with which the plates are compressed. The channel thickness
is critical in determining the fluid velocity. This in turn
greatly influences the convective heat transfer coefficient

and the residence time in the exchanger.

41

 

 

em)-
.78)‘

Q

Q

8 .76:-

O

F

0H

9

O

0

6..

'H

w .w-

h

0

$4

a

L".

G

‘4

E4

p 0.2%

d

0

'11
.73“
O$ L L 1 j 4
.0000 .0025 .0050 .0075 .0100 .0125

Plate Thickness, ft

Figure 12: Variation of Heat Transfer Effectiveness Due to
Changes in Plate Thickness

42

Figure 13 shows how important this parameter is in
determining the heat transfer effectiveness of an exchanger.
The relationship between channel thickness and effectiveness
is non-linear. The channel thickness determines the fluid
velocity which in turn is a non-linear parameter of the
convective heat transfer coefficient. The overall heat
transfer coefficient is a non-linear function of channel
thickness, therefore, the effectiveness is also non-linear.
As can be seen in Table 2 a change in channel thickness from
.005 to .030 ft increases the temperature of the outlet hot
fluid by more than 15 F.

Effect of plate thermal conductivity

The thermal conductivity of the plate is not a critical
factor in heat exchanger performance. Increasing the thermal
conductivity from 6 to 30 Btu/hr ft F, an increase of five
hundred percent, only increased the effectiveness from .744
to .783. The rise in material cost required to get the high
conductivity is not justified by the small increase in ef-

fectiveness.

Heat Transfer Effectiveness

43

.80.-

070 '

065 1 1 4 L L I

 

 

.000 .005 .010 .015 .020 .025 .030
Channel Thickness, ft

Figure 13: Effect of Channel Thickness on Heat Transfer
Effectiveness

SUMMARY

The primary goal of this study, the development of an
algorithm for the design and analysis of a plate heat ex-
changer has been achieved. The accuracy of the model was
demonstrated by comparison to experimental data.

The computer model was used in a parameter study of
those design factors affecting the performance of plate heat
exchangers. Fluid flow rates, channel thickness and plate
thickness were found to have significant influence on heat

transfer effectiveness.

44

SUGGESTIONS FOR FURTHER STUDY

The following suggestions for the use and improvement

of the model are in order:

1.

2.

3.

The Speed of the algorithm for determining the
initial conditions is highly dependent on the
objective function and search technique. Invest-
igation of various combinations of objective
function and search technique will greatly in-
crease the speed of the model.

The model, as presently programmed, is for series
flow only. The model should be expanded to in-
clude parallel and looped flow configurations.

The use of plate heat exchangers for viscous
fluids is expanding. The development of equa-
tions for fluid properties and heat transfer for
viscous fluids will extend the use of the model
to non-Newtonian fluids.

The parameter study indicated that maximum heat
exchanger effectiveness does not occur at equal
fluid flow rates. Optimization techniques should
be applied to find the most efficient flow rate
for a given job requirement.

45

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Indgfitrial and Engineering Chemistry: 15, 1,
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Beverloo, W. A. Hermans, W. F., and Muntjewerf, A. K.
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Perry, R. L. (1951). Factors influencing the performance of
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Institute of Chemical Engineering Journal: ‘15, 1,

39-46.

Troupe, R., Morgan, J., and Prifti, J. (1959). The plate
heat exchanger - versatile chemical engineering
tool. Northeastern University Publication.
Boston, Massachusetts.

Usher, J. D. (1970). Evaluating plate heat exchangers.
Chemical Engineering: 3: 90-94.

Watson, E. L. (1955). Certain flow characteristics in a
plate heat exchanger. Thesis for degree of M.S.,
University of California, Davis, California.

Wolf, J. (1964). General solution of the equations of
parallel - flow multi-channel heat exchangers.
International Journal of Heat and Mass Transfer:

1! 8’ 901‘918-

APPENDIX

Typical Fouling Factors (Marriot, 1971)

Fluid £921ing_fagi2r.x.lQ:E_BInZSa—II—E—hr

 

Water
Distilled 10.0
Towns (soft) 5.0
Towns (hard) 2.0
Cooling tower (treated) 2.5
Sea (coastal) or estuary 2.0
Sea (ocean) 3.3
River, canal, borehole, etc. 2.0
Engine jacket 1.7
Oils,lubricating 2.0-5.0
Oils, vegetable 1.7..5.0
Solvents, organic 3.3-10.0
Steam 10.0
Process fluids, general . 1.7-10.0

49

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