HEAT TRANSFER ANALYSIS or A
, HEA'I‘ EXCHANGER PLATE

Thesis for the Dogma of M. Sc,
*efiLCiCAN STRTE {EELE’ERSETY
Syeci Abduiiah Hassan

1962

TH Es]. ‘
o“ :0.

(0.31, LIBRARY . E
‘ chigz‘t 3th ;
Universit) ,i

 

 

HEAT TRANSFER ANALYSIS OF A

HEAT EXCHANGER PLATE

BY

Syed Abdullah Hassan

AN ABSTRACT
Submitted to the Colleges of Agriculture and Engineering
of Michigan State University of Agriculture and

Applied Science in partial fulfillment of
the requirements for the degree of

MASTER OF SCIENCE
IN
AGRICULTURAL ENGINEERING

Department of Agricultural Engineering

Approval @Mh/ W! 74} 12, /7(_}

February 1962

ABSTRACT

Plate type heat exchangers are very widely used in the
dairy and other food industries because they offer flexi—
bility, high rates of heat transfer, compactness and sani-
tary operation.

The objective of this study was to investigate the
variations of overall heat transfer coefficients and the
temperatures over a single plate. Thirty-eight pairs of
thermocouples were soldered onto the plate surface to obtain
the data. Tests were conducted in the actual operating
conditions, with the test plate in the regenerator sec-
tion of a high—temperature short-time milk pasteurizer.
The flow rate of the milk through the entire unit was kept
nearly constant at an average value of 6920 lbs/hr.

Contours of the overall heat transfer coefficients and
the temperatures were plotted over the plate area. The
average local overall heat transfer coefficients were

observed to vary between 300—800 BTU/hr ft2 OF. The

average value for the plate was about 550 BTU/hr ft2 oF.
The variations of both the overall heat transfer coefficient

and the temperature were pronounced near the ports due to

converging and diverging flows. These contours suggested

that the velocity profiles were nearly identical along the
length of the plate.

The overall effectiveness of the regenerator unit was
calculated and was found to be 79%. This value though

slightly lower, is comparable to the reported value of 82%.

HEAT TRANSFER ANALYSIS OF A

HEAT EXCHANGER PLATE

BY

Syed Abdullah Hassan

A THESIS

Submitted to the Colleges of Agriculture and Engineering
of Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

MASTER OF SCIENCE
IN
AGRICULTURAL ENGINEERING

Department of Agricultural Engineering

February 1962

ii

ACKNOWLEDGMENTS

The author expresses his sincere gratitude to Dr. Carl
W. Hall for his able guidance, timely advice and personal
encouragement which made possible this study.

Grateful acknowledgement is due Dr. T. I. Hedrick
for providing facilities of the Michigan State Dairy
Plant, where this study was carried out. The advice and
guidance of Dr. G. M. Trout, Food Science and Prof. D. J.
Renwick of Mechanical Engineering is also appreciated. The
author is indebted to Erland Kondrup, Paul Cooper and Peter
Hansen of the dairy plant; James Cawood and his staff of
the Agricultural Engineering Research Laboratory for their
help and assistance in making these tests.

The writer is also thankful to Dr. Arthur W. Farrall,
Head, Agricultural Engineering Department for providing
funds and use of facilities of the department.

Sincere thanks are due Dr. and Mrs. E. 0. Anderson for
their moral support and interest extended to the author
during their stay in Pakistan and here in Connecticut.

Personal appreciation is extended to wonderful friends
like Ram Misra, Harris Gitlin, and Gad Hetsroni for valua-
ble help at various stages.

Last but not least, deepest gratitude is expressed to
my father, Syed Mohsin Bokhari, whose inspiration for
knowledge influenced the writer in coming to this country

to pursue higher education.

iii

TABLE OF CONTENTS

Page
Summary . . . . . . . . . . . . . . . . . . . . . 1
Introduction . . . . . . . . . . . . . . . . . . . 3
Objectives . . . . . . . . . . . . . . . . . . . . 6
Review of Literature . . . . . . . . . . . . . . . 7
Presentation of Key Equation . . . . . . . . . . . 13
Equipment and Instrumentation . . . . . . . . . . 20
Procedure . . . . . . . . . . . . . . . . . . . . 29
Results and Discussion . . . . . . . . . . . . . 35
Conclusions . . . . . . . . . . . . . . . . . . . 50
Recommendations for Future Study . . . . . . . . . 51
References . . . . . . . . . . . . . . . . . . . . 52

Appendix . . . . . . . . . . . . . ... . . . . . . 54

LIST OF FIGURES

l. The advisor Dr. Carl W. Hall and the author

2. Schematic view of the test plate showing flow
arrangement . . . . . . . . . . . . . . . .

3. General view of the pasteurizing equipment
4. Flow diagram of the regenerator unit .
5. Test plate with thermocouples . . . .

6. Detail of the test plate at hot milk outlet
port

7. Detail of the test plate at the cold milk
inlet port . . . . . . . . . . . . . . . .

8. Thermocouple locations on test plate
9. Leeds & Northrup precision potentiometer

lO. Arrangement of thermocouple leads and the
switches . . . . . . . .

ll. Potentiometer circuit

12. Representative heat transfer areas for
thermocouples . . . . . . . . . .

13. Temperature distribution on the plate surface
(hot side) . . . . . . . . . . . . . . . . .

14. Temperature distribution on the plate surface
(cold side) . . . . . . . . . . .

15. U—plot on the test plate for group I

16. U—plot on the test plate for group II

iv

Page

13
19
21

23

24

24
26

30

3O

32

34

34

37
38

39

S UMMA RY

One of the gasketed plates from the regenerator section
of a milk pasteurizer was used as a test plate. Seventy—
six thermocouples, forming thirty-eight sets, were soldered
to the plate in a pre—determined configuration. Local
temperature differences across the plate wall were measured
by these sets. Moreover, four thermocouples, one in each
port, were placed to measure inlet and outlet temperatures
of the hot and cold milk streams.

The local values of the overall heat transfer coeffi-
cients were calculated for each of the twenty tests per-
formed. The averaged local values were found to occur in

the range 300-800 BTU/hr ft2 OF. The average value for the

plate was about 550 BTU/hr ft2 OF.

Contours of the overall heat transfer coefficients and
the wall temperatures were plotted over the plate area.
From these contours it was observed that the wall tempera-
tures remained fairly constant along the width of the plate.
The wall temperature along the length of the plate varied
in a straight line. Effect of local conduction of heat
from the main hot milk stream to the plate was noticed near

the hot milk inlet port. This resulted in higher temperatures

in the vicinity of the port.

The overall heat transfer coefficients were observed to
be higher in the middle of the plate than near the edge of
the corrugations. Here again, effect of local conduction
was observed. The overall heat transfer coefficients varied
little along the length of the plate.

The contours of temperature and overall heat transfer
coefficients suggested velocity profiles identical to those

obtained by previous investigations.

INTRODUCTION

Since the beginning of time, mankind has been con—
fronted with an inevitable need for heat energy, to keep
warm and to process raw materials. In the early stages
of life the needs were simple and few, allowing for the
direct exposure of the heat source. As the need became
varied and more intricate it became necessary to build
a device which would allow the heat to pass from the source
to the heated media by indirect methods, so that the un-
desirable gases of combustion could be avoided. This de-
vice is called a heat-exchanger.

There are numerous versions of heat-exchangers in use
today. Most of these are connected, in one way or another,
with the shell—tube type. Appreciable amount of research
has been done with this type and a wealth of information
is reported and available in any standard book on the
subject.

In recent years the popularity of portable gas-turbine
prime-movers enthused researchers to design a heat-
exchanger which in addition to being light, should be com-
pact and have high efficiency of performance. This was

further backed by the standing demand of the dairy and other

food industries for a flexible heat-exchange device, so
that different heat-exchange surfaces could be obtained
from the same equipment, depending upon the processing load.

Plate type heat-exchangers met the requirements for
weight, compactness and flexibility. Despite their failure
to qualify for use with the gas-turbine prime—movers,
because of the limitation in standing high temperatures
and pressures, they have been readily accepted in dairy
and other food industries.

A plate heat-exchanger consists, essentially, of
rectangular plates which are designed to form narrow
rectangular flow passages when pressed together. Higher
heat transfer efficiency is achieved by corrugations on the
plate which cause turbulence at a markedly small Reynolds'
number.

Although extensively used, surprisingly little work
is reported with this type of exchanger. The main objec-
tive of the study was to obtain basic information on the
overall heat transfer coefficients based on a single plate.

It is hoped that the findings of the investigation will
prove helpful in more economical use of the plate type heat—

exchangers.

 

 

The author

1:“: r-n-nrn 1

OBJECTIVES

The objective of this study was to determine the
local overall heat transfer coefficients on a Single plate,
and to plot their values along the entire heat-exchange
surface. Underlying interest was twofold:

1. To investigate the effectiveness of the heat
exchange area with the present design. This
involved determining U—values and temperatures
over the area of the plate.

2. To compare the results with the fluid flow anal-

ysis of previous investigators.

REVIEW OF LITERATURE

The earliest known patent on a device similar to the
plate heat exchanger was obtained in Germany in 1878 (9).*
However, the credit for the conventional design accepted
and in use today is generally given to an Englishman, Dr.
Richard Saligman, for his invention in 1923 (17).

A plate type heat—exchange unit consists of rectangular
metallic plates assembled face to face. The plates are
usually pressed out of stainless steel sheets, though
materials such as Hastelloy C, titanium and cupronickel
are also in use (9, 14).

The plates have corrugations called turbulence promoters
formed on the surface, with the finer design details varying
from one manufacturer to the other. These corrugations,
in addition to creating turbulence at Reynolds' numbers
as low as 180-200, add considerably to the plate strength
(7, 9, 14). The high degree of turbulence gives a higher
rate of heat transfer. Overall heat transfer coefficients
in the range 600—750 are quite common (9, 11). The thickness
of plate range between 0.05 inch to 0.125 inch, depending

on the size of the plate.

*Number in parentheses refers to the references given
at the end.

Alternate plates are provided with rubber gaskets which
run all along the periphery of the plate. The gasket serves
two purposes: first, it separates the adjoining plates,
thus forming a flow passage having a predetermined width,
usually 3—5 mm and, secondly, it prevents leakage of the
flowing fluid. The rubber used for the gasket is treated
to make the surface polar (4), which helps make a stronger
bondage with stainless steel plate. The gaskets so far
used cannot stand temperatures and pressures higher than
300°F and 150 psig (4, 9, 14), which accounts for one of
the major shortcomings of plate exchangers. Use of Telfon
and some of the silicones should lead to improved gaskets
that can be exposed to temperatures and pressures higher
than the present maximum (14).

The plates are mounted on a metallic frame having guide
bars on top and bottom. These are pressed together in
position by a screw—plunger or hydraulic press. On the
same frame two or more heat—exchange units can be mounted.
In that case, a spacer-block or terminal is placed between
the two units. In the dairy industry, for pasteurizing
milk, it is customary to use three heat-exchange units
assembled on one frame. The units are called the regener—

ator, heater and cooler.

Each plate has four holes (or ports), two at the top
and two at the bottom. The gasket is designed to allow
opening of only two holes, one on either end, on each side
of the plate. These form inlet and outlet ports for the
flowing fluids. The flow pattern of the flowing fluid
depends entirely on the design of the gasket on each plate
and the relative position of these plates in the unit. The
fluids may have a single pass, a multiple pass or a divided
pass through the unit. A combination of the last two is a
more common practice.

The plate heat exchanger has gained tremendous popu-
larity in many industries in this decade, because it provides:

1. High rate of heat transfer at relatively small
velocities.

2. Flexibility in obtainable heat-exchange area.
3. Ease in cleaning, sterilization and inspection.

4. Lesser possibility of contamination, the unit being
totally enclosed.

5. Adaptability of the unit to more than one operation
at the same time.

6. Saving in space.
E. L. Watson _E.§l, (16) made extensive studies of
velocity flow patterns and pressure drop for various flow

rates using three sets of plates. Each set had a different

design of corrugations.

lO

Velocity profiles were determined by two methods:
motion pictures, and electrical conductivity tests. Motion
pictures were taken at flow rates of 1000, 1700 and 21p lbs/
hr per plate, of a dye solution as it displaced water in the
space between the plates. These pictures were analyzed to
obtain velocity profiles and locate air-pockets. The
electrical conductivity tests were made with 0.1%isodium-
chloride solution. Fastest and slowest particles, defined
in relative terms, were determined as the conducting salt
solution displaced tap water in the flow channels. Conduc-
tivity changes were recorded on a recording potentiometer.
The results from these two methods were found to be in fair
agreement.

Air pockets were found to exist in inverse ratio to the
flow rates. The existence of air pockets was found to
reduce useful heat—transfer area and cause greater pressure
drop, It also indicated a greater possibility of cook-on
or milkstone deposits which impair heat transfer and increase
cleaning difficulty, a fact supported by V. Mennicke (12).

The pressure drop studies by the same authors showed
that for the same overall heat transfer coefficient the
plate exchanger gave smaller pressure drop compared to a

shell-tube unit. It was also found that divided flow,

11

although it gave a smaller pressure drop as against mul-

tiple flow, resulted in lower heat transfer coefficients

because of lower velocities and higher probability of air
accumulation.

A. A. McKillop and W. L. Dunkley, continuing the above
study, investigated the heat transfer characteristics. Heat
transfer coefficients were calculated by two methods: mathe—
matical analysis and empirical correlation by McAdams (10).

The mathematical analysis was based on the energy
balance of the system. Each flow configuration yielded
several simultaneous equations which were solved with a
computer. Plots of overall heat transfer coefficient ver-
sus flow rates were made for each of the three units under
study. These values were found to be higher compared to
ones calculated with McAdam's correlation. This difference
was attributed to the turbulence promoters, since McAdam's
equation predicts coefficients for clear-channel flow.

V. Mennicke (12) investigated the performance of the
plate heat exchangers as related to:

1. Flow arrangement,

2. Fluid flow ratio,

3. Fluid velocities, and

4. Heat exchange area.

12

He observed that:

l. The efficiency was very nearly the same for a combina-
tion of parallel and counter flow situations having fewer
parallel flows, as of an all—counter flow arrangement.

2. The heat transfer increased in proportion to the increase
in flow ratio, up to a ratio of four, beyond which the
increase was significantly small.

3. The heat transfer improved linearly with increase of
fluid velocities. Film coefficient ”h" was related to
velocity, V, as h = C Vn, where C is a constant. For
the two flow configurations studied, the value of ex—
ponent n was found to be 0.814 for divided path of flow
and 0.736 for continuous path of flow, respectively.

4. The heat transfer area versus efficiency curve assumed
asymptotic trend beyond an area of three square meters

and an efficiency of 85%.

To the best knowledge of the author, no attempt has been
made to study the variation of the overall coefficient of
heat transfer on a single plate, which in fact has been
assumed constant (11). The sole objective of this study

was to measure and evaluate these variations.

13

PRESENTATION OF THE KEY EQUATION

The following assumptions were made for the analysis:

1. Steady state exists in the unit.

2 Specific heats of the flowing liquids are constant.

3. Heat conduction along the plate surface is negligible.
4

Bulk temperature change of both hot and cold milk stream
occurs in a straight line from inlet to outlet ports of
the plate.

5. The Velocities are nearly constant over a cross-section
of the plate along the length.

The test plate, at position "17” in regenerator section,
with hot and cold products flowing on either side is shown
schematically in Figure 2a. The flow is a combination of
counter and cross flows. Since the length of the plate is
large compared to width (44 in to 13 in), a counter flow
situation can be approximated. This assumption seems accept-
able for a major portion of the heat exchange surface except
near the ports.

With the above assumption the situation simplifies to

the one shown (side View) in Figure 2b.

 

 

 

 

 

 

,A’ F
cold
milk
cold
milk
hot hét
milk mllk
r"’ l 1
(b)

Figure 2

14

Let
th = entering temperature of hot milk OF
1
th = exit temperature of hot milk OF
2
tC = inlet temperature of cold milk OF
1
tC = outlet temperature of cold milk OF
2
X = thickness of the plate in ft (0.00365 ft as
measured)
k = thermal conductivity of the plate material (18—8
stainless steel 302 series) 9.4 BTU/hr ft OF
At: = temperature difference across the thickness of
plate. OF
A = area of heat exchange perpendicular to the
p direction of flow (projected area) ftZ
U = overall coefficient of heat transfer based on
p projected area. BTU/hr ft2 OF.
Ad = developed area of heat exchange. ft2
2 = any location on the plate.

At any location on the plate, heat transfer 02 equals:
Atp
Q=kA —-’ (1)
‘5 £913 X2

Since the plate has the same thickness throughout and

is made of uniform material,

k = k :k :
£1 22
X = XL = XE = and

15

A = A = t = therefore
i P X

For a situation where overall heat transfer coefficient
U is constant, specific heats of the fluids are constant and

the flow rate is constant, the heat transfer is given by
Q=UA At (3)
p m

Where Atm is the mean temperature difference or the
difference of the bulk temperatures of the fluids flowing
on the two sides. Since U value is not constant in our

case, the above equation was modified for local conditions.

Q = U A at ) '4
f, 2. P1} In! ( )
(Atm)£ being the difference of stream temperatures of
the hot and cold products at location.£.
Atz
E uations (2) and (4) ive U A (At ) = kA ——— .

EL is based on the projected area.

 

 

The above equation can be rearranged to the form

At
At
m

 

 

1:

Substituting proper values of k and X

16

Atm 0

M

U = 2575

 

Values of Atfl were taken from the pairs of thermocouples
connected across the plate thickness. (Atm)1i were obtained
from the local stream temperatures, calculated from the
inlet and outlet temperatures of the flowing liquids.

Inlet and outlet temperatures of hot and cold milk
flowing over the plate were measured by placing thermo—
couples in the center of the ports, Figure 5. At the hot
milk outlet port, milk coming from the adjacent plate mixed
with the local stream. The temperature of the mixture
recorded by the thermocouple was higher than actual, since
the mixing stream was at a higher temperature. This neces-
sitated correction of th2

The corrugations on the two plates forming a flow
channel are reversed in the assembly, thereby exposing the
flowing stream to continually varying widths of the channel.
This causes turbulence and mixing of the fluid at every
location on the plate. The temperature of the fluid stream,
therefore, remains approximately constant along the width
of the plate and changes along the length only. At the
same time, the temperature difference between the fluid and

the wall surface is nearly constant at a cross-section along

the width.

17

Temperature profiles, Figures 13 and 14 made from actual
tests for the hot and cold sides of the plate showed that
plate temperatures were nearly constant along the width of
the plate but changed in a straight line along the length.
The hottest and coldest plate temperatures were found to
occur near the inlet and outlet ports, respectively. Since
the plate temperature changes in a straight line along the
length, the fluid temperature also changes in the same pat-
tern but at a constant amount higher than the former.
Therefore the outlet temperature of the hot milk, thz, can
be assumed to be the same amount higher than the coldest
temperature of the plate wall as the inlet temperature is
from the hottest temperature of the plate.

Values of th2, corrected on this basis, are shown in
Table 1 (appendix). To counter check this, an additional
thermocouple was placed in the hot milk outlet port (Figure
6). It was placed at 1/8” from the port periphery. Tests
were performed under similar conditions. For an average
hot milk inlet temperature, th , of 117.7910F, the outlet

1
temperature measured by the second thermocouple was 79.000

0F. From Table 1 corrected values of th for th in the

o o 2 1
range 117 F - 118 F are shown.

18

 

 

Hot milk inlet

Corrected hot milk

 

Test no. temperature outlet temperature
t t
hl h2
l8 117.5300F 79.5410F
6 117.8750F 80.3010F
15 118.0220F 79.917°F

 

The corrected values of t

the measured one.

h

2

compare reasonably with

19

 

General View of the pasteurizing equipment

Figure 3.

20

EQUIPMENT AND INSTRUMENTATION

Facilities of the Michigan State University Dairy Plant
were used in carrying out this study. Tests were made with
the high-temperature short—time (HT-ST) milk pasteurizing
unit during actual operation.

The HT-ST pasteurizer is a plate type heat exchanger
having three heat—exchange units, namely, heater, regenera-
tor and cooler.

Raw milk is pumped by a positive displacement pump to
regenerator section where it is heated by hot pasteurized
milk. The regenerator section contains 29 plates, the
heater 13 plates and the cooler 13 plates. Flow diagram
for the regenerator section is shown in Figure 4.

The heated raw milk from regenerator flows into the
"heater” unit. Here it is further heated by hot water, to
pasteurizing temperature. This is then routed through a
vacuum chamber and homogenizer before it enters regenerator
section. Regeneration efficiency*of 80—82% is common under
normal working conditions.

Cold water is used to cool the pasteurized milk in the

"cooler" section.

*Defined on p. 35.

21

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22

This investigation was made with the test plate held at
position "17" in regenerator section. At this position hot
pasteurized milk flowed from bottom to top on one side and
cold raw milk from top to bottom on the other side of the
test plate.

Corrugations or the turbulence promotors on the plate
were segmental in shape and curved upward when assembled in
the unit. The plates immediately on either side of the
test plate had corrugations curving downward for greater

amounts of turbulence.

Instrumentation

A difficult part of instrumentation was placing

thermocouple junctions on the test plate. Various bonding
materials were tried for this purpose. Duco cement was
tried first, as it had the advantage of quick setting.
A 2-1/4” x 3—1/2" size sample piece was used for these
trials. Material of this piece was the same as the test
plate, i.e. 18—8 stainless steel of 302 series having no. 4
finish. The cement bond came off when heated to about 1200
F in a water bath.

Epoxy glue was also used with type ”E" hardener. The

manufacturer's recommended procedure for initial setting

23

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. \.
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1 a
1
i

:\

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A ‘ ‘
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Figure 7. Detail of the test plate at the cold milk inlet port

25

was followed. The bond seemed to be very strong at room
temperature. The test sample was heated to 1650F, the
temperature the bond could be exposed to in the pasteuri-
zing unit, and maintained at that temperature. In about
fifteen minutes the glue started peeling off and therefore
was rejected.

Chemical adhesives were not considered because of
sanitary reasons.

Finally stainless steel solder with a proper flux was
tried. The results were satisfactory.

Cu—constantan (1938 calibration; 24 B & S gage) thermo—
couples were used for measuring the temperatures. Thermo-
couple junctions were made by soldering the copper and
constantan wires on the surface of the plate. The thinness
of the plate prevented boring or indenting the plate at the
junctions. The fact that two junctions had to be placed
opposite to each other, across the thickness of the plate
made boring or indentation even more difficult.

The soldering was done with extreme care so as to keep
the junction thickness to a minimum.

Seventy-six thermocouples were soldered to the plate
forming 38 pairs. The positions of these sets were arranged

so as to get adequate information for plotting U-values.

26

42

m._.<.._n_

emu...

ZO wzo_.r<00.._ MIEDOOOZm w I...

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36'

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27

The width of the plate was divided into six equal parts
with five dividing lines. Thermocouple junctions were
placed on these lines at the alternate ridges along the
length of the plate. Near the entry and exit ports, how-
ever, junctions were placed on each ridge so as to better
investigate these areas of diverging and converging flows.
In addition, thermocouples 15—16 and 25-26 were also placed
one ridge apart to allow the desired arrangement of junc-
tions at the ports (see Figure 5).

Lead wires from a junction were run along the segmental
shape of the corrugation that the junction was in, and
taken out of the plate at the rubber gasket, nearest to
the edge of the corrugation. Masking tape was used to keep
them in place. All Cu leads were taken out at one end of
the plate while all constantan leads were removed at the
other end. This arrangement proved helpful in connecting
leads to the outside switches. One hundred sixty leads thus
obtained (seventy-six junctions on plate surface and four
at inlet and outlet ports of hot and cold milk) were con-
nected to adaptor switches, each taking eleven leads. The
adaptor switches were mounted on wooden platforms to avoid

contact with water.

28

Stream temperatures of incoming and outgoing milk both
on hot and cold sides were measured by placing copper con-
stantan thermocouples in the flow passage. The arrangement
used is shown in Figure 6.

A reflecting galvanometer type Ieeds and Northrup
precision potentiometer (no. 8686) was used for measuring
thermocouple outputs (Figure 9). A common ice bath reference
junction was used with the potentiometer. As such, the
manufacturer's indicated accuracy for the instrument was I
.05% of reading + 3 mv. The potentiometer could be read up
to one thousandth of a millivolt or approximately 0.050F.

The thermocouples were read manually. It took about
25 to 30 minutes to complete one cycle of readings.

The flow rate of the product through the heat exchanger
was measured by timing flow of a measured quantity through

the unit. This was repeated several times to check and

confirm the rates, which were kept constant.

29

PROCEDURE

Test plate with the thermocouples was placed in the

pasteurizing unit an evening before the working day. This
was done twice a week, on Tuesdays and Thursdays, to conform
with the production schedule of the Dairy Plant.

In the heat exchanger alternate plates were gasketed
with rubber overlapping both sides of the edges. One of
these gasketed plates was used as the test plate because of
the ease in taking out thermocouple leads.

The position of test plate was seventeenth in regener—
ator section counted from the heater end (see Figure 4), or
the ninth gasketed plate. This position was selected be-
cause of counter flow of milk and moderate temperatures.

General arrangement of the unit and the test equipment
is shown in Figure 3.

Before starting the test the temperatures were stabilized
at a constant value. This was done by measuring the tem-
perature of the incoming hot milk and outgoing cold milk
until two consecutive readings were coincident.

The potentiometer was standardized before, during, and

at the end of each test.

30

 

Figure 9. Leeds & NOrthrup precision potentiometer

 

Figure 10. Arrangement of thermocouple leads and the switches

31

At steady-state the test was started by measuring the
incoming and outgoing temperatures of hot and cold milk.
Next the plate thermocouples were read. This was done in
such a way as to read consecutively the thermocouples
soldered opposite to each other on the plate. This insured
better accuracy in measurement of the temperature difference
because the time elapsed was at a minimum. Plate thermo-
couples were numbered from 5 to 42 on the hot side and from
43 to 80 on the cold side. Thus, the order in which
thermocouples were read was 5, 43, 44, 6, 7, 45, 46, 8 . . .

The potentiometer circuit is shown in Figure 11. The
copper lead from ice bath was connected to the negative
terminal of the potentiometer, while the constantan lead
was soldered to an adapter plug which fits in the adapter
switch connected to thermocouple leads. Positive terminal
of the potentiometer was connected to another plug by a
copper wire.

The two plugs thus obtained were moved simultaneously
and plugged in similar numbered switches. The thermocouple
output was measured at the potentiometer and values in
millivolts were noted. At the same time the plugs were
moved to the next position. It took two persons to do the

job, one reading the potentiometer and the other changing

32

POTE NTIOMETER

 

 

 

 

 

 

 

 

 

- +
I I
- I
Cu
7 . f7 Cu
Q0
Cn *
REFERENCE '
JUNCTION

 

 

 

 

 

 

CONSTANTAN LEADS

COPPER LEADS
OF THERMOGOUPLES

OF THERMOOOU PLES

FIGURE II. POTENTIOMETER CIRCUIT

33

the plugs and noting the e.m.f. values. On the average,
one cycle of readings was completed in about twenty-five
minutes. During this time port temperatures were recorded
five times so as to give a more realistic average.

The flow rate of the product was determined by timing
the flow of a measured quantity through the heat exchanger.
Product was pumped through the unit by a positive displace-
ment pump running at a constant setting of speed. Flow
rate checked at six occasions during the study showed a
maximum variation of 1.5% from the average value of 6920
lbs/hr of the whole milk.

At the conclusion of each test the test plate was
removed from the press before the unit was cleaned by CIP
cleaning system. This was done to avoid damage to the
thermocouple junctions and leads, since temperatures and
velocities of cleaning solution were much higher than those
of the product. Soon after the plate was taken out of the
exchanger it was cleaned with alkali-base cleaning powder
with light brushing and finally washed thoroughly with
warm water. Before the plate was put back into the heat
exchanger, the thermocouples were checked for any damage
to the junction or insulation coating on the wires. The

wires were repaired or replaced, as needed.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' l
,,/’F4? \\\\ ,
”’I t“ 0-395 :
,x’ 0.395 49 I
36 ' 0.710
' 0790
0685 0.3%:
"620 '0-948 . 35
I-00 ‘
I-580 '
- r500
3| |°OO o
. I-OO ' so
I00
[500 I500
. I00
26 l-OO . ° 25
I-00 '
I-soo
2| ' Iooo I-5oo
I'OO o .20
I-00 ‘
I-500
. -——40948I l-500
us 0895 .
. I5
0843 .
I-340 ’
I-l85
632
' 0580 IO
N 0623 - ’
\ ' '°
I ' . ,”
; 7 290 Osfflr’
5 1"”

 

 

FIGURE l2. REPRESENTATIVE HEAT TRANSFER AREAS FOR THERMOCOUPLES

34

35

RESULTS AND DISCUSSION

Overall Effectiveness of the Regenerator Unit

The inlet and outlet temperatures of hot pasteurized
milk and cold raw milk, measured for the entire regenerator
unit, yielded an overall effectiveness of 79%. Since flow
rate was equal for both hot and cold streams, effectiveness,

E, of the regenerator was calculated using the formula

 

IAtI
c
E - t.h - tlc
l l
where
t'h = temperature of hot milk inlet, OF
1
t'C = temperature of cold milk inlet, OF
1
and At22= difference of inlet and outlet temperatures of

cold milk stream, 0F.

This is lower than the average value of 82% commonly
reported. This was attributed to the fact that the gasketed
plate no. 14 (Figure 4) was assembled incorrectly by the
operators, and allowed no flow on the two sides. This
resulted in a lower effectiveness of that particular pass
as well as a lower effectiveness for the entire unit. This

was corrected after the tests were concluded.

69m .55 MAO/imam w._.<I_n_ 20 ZO_._.Dm_m._.m_o map—ammasfik in. meGE

6
3

Dev AAW

 

O
O

 

 

 

 

5
9

 

0
8

75
I00
I05
IIO -

5
8 9

 

M.H-.m.n_l_oo :wo 3m m...< 202 7:0... :39 ....m_o mm:...< mun. 2w... .3 mmnwi

 

 

 

\ Veg: V:Vi AAA
,3 AA: AAA

0/5 _
020 _

 

 

.H gnome mo“. up; 5m: 20 5.5-: .9 MES:

 

sq VmUm/f /V\/
J K a.)

 

 

39

HH anomo mom wk<4m wa... ZO POJnTD .0. mmaol

 

 

 

 

40

Temperature Measurements on the Plate

Plate temperatures were measured on both hot and cold
sides as a part of the information required for calculating
local overall heat transfer coefficients, Ug.

Constant-temperature curves over the plate, i.e. iso—
therms, were plotted. It was observed that:

l. for main body of the heat exchange area, the temperatures,
in general, were approximately constant along the width
of the plate. Near the ports, however, the tempera-
tures varied because of converging and diverging flows.

2. along the length of the plate the temperatures varied in

a straight line.

Figures 13 and 14 show typical isotherm plots for hot

and cold sides, based on data from test 3.

Overall Heat Transfer Coefficients

Local overall heat transfer coefficients were calculated
from equation

U

2575 At
9. _ At

m K
using notations given on page 14.
Values of (Atmlt for different locations were calculated

, t ; and corrected values

from measured values of th , t c
2

1 C1
of th as discussed earlier.
2

41

A total of twenty tests were performed under similar
operating conditions, keeping the test plate at position
"17" from heater end, in the regenerator section.

A close examination of the data showed that for all the
tests the temperature differential (thl- tCl) remained
nearly constant (about 57oF). However, the data came into
two clearly defined groups based on the temperature in-
crease of the cold stream.

In group I average temperature increase of cold milk
was observed to be about l9oF while it was 27°F for group II.
This variation, though not clearly understood, could be
attributed to one or a combination of the following:

1. Change in flow ratio: as is evident from Figure 4,

at the test plate the theoretical flow ratio of hot and

cold milk should be 3:5. Deviation from this value

would be expected:

a) if air was entrapped in one or both of the streams.

More air accumulation has been reported by E. L.
Watson (16), in a divided pass. Same reference
observed that air pockets were formed on the down-
flow side of the plate, in inverse ratio to the flow
rate. The entrapped air and the air pockets would

tend to affect the mass flow rate and the local

42

velocities, thereby effecting the temperature rise
of the flowing fluid.

b) if milkstone was formed on the test plate or the
adjacent plates contained in that divided pass.
This would block the flow channels and cause vary-
ing velocities and pressure differentials.

c) if the unit was assembled with different pressures,
causing increase or decrease of the width of the

flow channels.
2. _Shift in heat balance at the plate.

It was assumed that the hot stream at the test plate
lost the same amount of heat to the adjacent cold stream
on right as the cold stream gained from the hot one on its
left. This was approximated, on the assumption that the
adjacent streams had identical temperatures. A deviation
from this would mean a shift in heat balance resulting in
more or less amount of heat gained by cold milk stream

than lost by the hot stream at the test plate.
3. Change in degree of turbulence.

Varying degrees of turbulence caused by variations of
milk deposits, air pockets, entrapped air, pressure differ-
ential, etc. would affect the amount of heat transferred

and hence the fluid temperatures.

43

The situation is very complex with no direct and de-
finite answer. Since no solid ground was available to
discard either set of the data, both were treated equally.

Using values of local Atm (mean difference of local
bulk temperatures), the local overall heat transfer coeffi-
cients (U2) were calculated. These are shown in Table 2
(Appendix).

Representative heat—exchange areas were allocated to each
thermocouple junction, Figure 12. A weighted average overall
heat transfer coefficient, UAv’ was calculated for each test.
The mean and the deviations of UAV were calculated separately
for groups I and II, as well as for all the twenty tests.
Results are summarized in Table 4 (Appendix). Means of UAV
for group I and group II were within 7% of each other.

These values were found to be within 15% of McKillop's
results (11). However, significant difference was observed
when compared to values predicted by McAdams' (10) or Peeples'
(l3) empirical correlations for clear channel flows.

The local overall coefficients were also averaged for each
of groups I and II. Values are tabulated in Table 3 (Appendix).
Comparison between the values for group I and II showed

that these were within 10% of each other for an area extend—

ing from thermocouple 17 to the hot milk exit port. This

44

was better than two-thirds of the entire plate area. Near

the hot milk inlet port, however, variations were high.

This is explained by the fact that local conduction of

heat from main stream of hot milk to the plate is signifi-

cant. This effect is clearly obvious from Figure 13, which

shows a rather abrupt rise in plate temperature near the

hot milk inlet port.

Figures 15 and 16 show contours of the overall heat

transfer coefficients for groups I and II, based on the

average local values.

A close study of these contours revealed several facts.
The average overall heat transfer coefficient varied
from 300—800 BTU/hr ft2 OF over the plate.

U-values were higher in the middle, at any cross-
section along the width, and decreased towards the
plate edge.

U—values were more uniform in the vicinity of the hot
milk inlet port compared to any other location. This
may be due to superimposed effect of the local conduction.
U—value variations were very small at cross-sections
along the length compared to cross-sections along the
width. This may be due to the fact that the fluid

velocities at any cross—section along the length remain

45

nearly constant but vany, somewhat, along the width of
the flow channel.

5. U—value variation is not large for the major part of the
heat exchange area, beyond the port vicinities. For
processes encountering very small temperature rise of
the fluids, like in heater section of a milk pasteurizer,
assumption of constant U for the plate is reasonably

accurate.

The contours of temperature and overall heat transfer
coefficients suggested that the flow velocity was uniform
in the middle of the plate and was somewhat higher compared
to the sides. Also it showed that the velocity at any
cross—section along the length was constant. This meant
that the velocity profile was similar all along the length
of the plate, except near the ports. This observation
agreed with the motion picture analysis of E. L. Watson

t 3;. (16) .

Sample Calculations

a) Overall effectiveness of the regenerator unit.
Since an equal amount of milk was flowing in hot and

cold streams, the effectiveness is given by:

46

 

At'c
E = t'h - t'c
l 1
Using the data from test 21,
t'h = temperature of hot milk entering the regenerator
l = 170.8800F.
t'h = temperature of hot milk leaving the regenerator
2 = 64.318°F.
t'C = temperature of cold milk entering the regenerator
l = 49.8180F.
t'C = temperature of cold milk leaving the regenerator
2 = 145.360°F.
At' = t' - t' = 145.360 - 49.818 = 95.5420F.
c c c
2 l
and t' — t' = 170.880 — 49.818 = 121.062OF.
h c
l l
_ 95.542 _ o
-- E ‘ 121.062 ‘ 79‘

b) The local overall heat transfer coefficients.

Using data obtained in test 3,

th = hot milk inlet temperature = 120.5000F
l

tC = cold milk inlet temperature = 64.273OF
l

tC = cold milk outlet temperature = 82.5220F
2

the hot milk outlet temperature th as measured in the test
2

did not give proper values because of mixing of the adjacent
hot milk streams. It was corrected as given below:

tw = hottest temperature of test plate near the

h hot milk inlet port = 112.217OF

47

t - t = 120.500 — 112.217 = 8.283OF
1 h

”-
ll

coldest temperature of the test plate near the
hot milk outlet = 74.045°F.

According to the assumption that the bulk temperature
of the hot stream at inlet and outlet ports is higher than

the plate temperature, by the same magnitude, corrected

value of th will be th = 74.045 + 8.283 = 82.328OF,
2 2 corrected
knowing
t I t , t , and t
h2 h1 1 C2
Atl = 120.500 - 82.522 = 37.9780F
At2 = 82.328 - 64.273 = 18.055°F
Atl — At2 = 37.978 - 18.055 = 19.923OF

Using the assumption that bulk temperatures of hot and
cold milk change in a straight line, the plate length is
divided into thirty—six equal parts. Each region represents
an inverval of 0.56OOF which is a f 1% change of average

bulk temperature difference.

A +
t1 Atz _ 37.978 + 18.055

2 _ 2

 

= 28.016OF

Thus the value of (Atm) in the first interval will be

fl
18.055 + QLEQQ' or 18.3350F, for second interval it will be

48

18.335 + 0.560 or 18.895°F; for third interval 18.335 + 2

(0.560) or 19.455°F and so on.

The local overall heat transfer coefficients are cal-

culated from equation

At
Uh — 2575 At
m 2

Using proper values of (At) and (Atm)2' we find U

E. 18

(overall heat transfer coefficient for location containing
thermocouple junction 18).
z = 18 comes under interval 24 counted from the hot

milk outlet end, (Atm)18 will therefore be

(At ) = 18.335 + 23 (0.560) = 31.2150F
m 18

At as measured by the pair of thermocouples soldered on

either sides of the plate at 18 is 9.0080F.

. _ (9.008) _ 2 o
U18 2575 61.215) — 743 BTU/hr ft F

This value has to be corrected for extension of thermo—
couple junctions into the flow.

Heat lost by milk on hot side equals

w c. At = §%§§ (O.92)(38.l72) = 48,000 BTU/hr

h p h

Q

also

Av eff m

where

At

Av

and

49

 

 

l ' 2 _ 37.978 - 18.055 _ o
Atl _ in 37.978 _ 26'74 F
1n 25 18.055

average overall heat transfer coefficient for

test 3 = 696 BTU/hr ft2 OF

2

— effective heat exchange area of plate = 3.273 ft

696 (3.273)(26.74) = 60,900 BTU/hr

Thus heat transfer calculated from surface thermo—

couples is higher than actual.

Correction factor =

48 000
_1___=
60,900 0.79.

This factor will be constant for each test.

2 o

f. Corrected U = 0.79 (743) = 587 BTU/hr ft F.

18

50
CONCLUSIONS

The overall effectiveness of the regenerator unit was
found to be 79%.

The plate—surface temperatures were seen to be fairly
constant along the plate width, except near the ports.
The local conduction of heat from main stream of hot
milk to the plate near the hot milk inlet port was
observed.

The wall temperature changed linearly along the length
of the plate.

The local overall heat transfer coefficients were found

to be between 300—800 BTU/hr ft2 OF. The average U—

value of plate was about 550 BTU/hr ft2 OF.

The contours of the overall heat transfer coefficient
showed the values to be higher in the middle of the
plate, decreasing gradually towards the plate edge.

The overall heat transfer coefficients were observed

to be reasonably constant along the length of the plate.
The overall heat transfer coefficient for the plate can
be assumed constant for processes encountering very
little temperature change of the flowing fluids between

inlet and outlet ports. This would apply to the heating

section of a plate heat exchanger.

51

RECOMMENDATIONS FOR FUTURE STUDY

Determine the effect of different flow rates on the
distribution of the overall heat transfer coefficients

over the plate.

Investigate the effect of port design, i.e. size and
center to center distance of the two ports on the same

end of plates, on the heat transfer characteristics.

Study the effect of plate dimensions on the heat

transfer.

52

REFERENCES
Anonymous
1955. Heat exchange conditions in plate type
pasteurizer. Dairy Engineering 72 (ll):
35.
Anonymous
1958. Improvements in and relating to plate type
heat exchanger. Dairy Engineering 75 (2):
62.
Anonymous

1958. Constructional details of a plate heat
exchanger. Dairy Engineering 75 (5):
137-139.

Anonymous
1954. Polarizing heat—exchanger gaskets. Dairy
Man 71 (10): 312.

Coulson, J. M. and Richardson, J. F.
1956. Chemical Engineering, Vol. I., 384 pp.
New York: McGraw-Hill Book Co.

 

Giese, H. and Bond, T. E.
1952. Plate heat exchanger design and construction.
Agricultural Engineering 33 (10): 617—622.

Goodman, H. F.,
1953. Some aspects of heat transfer in the plate
heat exchanger. Proceedings International
Dairy Congress 13 (3): 772-774. June.

Hansen, S. A., Wood, F. W. and Thornton, H. R.
1953. Some mechanical features of a plate—type
HT-ST pasteurizer. Canadian Journal of
Technology 31: 231—239.

Lawry, J. F.
1959. Plate type heat exchangers. Chemical
Engineering 66 (13): 89—94, June.

10.

ll.

12.

l3.

14.

15.

l6.

17.

53

McAdams , W. H.
1954. Heat Transmission. 3rd ed. New York:
McGraw-Hill Book Co.

McKillop, A. A. and Dunkley, W. L.
1960. Plate heat exchangers: heat transfer.
Industrial and Engineering Chemistry 52
(9): 740—744.

Mennicke, V. V.

1955. Wérmetechnische voraussetzungen und
forderungen fur den betricb von
plattenerhitzern fur milch. Fette Seifen
Anstrichmitted. 57 (4): 256—262.

Peeples, M. L.

1960. Forced convection heat transfer charac-
teristics of fluid milk products. Unpub-
lished Ph.D. thesis, Ohio State University,
January.

Troupe, R. A., Morgan, J. C. and Prifti, J.
1960. Plate heaters. Chemical Engineering
Progress 56 (1): 124—126.

Trout, G. M. and Hall, C. W.
1962. Pasteurization 9f Milk (in process).

 

Watson, E. L., McKillop, A. A., Dunkley, W. L. and
Perry, R, In
1960. Plate heat exchangers: flow character—
istics. Industrial and Engineering
Chemistry. 52 (9): 733-740.

Whitaker, J. R.
1947. Plate heat exchangers and their applica-
tions. Australian Journal of Dairy
Technology. 2 (3): 110-118, July-September.

APPENDIX

54

55

REYNOLDS' NUMBER CALCULATIONS

The corrugation design and the assembly of the plate
unit was such that it was not possible to measure accurately
the width of the flow channel. The difficulty was overcome
by filling, with water, the flow passage of chilled water in
the cooler unit. The cooler unit had plates exactly iden—
tical to the ones in the regenerator section. The water was
drained and measured. Volume of this water equalled that of
the six flow channels andtie approximately 2—3/4" diameter
x 9—7/8" long fluid passage. Since dimensions of plate area
were known, the average width of the flow channel was
calculated.

8,475 cc

Volume of water collected
= 517.5 cubic in

Volume of 2-3/4” dia. x _ 2 _ ,
9—7/8” long flow passage — n/4(2.75) (9.875)—58.7 cu in
Volume of six flow

= 517.5 - 58.7 = 458.8 cu in
channels

volume/flow channel = é§%*§' = 76.5 cu in

Average heat exchange _ .

length of plate — 38.5 in (measured)
Average area of cross-

, section of the flow _ 76.5 _ 1 987 . 2

'° channel perpendicular to 38.5 ° 1n
the direction of flow

56

Average width of plate 13.0 in (measured)

Average width of the _ 1.987 _ .
flow channel 7 13.0 O°l53 1“

 

Average flow rate 6,920 lbs/hr of whole milk

(measured)
6,920 _
— (8.6)(7.48) 107.5 cu ft/hr

 

The total flow of 107.5 cu ft/hr flows into five channels
on the hot side in the divided pass which contains position
"17" where the test—plate was inserted. While on the cold
side it flowed into three channels. Obviously Reynolds' num-
ber will be smaller for the hot side compared to the cold,
since more quantity of the product is flowing through the

latter. Considering the hot side only,

 

Flow rate/channel = lggLé = 21.5 cu ft/hr
Velocit throu h one channel = 21°5 - l 560 ft/h
y g 1.987/144 ' r

0.433 ft/sec

 

D
Reynolds' number (Re)is given by: Re = —%f!
where
4 _ ' _
D = hydraulic diameter = (area Of X section): 2.52 x 10 2ft
e wetted parameter

p = specific weight of whole milk = 64.3 lbs/cu ft
u = viscosity of whole milk = 1.423 centipoise

at lOOOF = 9.57 x 10-4 lbs/ft sec

_2
Reynolds' number = 42'52 X 10 )(64.3)(0.433) = 732

9.57 x 10"4

 

57

In plate heat exchangers turbulence is reported to occur
at 180-200 (7, 9, 14). Therefore the flow was turbulent on

both sides of the test plate for this investigation.

58

CALCULATION OF U FROM EMPIRICAL CORRELATION

Investigations of heat transfer in turbulent flow have

resulted in many semi—empirical correlations based on the

experimental results. Most of these are of the type
m n
Nu = C(Re) (Pr) (1)
where
hD . .
Nu = ]:'= Nusselt number, dimenSlonless
D . .
Re = _fiX. = Reynolds' number, dimenSlonless
uC
Pr = ‘E2' = Prandtl number, dimensionless
C = constant

and m, n = exponents
Values of C, m and n vary with each investigator.
Peeples, M. L. (13) studied the flow of whole milk

through a tubular heater and proposed the following equation

22': 0.27 R 0°577 Pr0°4 (2)
k e

Modifying this for rectangular channel (D=De), film
coefficients hh and hC (on hot and cold sides) can be

obtained. Then overall heat transfer coefficients is

calculated from

cIH
wlx

l
= —-+
h

+ ,1;— (3)
h c

59

a) Hot side of the plate:

+
Average bulk temperature of hot milk = ll§_§L = 100.00F
110+ 4
Average temperature of plate surface = ——§—Z- = 92.00F
00+
Average film temperature = l_3_22 = 96.00F

p = specific weight of whole milk

at 1000p 64.3 lbs/cu ft

C = heat capacity of whole milk

._ . /
at 1000F 0 92 BTU lb

"0
I

k = thermal conductivity of whole
milk at 10OOF

0.358 BTU/hr ft OF

u = viscosity of whole milk at 96oF 9.57 x 10.4 lbs/

 

 

 

ft sec
V = velocity of milk through the _ 0.433 ft/sec
channel (calculated)
D = hydraulic diameter = 2.52 x 10-2 ft
e
(calculated)
Substituting these values in equation (2)
_2 . _2 0.577 _4 0.4
!2.52x10 u _ /2.52x10 x64.3x0.433 \ ,9.57x10 x3600x0.92‘
hh‘ 0 358 ' _ 0'27K —4 ’ K 0 358
' ' 9.57x10 ’ ‘ '
or
0.27 45 2.39
hh = i )( )( 2 )= 413 BTU/hr ft2 OF

7.04 x 10‘

60

b) Cold side of the plate:
61 + 83 0

Average bulk temperature of cold milk = 2 = 77.0 F
100 + 70

Average temperature of plate surface = ———Er———'=85.OOF
+ 85

Average film temperature = ZZ_§———'= 81.00F

p = at 77oF = 64.3 lbs/cu ft
Cp = at 77oF = 0.93 BTU/1b
O O
k = at 77 F = 0.347 BTU/hr ft F
o -4
u = at 81 F = 11.4 x 10 lbs/ft-sec

V = 5/3(0.433) = 0.722 ft/sec

assuming flow ratio (Wh:WC) of 3:5 at the test plate

 

 

 

De = same as on hot side = 2.52 x 10'2 ft
2 2 (1577 4 0,4
2.52x16 2.52x16 x0.722x64.3 (11.7x16 x3600x0.93
h 0 347 = 0'27 -4 \ 0 347
C ' 11.7 x 10 '
or
hc = 0'27(53'8)(3564) = 528 BTU/hr ft2 OF
7.26 x 10
Therefore
1_= 1 + 0.00365 + 1
U 413 9.4 528
or
2 0

U 215 BTU/hr ft F

This is significantly smaller than the mean UAv
2

(550 BTU/hr ft OF) obtained in this study. This can be

61

attributed to the fact that the Peeples equation predicts

U values for clear channel flows only. Turbulence promoters
provided on the test plate create turbulence at relatively
small Reynolds' number (200 compared to 2100 for clear
flow). Therefore higher heat transfer rates are obtained

at comparatively smaller flow rates.

62

Table 1

. 0
Values of Hot Mllk Outlet Temperature F

 

 

 

Inlet temp: Hottest Coldest Corrected hot
Test of ho: milk plateO plateO milk ouglet
no. F temp: F temp: F temp: F
th th =
1 2
(A) (B) (C) c + (A-B)
8 115.875 107.708 68.909 77.076
7 115.875 104.957 69.261 80.179
9 116.304 106.130 68.409 78.583
11 116.565 105.833 66.227 76.959
12 117.083 105.000 66.136 78.219
10 117.125 106.043 66.955 78.037
4 117.167 109.458 72.818 80.527
18 117.530 109.250 71.261 79.541
6 117.875 109.791 72.217 80.301
15 118.022 107.583 69.478 79.917
14 118.168 108.522 71.826 81.472
13 118.581 109.208 71.261 80.634
17 118.751 108.957 70.773 80.570
5 118.870 109.167 73.304 83.007
16 119.562 110.435 72.136 81.263
1 119.750 110.609 73.739 82.880
3 120.500 112.217 74.045 82.328
2 121.333 114.333 77.818 84.818
20 123.610 114.625 73.779 82.764
19 123.625 114.792 73.739 82.572

 

vmamnmnnmmm

run 2

In III/h: 2:2 '9.

63

 

 

 

W
6009" Group I: Tut Nun-bore Group M: Tu: Nut-born
m
1 2 3 4 5 6 13— i4 41 18 _19 20 J 8 9 10 11— 121 ll 1L
5 657 608 615 564 550 579 635 614 658 668 643 596 667 688 690 790 821 798 743 707
6 622 602 572 452 451 482 678 603 665 629 529 526 751 746 750 781 684 677 670 656
7 388 381 361 300 291 293 462 399 381 362 361 349 358 357 356 428 403 397 M7 326
8 686 684 645 642 640 661 720 704 733 717 664 672 740 810 821 898 889 814 841 804
9 676 672 622 605 604 628 632 592 634 585 626 641 799 882 876 797 832 749 713 617
10 573 577 524 585 557 566 587 564 494 553 434 521 618 674 630 660 653 615 817 786
1 1 585 592 617 555 512 592 572 605 621 622 675 655 784 760 720 656 615
12 435 470 476 477 470 493 508 477 477 526 546 463 485 519 536 617 573 556 645 537
13 575 452 527 619 656 658 719 681 653 661 708 696 718 780 760 798 781 734 692 639
15 576 554 554 523 524 500 611 572 585 592 600 644 619 639 645 682 685 631 603 683
15 632 619 629 568 514 574 668 646 617 592 600 552 612 640 602 709 686 673 656 725
16 537 562 520 538 476 501 623 557 524 531 557 540 579 584 621 690 686 614 602 651
17 498 413 51 1 472 508 516 562 493 569 527 574 508 657 693 685 757 713 659 539 61 1
18 602 600 583 592 589 603 617 548 643 677 656 642 609 647 640 707 642 615 650 645
19 415 392 370 399 332 373 399 353 409 391 367 310 388 395 376 444 439 398 419 447
20 485 453 538 545 515 568 463 380 440 440 369 288 503 537 525 527 562 495 537 536
21 528 541 489 512 488 559 544 477 511 571 554 534 507 580 602 608 636 656 594 615
22 387 396 418 396 386 421 369 347 423 467 354 294 387 465 446 407 430 417 410 466
23 620 623 664 634 618 666 696 618 737 706 691 716 597 720 685 724 719 696 742 728
24 543 487 486 442 446 447 497 449 478 448 438 557 391 475 501 447 454 438 426 480
25 518 558 554 470 436 459 514 527 521 469 489 502 543 634 643 522 506 507 487 488
26 460 448 463 392 404 402 522 469 474 440 512 427 377 370 342 512 488 470 439 391
27 667 642 672 601 569 586 594 589 561 510 636 583 512 565 557 601 558 519 516 579
28 815 820 867 717 675 743 731 699 701 729 643 656 722 788 851 804 808 710 700 764
29 561 582 551 556 518 542 596 543 503 609 619 604 537 584 499 578 616 516 491 565
30 376 478 397 272 318 309 371 346 394 382 935 391 412 409 415 340 366 348 338 444
31 467 483 483 457 506 523 479 470 526 567 550 578 493 527 533 551 535 519 538 556
32 .338 422 443 430 389 433 407 418 471 462 462 434 376 397 484 427 450 406 433 438
33 57, 300 7‘2 534 595 741 792 648 800 731 776 732 708 816 813 766 794 743 695 753
34 441 469 516 453 422 442 472 473 461 420 51 1 515 452 499 477 524 510 447 501. 523
35 472 425 539 529 448 516 572 530 587 606 517 552 507 548 585 532 534 480 587 547
36 620 626 609 641 564 590 655 581 613 638 594 551 581 628 638 646 659 599 512 597
37 656 536 694 556 534 590 497 444 364 435 559 562 406 468 484 459 432 398
38 502 566 535 505 505 537 563 678 i 518 648 622 641 536 534 561 632 661 642 519 640
39 637 593 644 649 576 593 749 747 663 792 681 717 516 611 638 654 701 513 700 766
40 601 605 679 663 595 661 739 734 648 694 763 780 616 602 672 666 754 725 634 605
41 273 354 245 268 239 282 351 314 352 358 317 317 207 274 254 287 248 299 277 324
42 414 431 449 567 502 571 527 518 548 508 478 437 412 428 467 511 511 568 615 558

 

64

Table 3

Average Local Overall Heat Transfer Coefficients,
BTU/hr ft2 OF, for Group I and II

 

 

 

Thermo- Average Average Thermo— Average Average
couple U for U for couple U for U for
kxation group I group II location group I group II
5 615 738 24 476 451
6 567 714 25 501 541
7 360 396 26 451 423
8 680 827 27 600 550
9 626 785 28 733 768
10 544 681 29 565 548
11 583 685 30 372 384
12 485 558 31 507 531
13 633 737 32 425 426
14 570 648 33 734 761
15 600 662 34 466 492
16 538 628 35 524 547
17 512 664 36 607 607
18 612 644 37 535 529
19 376 413 38 568 590
20 457 527 39 670 637
21 525 600 40 680 659
22 388 428 41 306 271
23 665 701 42 507 509

 

 

 

65

Table 4

weighted Average Overall Heat Transfer Coefficient
for individual tests. BTU/hr ft2 OF

Group I

 

 

 

Test 1 2 3 4 5 6 13 l4 17 18 19 20

 

UAV 537 538 547 522 501 533 568 527 545 552 549 543

 

Mean = éflé; = 538 BTU/hr ft2 OF

2 0
Deviation from mean UAV of 538 BTU/hr ft F is i 6.9%.

 

 

 

 

Group II
Test no. 7 8 9 10 11 12 15 16
UAV 536 563 582 603 604 566 565 586
Mean = 4605 = 575 BTU/hr ft2 OF

 

8

Deviation from mean UAv of 575 BTU/hr ft2 0F is i 6.8%

Mean UAV of group II (575) is within 6.9% of mean of
group I.

A STATE UNIVERSITY LIBRARIES

13111 1 11111111111 1

93 030l5 0014

MICHIG