WERMAL DIFFUSIVITY BY FENI‘FE
DEFFERENCES AND CORRELATQON WITH
PHYSICAL PROPERI’IES OF
HEAT TREATED POTATOES

Thai: for the Diem of DE. D.
HICHEGM STH’E HNWERSETY
Floyd V. Matthews, Jr.

1966

   
   
   

  

LIBRARY ‘

Michigan State
University 4

mli\\l|1\lL\,||19|\fl1\\lLUlflMJkfllWW

 

WW3]

fianA

. 1.9.1}
V -.y_

~—

fly-”
_.'~f V

o

_ t.‘*":'~5";3

a?

“to" " “

Epfflbbe: or sum-.1 .4: glam-d Mi 32"“;t' ‘ "
, “' '*' h r I ‘ ‘ . 3 I
H ‘t -

 

ABSTRACT

THERMAL DIFFUSIVITY BY FINITE DIFFERENCES AND CORRELATION
WITH PHYSICAL PROPERTIES OF HEAT TREATED POTATOES

by Floyd V. Matthews, Jr.

Accurate information on the thermal properties of

a vegetable is needed to establish the energy requirements

of a particular heating or cooling process. In the freez-

ing region of a few vegetables, some of the thermal prop—

erties have been determined. In the heating and cooking
regions, these properties have not been determined in terms
useful for engineering design parameters. Therefore, an
investigation was made of the variations in thermal dif—
fusivity of a potato section from the raw state to the

cooked state. Physical properties were also evaluated

to determine correlations with thermal diffusivity.

In the cooling and freezing region of vegetables,
previous investigators have used the guarded hot plate
method or the Cenco—Fitch apparatus to determine thermal
properties. The guarded hot plate requires considerable
time and involves a steady state heat transfer process.
The Cenco-Fitch apparatus involves a rapid transient heat
process with errors of approximately 5% or larger.

In the procedure used, a heated cylinder of sili-

cone rubber or steel was placed in direct contact with a

Floyd V. Matthews, Jr.

cylindrical section of Excel potato (Solanum tuberosum).

The temperature history at X = O and at X = L of a given

length of the potato section was used to calculate the

thermal diffusivity by a finite difference method. Thermal

diffusivities were determined at the beginning and ending

of each heat treatment. After the thermal diffusivity was

determined, the calculated and the measured temperatures

L differed by a root mean square value of O.43°F.
= O

at X =

Simultaneous recordings of temperatures at X

and X = L permitted a measurement of the temperature—time

area between the l60°F line and higher temperatures up to

215°F. The degree-minute area was related to the heat ex-

posure of the potato section and was a parameter of the

study. Specific gravity was determined for the raw potato

sections. Elastic modulus was determined for both the raw

and heat treated potato sections.
The following results were obtained:

1. The thermal diffusivity of the potatoes de—

creased during a 15—day storage at 40°F.

2. The specific gravity of the raw potato sections

was not related to the 15—day storage, thermal diffusivity,
or elastic modulus.

3. As heat exposure increased, thermal diffusiv-

ity increased up to a maximum and then decreased.

4. The addition of heat to the potato section in-

itially increased the elastic modulus. As cooking progressed,

Floyd V. Matthews, Jr.

the elastic modulus decreased rapidly.
5. A rapid decrease in the elastic modulus of the
potato sections was accompanied by the maximum increase in

the thermal diffusivity.

Approved 1% MW

Major Professor
and Department Chairman

kw. 2.}, {4((
Date

 

THERMAL DIFFUSIVITY BY FINITE DIFFERENCES AND CORRELATION

WITH PHYSICAL PROPERTIES OF HEAT TREATED POTATOES

BY

Floyd V. Matthews, Jr.

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1966

 

ACKNOWLEDGMENTS

Thanks and appreciation are extended to:

Dr. Carl W. Hall, chairman of the Agricultural Engineering
Department, for his constant encouragement and
finesse in asking the right questions at the right
time.

Dr. A. M. Dhanak (Mechanical Engineering) for his depth
and thoroughness in teaching heat transfer at the
graduate level. Consultations were freely given
and most rewarding.

Dr. F. H. Buelow (Agricultural Engineering) for serving
as a guidance committee member and for suggested
solutions to instrumentation problems.

Dr. Clifford Bedford (Food Science) for serving as a guid-
ance committee member and for his realistic approach
to problems in the food science area.

Charles C. Mueller for the photographs in this thesis.

John Hornik for the use of his thermal diffusivity computer
program.

Dr. R. L. Green, chairman of the Agricultural Engineering
Department, University of Maryland, for his admin—
istrative assistance in obtaining leave time for

the completion of this educational experience.
ii

3.1L

  

than: or coxvzmms

 
  

I

’33» murmurs . . . . . . . . . . I . . . 1.1
- $13? or TABLES.
O

\

 
    

      

Lxsr or 7:3'.a.. . . . . aufl
For their personal sacrifices and cooperation
NOMEIJCT is: ' " .'

  
  

Ch f ._'

 
 

To my wife, Gloria

  
  
  
  
  
  
 

and children, Ruth
Marilyn
Roger
Keith
Bruce

Craig

 

ACKNOWLEDGMENTS . .

LIST OF TABLES.

LIST OF FIGURES . .
NOMENCLATURE. . . .
Chapter

1. INTRODUCTION

TABLE

2. LITERATURE REVIEW. .

OF CONTENTS

2.1 Thermal Properties. . . . .

2.1a Thermal Conductivity.

2.lb Specific Heat . . . .

2.lc Thermal Diffusivity .

2.ld Heat Exposure . . . .

2.2 Physical Properties . . . .

2.2a Specific Gravity. . .

2.2b Elastic Modulus . . .

3. THEORETICAL CONSIDERATIONS . . .

3.1 Heat Conduction Equations .

3.2 Thermal Diffusivity by Finite

Differences

4. EXPERIMENTAL EQUIPMENT AND PROCEDURES. . . . .

4.1 Objectives. . .

4.2 Equipment . . .

iv

14
21
27
3O
3O
32
34
34
36
38
38
39

Chapter

6.

4.3

 

fi

Experimental Procedure. . . . . . . . . . .
4.3a Flow Chart of Experimental Procedure.
4.3b Heat Sources. . . . . . . . . . . . .
4.3c Potato Sections . . . . . . . . . . .
4.3d Elastic Modulus Determinations. . . .

4.3e Heat Transfer and Thermal Diffusivity
Tests. 0 I O O I I O O O O I O I O 0

Discussion of Experimental Techniques . . .
4.4a Potatoes. . . . . . . . . . . . . . .

4.4b Heat Transfer and Thermal Diffusivity
Tests. I O O O O O I O I O O O I O O

4.4c Specific Gravity Tests.

4.4d Elastic Modulus Tests . . . . . . . .

RESULTS AND DISCUSSION . . . . . . . . . . . . .

Thermal Diffusivity . . . . . . . . . . . .
Elastic Modulus . . . . . . . . . . . . . .
Specific Gravity. . . . . . . . . . . . . .
Heat Exposure . . . . . . . . . . . . . . .
Correlation of Parameters . . . . . . . . .
5.5a Thermal Diffusivity and Storage Time.
5.5b Thermal Diffusivity and Heat Exposure

5.5c Thermal Diffusivity and Maximum
Temperature at X = L . . . . . . . .

5.5d Elastic Modulus and Heat Exposure . .

5.5e Thermal Diffusivity and Elastic
Modulus. O O D O I I I O O I O I O I

5.6 Application of Results. . . . . . . . . . .

CONCLUSIONS 0 O o o O o I O o o D I I I t O O o c

Page
48
48
48
49
53

54
55

55

56
58
58
6O
62
65
66
66
67
67
69

72
76

82
82
84

‘ bin at Mares

, um.
£005.10...

lbgrmal Uiffliuui'
I! B

O O O O

Compe:.ru' ' —
’meim a: J . - , 1 ' ' - . m 50!. 10°
7 . v ,A ' .

 

Table
2.1.

5.1.

 

LIST OF TABLES

Thermal diffusivity of beef in cans.

Comparison of root mean square values of tem—
peratures resulting from thermal diffusivities
calculated after 50 seconds and 100 seconds .

Date and description of tests tabulated with
average values of thermal diffusivity and

heat exposure . . . . . . . . . . .

Date and description of tests tabulated with
average values of the parameters. . . . . . .

Summary of data and results. . . . .

Summary of average values of data and results.

vii

Page
23

61

7O

75
97
99

LIST OF FIGURES

Figure Page

3.1. Node notations for position and time . . . . . 35

4.1. Specimen holder with electric heating unit and
black glass foam insert . . . . . . . . . . . 40

4.2. Specimen holder with red silicone rubber heat
source and microswitch (black). . . . . . . . 40

4.3. Equipment during a test. From left to right:
recording potentiometer, specimen holder,
autotransformer, and recording potentiometer. 40

4.4. Elastic modulus test equipment. From top to
bottom: dial gauge, load cell (below hori-
zontal bar), and parallel plates with potato

section in place. . . . . . . . . . . . . . . 4l

4.5. Heat sources: electric heating element with

steel cylinder and silicone rubber cylinder . 41

46

4.6. Weighing potato section in air . . .

4.7. Weighing potato section in water . . . . . . . 46

4.8. Potatoes and cutting equipment. From left to
right: aluminum ring assembly 1 1/32 in.
long, potato cylinder and ring for cutting
potato section to proper length, and boring
tool for removing cylindrical section from

potato o I o o u o o o o a o o I 50

4.9. Semi-infinite portion of potato in specimen
holder with thermocouple at X = L . . . . . . 50

5.1. Relationship between thermal diffusivity and
date Of test. 0 a O a o o I I o o 0 a I a O a 68

5.2. Parameters of thermal diffusivity and elastic
modulus versus heat exposure. . . . . . . . . 71

5.3. Relationship between the change in thermal
diffusivity and the maximum temperature at

X=Loaooloouoooooooooooo

74

viii

Figure Page
5.4. Representative heat treated potato sections
and corresponding semi-infinite cylinders.
Test series numbers are, from left to right,
717, 714, and 719 I I I I I I I D I I I I I I 78
5.5. Rupture of heat treated potato section repre—
sentative of test series number 719 . . . . . 78
5.6. Representative ruptured heat treated potato
sections. Test series numbers are, from left
to right, 717, 714, and 719 . . . . . . . . . 78
5.7. Representative force-time curves of 717 test
Series. I I I I I I I I I I I I I I I I I I I 79
5.8. Representative force-time curves of 714 test
Series. I I I I I I I I I I I I I I I I I I I 80
5.9. Representative force—time curves of 719 test
I I I I 81

series. . . . . . . . .

 

NOMENCLATURE

Abbreviations
Btu British thermal units
°F degrees Fahrenheit
ft feet
in. inches
lbf pounds force
lbm pounds mass
min minutes
psi pounds/inch2
rms root mean square
sec seconds
Greek Symbols
QC thermal diffusivity (ftE/hr)
(0 density (lbm/ft3)
A small increment
Letter Symbols
A area (ft2)
C specific heat (Btu/(lbm °F))
E elastic modulus (psi)
F force (lbf)
HE heat exposure (°F-min)

 

i________—————————————----::::JIllllIIIIIIIIIIIIIIIIIIII

thermal conductivity ((Btu ftn)/(hr ft3L 017))

M a dimensionless number defined by equation (3.5)

n node number

qm internal heat generation (Btu/(hr))

T temperature (°F)

t time (min or sec)

X coordinate axis distance (in)

Y coordinate axis distance (in)

Z coordinate axis distance (in)

Subscripts

n distance measured parallel to the vector of a
quantity

* distance measured perpendicular to the vector of

a quantity

xi

1. INTRODUCTION

When designing a heating or cooling process for
a vegetable, one must make an energy balance of the system
and calculate the net energy requirements. An energy bal-
ance equates energy losses and consumption to energy input.
To determine the net energy requirements, the vegetable
can be treated as an engineering material. The thermal
properties of the vegetable should be known over the oper—
ating range of the process. To calculate net energy re-
quirements, one can estimate the values of thermal prop-
erties and also assume that these properties remain con—
stant during the heating or cooling process. With the
present development of the science of heat transfer, an
engineer should not have to rely on these estimates and
assumptions. Hence, the objective of this research was
to define and evaluate the engineering parameters that
influence the thermal properties of a vegetable.

The thermal properties considered in this research
are thermal conductivity, specific heat, density, and
thermal diffusivity. The physical properties considered
are specific gravity and elastic modulus. Researchers
have determined relationships between the specific gravity

of potatoes and other physical properties.

 

‘35

IIN '''''''''''''''''''''''''''''''''''''""""""‘——‘_———__1!

2 n

The elastic modulus of a heated potato specimen
was used as an indication of the degree of cooking or proc-
essing. The elastic modulus was used because of its previ—
ous use in work on potatoes (Finney, 1963).

Blanching is a heat process used by food processors
to inactivate enzymes in vegetables. Food scientists and
others have found that enzymes can be inactivated if the
vegetable is held for a specified time in a heating medium
that is maintained at a given temperature (Tressler and
Evers, 1957; Melnick, Hochberg, and Oser, 1944). But to
the engineer, these specifications do not describe the en-
ergy balance or the heat requirements of the system. The
engineer must know the mass rate (1bm/hr) of vegetables
to be blanched, the initial and final temperatures of the
vegetables, and the thermal properties of the vegetables.
The food researchers have defined an end point in terms
not amenable to engineering solutions.

While being heated, the vegetable changes from a
raw state to a partially cooked state and the physical
properties are changed (Finney, 1963; Personius and Sharp,
1938; Simpson and Halliday, 1941; Weier and Stocking, 1949;
Crafts, 1944; Kaczmarzyk, Fennema, and Powrie, 1963). Would
not the thermal properties also change under such conditions?
A correlation between thermal properties and physical prop—
erties would enable an engineer to obtain thermal proper-

ties with a minimum of equipment and time. With accurate

 

 

values of thermal and physical properties of a vegetable,
an engineer could apply an energy balance to heating and
cooling processes. Thus he could design more efficient
equipment and production facilities for the food process—
ing industry. Properly designed facilities would reduce
the investment in over—sized equipment and reduce the haz-
ards of inadequate facilities. As the size, complexity,
and competition of the food processing industry increases,
a carefully engineered production facility becomes imper—
ative.

The change in thermal conductivity of metals with
temperature is well known and is described by a simple
equation (Schneider, 1955). Because a vegetable undergoes
physical and chemical changes during the heat treatments,
one might reasonably expect its thermal properties to change
not only with temperature but with other factors.

Heating processes for vegetables are usually tran-
sient processes. The temperature difference between the
vegetable and the heating medium changes with time and
theoretically the vegetable does not reach the temperature
of the heating medium. Steady state processes are denoted
by a constant temperature difference or gradient between
the heating medium and the product. Some researchers have
Used a guarded hot plate, a steady state device, to deter-
mine the thermal conductivity of meat (Miller and Sunderland,

1963). Others have used a modified Cenco-Fitch apparatus,

I ———————:‘

4

a transient state device, to determine the thermal conduc-
tivity of meats, fruits, and vegetables (Walters and May,
1963; Bennett, Chace, and Cubbedge, 1962, 1964). The dis—
advantage of the guarded hot plate is that the transient
process found in industrial practice is not duplicated.
The modified Cenco—Fitch duplicates the transient process
but is subject to errors of approximately 5% (Bennett,
Chace, and Cubbedge, 1962; Wing and Monego, 1959). When
the thermal and/or physical properties of a vegetable vary
with the heat absorbed, one must use other means to deter—
mine them.

The research described in this thesis utilized a
transient process in which the heat received by the potato
was related to heat exposure. The method involved the
transfer of heat through a finite length of a semi—infinite
cylinder of a potato specimen. The method of finite dif-
ferences was used to make the thermal diffusivity calcula-
tions.

Equally as important as the quantitative results
of the research was the development of equipment and pro—
cedures for determining the thermal properties of foods
in the solid state. The same principles have been used
to determine the thermal properties of metals (Beck, 1963).
The advantages of this transient process over the methods
using the guarded hot plate or the Cenco-Fitch apparatus

are discussed.

 

 

2. LITERATURE REVIEW

2.1 Thermal Properties
2.1a Thermal Conductivity

Eucken (1940) was probably the first to examine
the thermal conductivity of a material composed of several
substances. Eucken (1940) applied a formula, derived by
Maxwell (1904), that expressed the thermal conductivity
of a material as a function of the relative volumes and
conductivities of the different particles of which a mate-
rial is composed.

The following quotations from Long (1955) are de—
scriptions of fish muscle as related to the theoretical
equation of Maxwell—Eucken. "Briefly, the major component
is water, in which are dissolved various inorganic salts,
organic substances such as proteins and fats being dis—
persed through this medium, either in the form of an emul-
sion or in a colloidal state, the whole mass being held
loosely together by connective tissue." "The fish muscle
is considered to be, at any one temperature in the freez—
ing zone, part ice, part salt solution of determinable
concentration, and part protein. The thermal conductivity
was calculated from the relative proportions of these con-

stituents present at each of a number of temperatures."

 

 

Long used a specially designed cylindrical calorim-
eter with a heat source along the cylinder axis and a heat
sink at the radius. Axial guard sections were used to
eliminate end-losses; the heat flow was radial from source
to sink. No analysis of errors was presented.

Long determined_the thermal conductivity of fish
muscle from 40°F to —15°F and compared the experimental
results with the theoretical equation of Maxwell-Eucken.
The resulting theoretical curve was well within the dis—
persion of the experimental data. The experimental thermal
conductivity appeared to be constant between 30°F and 40°F.
Below 30°F, the thermal conductivity increased as the tem-
perature decreased.

Kethley, Cown, and Bellinger (1950) estimated the
average thermal conductivities of some fruits and vegetables
over the range of 80°F to 0°F. These authors were inter-
ested in the cooling of fruits and vegetables as a tran-
sient heat transfer process. Solid objects of food as well
as canned foods were suddenly immersed in a cold constant
temperature medium. After measuring the temperature his—
tory of the objects, Kethley §t_al. used the graphical
method of Gurney and Lurie (1923) to determine the thermal
diffusivity of the foods. (These temperature-time charts
are now found in most conduction heat transfer textbooks;
Eckert and Drake, 1959; Kreith, 1958; and Schneider, 1955.)

For the specific heat of a fruit or vegetable, Kethley st 21.

.4

 

._.I~.,

used an average apparent specific heat which was defined
as “the quotient obtained by dividing by 80 the total Btu
required to raise the temperature of one pound of the sub-
stance from 0°F to 80°F."

For the temperature interval of 80°F to 32°F,
Kethley §£_§1. (1950) found that the average thermal con—
ductivities of strawberries, Irish potato flesh, English
peas, and peach flesh ranged from 0.61 Btu/(hr ft2°F)/ft
thickness to 0.78 Btu/(hr ft2°F)/ft thickness. No analysis
of errors was given.

Lentz (1961) used a guarded hot plate apparatus
to determine the thermal conductivity of several concen-
trations of gelatin gels from 5°C to —25°C. Gelatin gels
were used because models of such material are frequently
used in studying the effects of physical factors on cool-
ing and freezing rates of foods. Using the guarded hot
plate to determine the thermal conductivity of ice, Lentz
obtained results that were reproducible to within I 1%.
The thermal conductivities of ice as determined with the
guarded hot plate were about 1% lower than the most reli-
able values available. In experiments with heat flow both
parallel and perpendicular to the grain of meat, Lentz
(1961) also determined the thermal conductivities of sev-
eral meats from 10°C to —25°C. Some of his conclusions
were:

1. At temperatures above freezing, the thermal

 

conductivities of all the meats tested were
about equal and about 10% below the established
value for water.

2. Thermal conductivity curves for meat were all
linear at temperatures below -10°C; the thermal
conductivity increased as the temperature was
decreased.

3. The thermal conductivity of meat did not appear
to be directly related to moisture content or
fat content.

4. Heat conduction was 15% to 30% greater along
the fibers than across them.

Lentz (1961) also applied the Maxwell—Eucken equa-

tion to 6%, 12%, and 20% gelatin gel solutions to obtain

a theoretical thermal conductivity. The theoretical and
experimental values were in good agreement (—2.4% to +0.4%
difference) for the 6% and 12% gel solutions but not for
the 20% gel solution (+4.3% to +14.1% difference).

A tabular summary of thermal conductivities of
meats and fats from published reports was given by Lentz
(1961). Most of the thermal conductivities were from 0°C
to —20°C. The increase of thermal conductivity with de-
crease in temperature was evident in all the results shown.

Bennett, Chace, and Cubbedge (1962) used a modified
Cenco-Fitch apparatus to determine the thermal conductivity

of samples of Marsh grapefruit rind and samples of Valencia

 

 

orange rind. The National Bureau of Standards used a
guarded hot plate to determine the thermal conductivity
of the sample of silastic silicone rubber that Bennett 22
21. used for equipment calibration. The average error of
the modified Cenco—Fitch apparatus was approximately 5%
with variations from -2% to +13%.

The modified Cenco-Fitch apparatus used by Bennett
33 31. consisted of a sample of orange rind held between
a plate and a plug. The plate was maintained at a constant
temperature during the test and the plug was initially at
a lower uniform temperature. As the test progressed, the
temperature of the plug increased due to the heat flow from
the plate through the rind sample. Bennett gt_gl. (1962)
found that the thermal conductivities were significantly
lower for plate and plug temperatures of 212°F and 78°F
respectively than the thermal conductivities obtained with
plate and plug temperatures of 130°F and 78°F respectively.
It was stated that the above variations showed the neces—
sity for exercising care in selecting the optimum plate
and plug temperatures. These variations could have been
due to moisture lost from the sample in contact with the
212°F plate. Voids resulting from the loss of moisture
would have an insulating effect and thus a lower value of
thermal conductivity. No physical properties of the grape—
fruit or orange rinds were given in the report. Bennett

23,31. did not consider the initial temperature of the

 

M

The report of Bennett, Chace, and Cubbedge (1964)

rind samples.

was a continuation of the research described in 1962.
Bennett gt 21. altered the Cenco—Fitch apparatus to obtain
a constant pressure on the samples during testing. Other
modifications resulted in an equipment error of 2.68% as
contrasted to the previous average of 5%. In addition to
the experimental determinations of thermal conductivity

of orange and grapefruit rind, Bennett 35 21. (1964) also
experimentally determined the thermal conductivity of the
juice vesicles of the fruit. By assuming that the rind

and the juice vesicles comprised two concentric, hollow
spherical shells, the authors derived an equation for the
apparent thermal conductivity of the whole fruit. The cal-
culated values of apparent thermal conductivity compared
well with values that Bennett gt _1. found in the litera—
ture. In the discussion following the paper of Bennett
g£__1., the authors noted relationships between specific
gravity and thermal conductivity and between moisture con—
tent and thermal conductivity.

Miller and Sunderland (1963) used a guarded hot
plate to determine the thermal conductivity of beef with
heat transfer perpendicular to the grain. The guarded hot
plate was calibrated with two materials of known thermal

conductivities; agreement was within 0.5% and 1.35% of the

known values. An analysis showed that the error in the

 

n I

results was less than 12.75% and was quite possibly within

11%. Miller and Sunderland (1963) used mean sample temper-

atures from 42°F to 2°F. Below 32°F the thermal conductiv-I

ity of the beef increased as the temperature decreased.
Above 32°F the thermal conductivity increased slightly as
the temperature was increased. The last statement contra—
dicts the results of Lentz (1961), but Miller and Sunder—
land used beef that had been previously frozen and whose
moisture content was approximately 5.5% less than the beef
used by Lentz. The results of Miller and Sunderland showed
that the thermal conductivity of beef depended on tempera—
ture, moisture content, and direction of heat transfer.
Walters and May (1963) used a Cenco-Fitch apparatus
to determine the thermal conductivity of chicken breast
muscle and skin. The Cenco—Fitch apparatus was chosen
because the test durations of 10 to 20 minutes would have
less effect on the moisture content and physical properties
of the chicken than the several hours required for each
test when using a guarded hot plate. The equipment error
of these authors was found to be 11.1% when the equipment
was calibrated with a sample of material whose thermal con-
ductivity had been determined by the National Bureau of
Standards. Walters and May (1963) found no significant
effect on thermal conductivity from variations in percent
moisture or percent fat of the muscle and skin. The mois—

ture content varied from 69.1% to 74.9% and the fat content

 

12 W

was from none detected to 5.9%.

Charm (1963b) used an equation from Ball and Olson
(1957) to derive expressions for determining the thermal
conductivity of a finite cylinder of frozen material. The
equation in Ball and Olson (1957) was based on heat pene—
tration data. The thermal conductivity values obtained
by Charm included the container with the material and were
averaged over the range of the heat penetration data. The
value of thermal conductivity obtained by such a method
failed to reflect the change in thermal conductivity with
temperature as had been noted by other authors. Even though
the calculated error for thermal conductivity was 9.3%,
Charm (1963b) stated that the values of thermal conductiv-
ity obtained for frozen codfish were in the range of pre—
vious literature values.

Parker and Stout (1966) calculated the thermal
conductivity of cherry flesh from measurements of density,
specific heat, and diffusivity of cherry flesh between
80°F and 40°F. The following equation was obtained by
multiple correlation analysis:

kfl = -0.275 — 0.000953 . 0.280 Pfl + 0.327.:fl
where kfl is estimated flesh thermal conductiv-

ity (Btu/(hr ft °F))
SS is flesh soluble solids content (%)
€21 is flesh density (gm/cc)

cfl is flesh specific heat (Btu/(lb °F))

 

 

 

13

Standard error of kfl was 1 0.0025 Btu/(hr ft °F) and the
average kfl for 20 samples was 0.298 Btu/(hr ft °F).

With respect to thermal conductivity and the ob-
jective of the research in this thesis, the following is
concluded from the literature reviewed:

1. Determining the thermal conductivity of food

products with the guarded hot plate

a. does not duplicate the transient proc-
ess found in industry,

b. is of such duration that variations due
to moisture content are not discernable,
and

c. the apparatus has an error less than 3%.

2. Determining the thermal conductivity of food
products with the Cenco—Fitch apparatus

a. duplicates the transient process,

b. requires much less time than the guarded
hot plate, but

c. usually has errors larger than 3% and
up to 5%.

3. Above freezing, the thermal conductivity of
food products may vary with temperature, mois-
ture content, specific gravity, direction of
heat transfer, soluble solids, and specific
heat.

4. During thermal conductivity tests, food products

 

10.

 

14

should be subjected to constant pressure.

The graphical method of Gurney and Lurie (1923)
and the method of Charm (1963b) do not account
for influences of physical properties on thermal
conductivity.

Approximately half of the authors did not make
an error analysis.

Most authors checked the equipment with samples
of known thermal conductivity.

No information was found on the thermal con—
ductivity of vegetables or food products above
100°F except for the preliminary work of Bennett
_£ 21. (1962). Most investigations were con—
cerned with the cooling and freezing range.

No one has reported any relationships between
thermal conductivity and shear strength, com-
pression strength, or elastic modulus of vege-
tables or food products.

Thermal conductivity as a function of heat ex-
posure of a vegetable or food product has not

been reported.

2.lb Specific Heat
The work of Siebel (1892) is the first reported

on the specific heat of foods in which he considered food

to be composed of water and solids. Above freezing, the

 

_ n. .18

15

specific heat of food was estimated as the percent of water
times the specific heat of water plus the percent of solid
matter times 0.2.

Short, Woolrich, and Bartlett (1942), using a spec—
ially constructed calorimeter, showed specific heat data
on five vegetables, two fruits, fresh ham and fresh shrimp.
The data covered the range from 70°F to —35°F. Above freez-
ing, the data did not agree with the calculations proposed
by Siebel. Most of the data above freezing showed that
specific heat increased slightly as temperature increased.

Short and Bartlett (1944) improved the calorimeter
and changed the procedure and calculations from that used
by Short §E_gl. (1942). Essentially, transient state data
was averaged to a steady state condition and then used to
calculate the specific heat of the fruits and vegetables.
Thus, above freezing and up to 70°F, the specific heat was
treated as being constant for all fruits and vegetables.
The specific heats of various concentrations of sugar so—
lutions were also constant for the same temperature range.

Using similar equipment, in the range of 40°F to
—40°F, the findings of Staph (1949) agreed with the results
of Short and Bartlett (1944); the specific heats of fruits
and vegetables were constant above the freezing point.
But from a few preliminary tests above freezing, Staph
noted, "indications are that at temperatures above the

freezing point the specific heat increases slowly with

I‘ll-IFW'"

l6

temperature rise.“ The author also stated that “data do
not follow Siebel's rule since the specific heats of green
beans, honeydew melons, and Bartlett pears are nearly the
same and yet the water contents vary considerably. Pears
have 79% water content, green beans 88%, and melons 93%."
One objective of Staph was "to determine a relationship,
if any, between heat capacity and water, fat, and water-
soluble solids content.“ The results did not show the ex—
istence of a relationship that could be represented by an
equation.

Kethley, Cown, and Bellinger (1950) determined an
average specific heat or a specific heat factor of some
fruits and vegetables. The quantity of heat required to
raise one pound of the fruit or vegetable from 0°F to 80°F
was determined. This quantity, in Btu, was then divided
by 80 to obtain an average specific heat. Because the
value for specific heat was an average, no factors were
identified that influenced the specific heat of the fruits
and vegetables. No comparison was made between the aver—
aged values and the values obtained by other researchers
or by other methods.

The work of Staph and Woolrich (1951) was a con-
tinuation of the studies reported by Short §t_al. (1942),
Short and Bartlett (1944), and Staph (1949). Again, the
calorimeter was modified and the results obtained between

freezing and 70°F were different than those reported

 

17

previously. The specific heat of carrots, turnips, green
beans, and cauliflower between freezing and 70°F can be
expressed with a quotation from Staph and Woolrich. "When
the fusion point (of the vegetable) has been reached, the
specific heat drops almost instantaneously to values about
1.0 to 0.90 Btu per lb per °F. From this point on (to 70°F)
the specific heat decreases slightly with temperature rise,
and in some cases begins to increase again with further
temperature rise." Staph and Woolrich (1951) determined
the water content, fat content, and water soluble solids
content of the fruits and vegetables but did not make any
correlation between these components and specific heat.
Riedel (1951) devised an elaborate calorimeter to
determine the heat content of fruits and vegetables. The
accuracy of the calorimeter was stated thusly: “After
calibrating the calorimeter by electric heating, check
tests made with pure water gave values for the specific
heat of water and the latent heat of fusion of ice which
agreed within 0.2 percent with the best data given in the
literature." Riedel noted that most physical properties
of fruit juices do not depend on the kind of fruits but
on their dry substance content. The dry substance content
of fruit juices was determined by measuring the refractive
index of the juice at 20°C. Between 0°C and 20°C, the data
of Riedel (1951) showed that the specific heat of juices

of fruits and vegetables was a linear function of the dry

W"

 

18

substance content; the specific heat decreased as the dry

substance content increased. The relationship was expressed

by the equation
cj = 1.00 — 0.57 x0
where: cj is the average specific heat, 0°
to 20°C.
x0 is the dry substance content, a dec—
imal.
Riedel expressed the specific heat of a fruit or vegetable
as the sum of the specific heat of the juice plus the spe—
cific heat of the insoluble dry substance content. From
a series of tests, Riedel found that the specific heat of
the insoluble dry substance was 0.29 and was sufficiently
accurate for any temperature and any kind of fruit or vege—
table.
Moline, Sawdye, Short, and Rinfret (1961) were in—

terested in the specific heat of foods between the temper-

atures of —40°C and -160°C. Using a rather simple calorim—

eter, beef was simulated by a model composed of 17.6% pro—
tein, 18% fat, and 64.4% water. The measured values of
the specific heat of the model were compared with the com-
puted values based on the fractional concentration of the
components. The computed values of Moline 23 21. were

lower than the experimental values by a factor of 1.11 1

experimental values
0.03 (= ii_i_, )
computed values

 

When natural meats were compared with the model, the com—
puted values were lower than the experimental values by
a factor of 1.14 I 0.06. Thus the data indicated that the
specific heat of frozen meat could be predicted with an
average error of 4.4% and a maximum error of 10.5%. Based
on Siebel's method of water content, the error would have
been about 35%.
Charm (1963a) gave the following equation for es-
timating the specific heat of foods:
cp.= 0.5Xf + 0.3xs + le
where: Cp is the specific heat
XP is the mass fraction of fat
X5 is the mass fraction of solids
Xm is the mass fraction of moisture
The above equation does not account for the temperature
dependence of specific heat as found by Staph (1949).
Charm (1963a) did not cite any references for the equation.
To calculate the specific heat of frozen codfish
in cans, Charm (1963b) stated that "the specific heat of
many materials in the frozen state may be estimated from
Cp = 0.49m + 0.6F + O.33[l-(m + F)]
where: Cp is the specific heat
m is fraction moisture in material and
F is fraction fat"
Again, no references were cited for the equation.

The only physical properties noted in the literature

20

with respect to specific heat were water content and dry

substance content. No information was found that consid—
ered or related shear strength, compression strength, or

elastic modulus with the specific heat of foods or vege—

tables.

In the temperature range of 80°F to 40°F, Parker
and Stout (1966) found that the specific heat of cherry
flesh was related to soluble solids and flesh weight by
the following regression equation:

c = 0.900 — 0.005135 + 0.020 W

f1 f1

where cfl is estimated flesh specific heat
(Btu/lb°F)
SS is soluble solids content of the
flesh (%)
Wfl is flesh weight of each cherry (gm)

The standard error of c was i 0.060 Btu/lb°F, and the

fl

average c was 0.906 Btu/1b°F. The authors noted that

f1
the combined effects of both independent variables tended
to cancel each other.

With respect to specific heat and the objective
of the research in this thesis, the following is concluded
from the literature reviewed:

1. Based on today‘s needs, Siebel's method for
the calculation of specific heat is not suf—
ficiently accurate.

2. Between freezing and 70°F, the specific heat

21

of some vegetables may increase slightly as
the temperature is increased.

3. No one has reported the specific heats of vege-
tables at temperatures above 70°F.

4. No one has reported any relationships between
specific heat and shear strength, compression
strength, or elastic modulus of vegetables or
food products.

5. The specific heat of fruits and vegetables may
be a function of the insoluble solids content.

6. Specific heat as a function of heat exposure
of a vegetable or food product has not been

reported.

2.1c Thermal Diffusivity

Olson and Jackson (1942) used the data from experi—
mental heating curves to derive equations for the thermal
diffusivity,c(, of various shaped objects: brick, rectangu—
lar rod, infinite slab, finite cylinder, infinite cylinder,
and sphere. In all the equations, thermal diffusivity was
a function of the dimensions of the object and an f—value.
The f—value was defined as the time in minutes for the heat—
ing curve to traverse one log cycle when the log of the
temperature difference between the heating medium and the
object was plotted against time of exposure in minutes.

The f—value represented the reciprocal of the slope of the

—_—————M

22

heating curve and was a characteristic of the material
being heated. No information was given that related f-
values to the physical properties of the material.

Kethley, Cown, and Bellinger (1950) recorded the
thermal histories of some individual fruits and vegetables.
The thermal history data and the graphical method of Gurney
and Lurie (1923) were then used to estimate the average
thermal diffusivities of the fruits and vegetables for the
temperature range of 80°F to 0°F. The authors noted that
the estimated diffusivities were of the same order of mag—
nitude as the diffusivity of water in the temperature range
of 80°F to 32°F. The diffusivities of the foods for the
80°F to 32°F range were determined and compared with the

known values for water. The values for the fruits and

3 3

vegetables ranged from 5.35 x 10‘ ftZ/hr to 6.15 x 10‘
ft2/hr. Because average values of thermal diffusivity were
estimated, there was no correlation with temperature or
other physical properties.

In studies on the processing of beef in cans,
Hurwicz and Tischer (1952) found that the temperature of
the processing medium and the time at which the temperature
measurement was made on the beef were highly significant
factors in determining the thermal diffusivity of the beef.
The authors noted that the variation in thermal diffusiv-
ity was rather small and could be assumed to be constant

for practical purposes. The thermal diffusivities shown

23

in Table 2.1 were the experimental values at different 10—

cations in the container.

Table 2.1 Thermal diffusivity of beef in cans

 

Retort Temperature = 225°F

°<30 min.(cmz/min) °<90 min'(cmZ/min)
0.09264 0.10091
0.08734 0.09795
0.08230 0.09581
Retort Temperature = 255°F
30 min.(cmZ/min) °<90 min.(cmZ/min)
0.09454 0.10849
0.09429 0.10463
0.07196 0.10388

 

The thermal diffusivity increased as time increased
at a given retort temperature. The thermal diffusivity
also increased with an increased retort temperature.

In later studies on the processing of beef in cans,
Hurwicz and Tischer (1956) found that the thermal diffusiv—
ity of beef increased with retort temperatures between
225°F and 261°F. The thermal diffusivity decreased with
increased retort temperatures between 279°F and 315°F.

The authors noted that "the retort temperature range of
261°F to 279°F may be located in the critical region for

processing beef where most of the physical characteristics

24

assume their extremes." The authors also commented that
"there were no significant differences in thermal diffusiv-
ity due to location in the container" and that "a possibil-
ity existed that chemical and moisture changes occurring
during processing might have affected the thermal proper-
ties of the beef to different extents depending on the dis-
tance of the region in the can from the source of heat."
Evans and Board (1954) measured the thermal difi
fusivity of cans of bean-bentonite mixture and found that
the thermal diffusivity increased when the temperature of
the heating medium was increased; thermal diffusivity was

3

1.35 x 10- cm2/sec for a 104°F water-bath temperature and

3 cm2/sec for a 240°F retort temperature. Evans

1.70 x 10'
and Board suggested that the increase in thermal diffusiv—
ity could have been due to condensation of moisture in the
can head space from the bean—bentonite mixture and also
could have been due to a small amount of convection heat—
ing being superimposed on heating by conduction.

From the reported values for the thermal diffusiv-
ity of water, Evans (1958) noted that the thermal diffusiv-
ity of water increased by approximately 19% between 68°F
and 248°F. Based on theoretical calculations, heating and
cooling curves were constructed for water with constant
thermal prOperties and for water with variable thermal

properties. The author noted that the slopes of both

curves had values near that for constant thermal properties

(J

(.J'

’(J

(N

 

25

when using a diffusivity corresponding to the final temper-
ature. Evans cited evidence that the thermal diffusivity
of foods is less than that of water. The diffusivities

of foods compared with water undergo a smaller variation
with temperature. In additional experiments with cans of
bean—bentonite mixture and cans of agar gel, Evans found
that the thermal diffusivity increased with increased tem-
peratures.

Dyner and Hesselschwerdt (1964) used a mathematical
model and specimens of agar-gel to predict temperature-time
characteristics during food precooling. Thermal diffusiv-
ity was assumed to be constant in order to simplify the
mathematical manipulations. The authors noted, however,
that thermal diffusivity was a function of temperature,
and preliminary test work showed a slight initial decrease
in thermal diffusivity as the temperature was reduced.

The temperature range was not given. The effect of a vary-
ing thermal diffusivity was considered to be minor.

Parker and Stout (1966) determined the thermal
properties of tart cherry flesh in the temperature range
of approximately 80°F to 40°F. Thermal diffusivity was
calculated from temperature history data; the method was
not amenable to showing thermal diffusivity variations
with temperature. A multiple regression analysis showed
that in the temperature range of approximately 80°F to 40°F

the thermal diffusivity of cherry flesh was a function of

 

26

soluble solids; thermal diffusivity decreased as soluble
solids content increased. The thermal diffusivity of cherry

3

flesh was given as 5.104 x 10' ftZ/hr with a standard error

of 10.416 x 10‘3

ft2/hr.

With respect to thermal diffusivity and the objec-
tive of the research in this thesis, the following is con-
cluded from the literature reviewed:

1. Thermal diffusivity was a function of the re—

ciprocal of the slope of the heating curve.

2. The reciprocal of the lepe of the heating
curve has not been related to the physical
properties of the food.

3. The thermal diffusivity of canned beef increased
as the heating medium temperature increased
to 261°F. Thermal diffusivity decreased as
the heating medium temperature increased from
279°F to 315°F.

4. The thermal diffusivity of tart cherry flesh
was a function of percent soluble solids.

5. Variations of thermal diffusivity with temper-
ature up to 255°F may be small enough to ne-
glect for practical purposes.

6. No one has reported any relationships between
thermal diffusivity and shear strength, com-
pression strength, or elastic modulus of vege-

tables or food products.

 

27

2.ld Heat Exposure

 

For the purpose of this thesis, heat exposure is
defined as the area under a heating or cooling curve when
the dependent variable temperature is plotted against the
independent variable time. Thus if a vegetable were sud-
denly immersed in a heating medium, time would begin at
the instant of immersion and temperature would be that of
any selected point at any instant of time. When an immersed
object attains the temperature of the heating medium, the
transfer of heat ceases (no temperature differential).

But when the object remains immersed after attaining the
temperature of the heating medium, the thermal and physical
properties of the object may be influenced by the total
exposure to the heating medium. No direct references to
heat exposure were found in the literature. But some of
the data tabulated in the references could be examined from
the standpoint of heat exposure.

As cited previously, Hurwicz and Tischer (1952)
found that the temperature of the processing medium and
the time at which the temperature measurement was made on
the beef were highly significant factors in determining
the thermal diffusivity of the beef. The data given in
Table 2.1 shows that thermal diffusivity appears to be a
function of the temperature-time exposure of the product.

The report of Evans and Board (1954) did not give

heating curves or degree-minute data but the tabulations

 

28

showed a larger thermal diffusivity for cans of bean—ben-
tonite mixture heated in a 240°F retort as compared to
heating in a lO4°F water-bath. The area under a heating
curve from an initial temperature of 75°F to a 240°F retort
temperature was probably larger than the area under a heat-
ing curve from an initial temperature of 32°F to a 104°F
water-bath temperature. Thus a possibility exists for a
relationship between the heat exposure and thermal dif-
fusivity.

Nicholas and Pflug (1961) processed fresh cucumber
pickles at several combinations of temperature and time:
lSO°F to 204.S°F and 7 min to 166 min. The pickles became
softer as the area under the heating curve was increased.

Blanching temperature, blanching time, and green
bean firmness data was given by Kaczmarzyk, Fennema, and
Powrie (1963), but the relationships among the three vari-
ables were too erratic to consider firmness as a function
of some temperature-time area. Firmness was related to
temperature intervals and not directly to time and/or tem-
perature.

The effect of cooking temperature and time on the
tenderness of beef was reported by Tuomy, Lechnir, and
Miller (1963). Shear values measured with a Kramer shear
press indicated the tenderness of the beef. From a plot
of lines of constant meat temperature on a graph of shear

press values vs. time, the authors noted that the "curves

 

29

show that the initial effect of heat in the meat was a
toughening and, as the temperature was increased, the de-
gree of toughening increased. After the initial toughen-
ing, which occurred very rapidly, the resulting tenderness
depended upon temperature and time. If the temperature
was below 180°F, time resulted in little or no tenderizing.
If the temperature was 180°F or above, the meat became ten—
der at a rate and to a degree dependent on both time and
temperature.” Thus the heat exposure had an effect on the
physical properties of the beef.

Zaehringer, Cunningham, Le Tourneau, and Hofstrand
(1963) cooked potato slices in boiling water (98°C, high
altitude) for periods of 5 min to 25 min. The potato slices
gained weight during the first 5 min interval of cooking,
and maintained that weight during the second 5 min inter-
val of cooking. After 10 min of cooking, the potato slices
lost weight and the tissue progressively disintegrated with
time. Thus, the heat exposure may have affected the phys—
ical properties of the product.

No information was found on the comparative effects
of short time and high temperature versus long time and
low temperature.

With respect to the heat exposure and the objective
of the research in this thesis, the following is concluded
from the literature reviewed:

1. The extent of heat exposure of a vegetable

 

30

affects the physical properties and thus may
affect the thermal properties.

2. No reports were found that were directly con-
cerned with heat exposure and its influence
on the thermal and physical properties of a

biological product.

2.2 Physical Properties
2.2a §pecific Gravity

Researchers have correlated specific gravity with
various physical and chemical properties of potatoes. A
chart for converting specific gravity readings to percent—
age total solids and starch content is used by the United
States Department of Agriculture, Finney (1963).

Whittenberger and Nutting (1950) noted that potato
tissues of highest specific gravity occurred on both sides
of the vascular ring. Tissues of lowest specific gravityh
were in the central section.

Sharma, Isleib, and Dexter (1958) determined the
specific gravity for each of the three concentric zones
within a potato. Zone one was defined as extending from
the tuber surface approximately to the vascular ring. Zone
two was considered to be bounded peripherally by the vas-
cular ring and extended slightly less than halfway toward
the center of the potato. Zone three comprised the re—

mainder of the tuber. A two—year study of nineteen

 

31

varieties showed that zone two had the highest specific
gravity, followed by zone one and then three. Sharma 33
2£° (1958) concluded that "there was generally little dif—
ference in specific gravity between zones one and two.
Specific gravity of zone three was relatively uniform be—
tween varieties.“

Sharma, Isleib, and Dexter (1959) investigated the
influence of specific gravity and chemical composition on
hardness of potatoes after cooking. The authors concluded
that “tubers or parts of tubers with high specific gravity
are firmer after cooking than are those with a low specific
gravity."

An investigation of several rupture parameters of
potatoes by Finney (1963) showed that no linear relation-
ship existed between the parameters and specific gravity.
Finney concluded that "specific gravity and tuber strength
are not linearly related."

Lujan and Smith (1964) used a shear press, (Kramer
and Twigg (1962)), on raw potatoes cut into cubes to deter-
mine that the correlation of shear force values with spe-
cific gravity was negative and significant at the 1% level.

Porter, Fitzpatrick, and Talley (1964) determined
regression equations for the relationship of specific grav—
ity to total solids of potatoes.

With respect to specific gravity and the objective

of the research in this thesis, the following is concluded

 

32

from the literature reviewed:

1. A known relationship exists between specific
gravity of potatoes and their total solids and
starch content.

2. Specific gravity of a potato may be related
to firmness after cooking.

3. Specific gravity of a potato varies with loca-
tion within the potato.

4. Specific gravity and tuber strength are not
linearly related.

5. Specific gravity has been correlated to the

shear force of raw potato.

2.2b Elastic Modulus

Finney (1963) made an extensive study of the design
parameters of five varieties of potatoes. Raw potato cyl-
inders of various cross-sectional areas and l in. long were
subjected to a uniaxial compression test between parallel
plates. The elastic modulus was calculated from the stress
and deformation data. The mean elastic modulus for Russet
Rural potatoes was 543 psi with a 7.9% coefficient of var-
iation.

Finney also determined the elastic modulus on cy—
lindrical sections of Arenac potatoes. The whole potatoes
were kept in various constant temperature chambers prior

to testing. "Below 60°F, however, and above 105°F the

 

 

33

elastic modulus varied inversely with temperature from a
maximum of 545 psi at 40°F to a minimum of 355 psi at 135°F.
This decrease in elastic modulus with rising temperature
was in agreement with results reported for other materials."
”Within the 60 to 105°F range, the elastic modulus was un-
affected by temperature variations." The elastic modulus
was approximately 490 psi in the 60°F to 105°F range.

With respect to elastic modulus and the objective
of the research in this thesis, the following is concluded
from the literature reviewed:

1. An increase in the temperature of a potato can

cause a decrease in the stiffness or elastic

modulus of the potato.

3. THEORETICAL CONSIDERATIONS

3.1 Heat Conduction Equations
The general heat conduction equation that results
from an energy balance on a small volume of material is
given in heat transfer texts (Schneider, 1955) (Carslaw

and Jaeger, 1959) as:

 

3T 5 3T 5 3T gm 3T
5%(km 53?) + 570%“ 5?) +57(km 5?) + V — Cpat (3.1)
where: km = thermal conductivity of the material
Btu ft"
( 2 )
hr ft, °F
T = temperature (°F)
q = internal heat generation (Egg)
m hr
V = volume (ft3)
c = specific heat (gfifi-ggd
F) = density of the material flag
ft3

t time (hr)

Considering a body with the following characteris-
tics,
1. km independent of position and temperature,

2. one dimensional heat flow in the X direction,

and

3. no internal heat generation,

34

 

35

equation (3.1) reduces to:

921' 31‘
N * = —
9X2 at (3.2)

where: CKZ= thermal diffusivity

1‘3 (ft2»)/hr

Pc

A body subjected to a heat transfer process may

be divided into nodal points that are a distancezix apart.
About any node an energy balance can be written and ex-
pressed in finite difference form (Schneider, 1955). Tem-
peratures in the body can be expressed with respect to
position and time by means of subscripts and superscripts

n and t respectively, Figure 3.1. For one dimensional heat
flow in the X-direction in a finite body, nodes are located
at X = 0, X = X, and X = L. Temperature boundary condi-

tions may be specified at X = 0 and at X = L.

H x-%
O O

t+l O
t 0 0 0
n—l n n+1

Fig. 3.1. Node notations for position and time

In finite difference form, equation (3.2) becomes:

 

 

t+l t+l t m t+l t
o( Tn-l Tn +Tn+l n = n t n (3.3)
(4x)2 4

Equation (3.3) can be solved for the temperature at node

n for time t = t+l.

 

t+l T + T + T (M-l)
Tn = n—l n+1 n (3.4)
M + l
where:
2
(AX) .
M = —————. -
°< At a dimenSionless number (3.5)

3.2 Thermal Diffusivity by Finite Differences
A computer program using finite differences and
based on the method of Beck (1963) was used to calculate
thermal diffusivity from temperature measurements. The
basic operations of the program were:
1. The magnitude oleX was determined.
2. At the first and last node, a programmed time
step was used to calculate temperatures with

respect to time;

Tt, Tt+l, ... Tt+i

where: (t+l) - t programmed time step

(t+i) - t = time interval of data

3. The finite difference equation (3.4) was used
with an assumedcx_to calculate temperatures
at each node. Calculations were made in two
”passes"; an "odd pass" proceeding from first
to last node and an "even pass" proceeding
from last to first node.

4. The method of least squares was used to mini-
mize with respect to octhe difference between

the calculated and measured temperatures.

37

5. The change in diffusivity was calculated and
added to the assumedcx.to obtain a new value
ofOC.

6. The new value ofCK.was used in an iteration
procedure to determine a more accurate value
forCK.

The above program was based on the following as-

sumptions:

1. Initial and boundary conditions of the body

were:
a. T (X,O) = O
C. T (w,t) = O

2. One dimensional heat transfer.
3. Constantcx with respect to time and temperature.
4. The last node was at X =00.

The complete program is shown in Appendix A.

4. EXPERIMENTAL EQUIPMENT AND PROCEDURES

4.1 Objectives

 

The objectives of the research were:

A. To determine the thermal diffusivity of an in-
ternal section of a potato after the section
had received
1. a small heat treatment,

2. sufficient heat treatment to change some
of the physical properties of the section,
and

3. sufficient heat treatment to nearly cook
the section.

B. To investigate the correlation between thermal
and physical properties of the potato section
for the parameters of
1. thermal diffusivity,

2. heat exposure,

3. specific gravity, and

4. elastic modulus.

The first objective was accomplished by holding

a cylindrical heat source in direct thermal contact with
a Cylindrical section of potato. Temperature histories

of the semi-infinite potato cylinder were recorded at X=0

38

 

39

(interface of heat source and potato), X=L, and X=infinity.
Temperature histories were used to calculate the thermal
diffusivity of the potato section at X=L.

The heat exposure of the potato section was ob-
tained as the area between the temperature histories at
X=0 and X=L for the duration of the experiment. Specific
gravity was a routine test and the elastic modulus was de-
termined from data of the force applied to a potato section

and the resulting deformation of the potato section.

4.2 Equipment
The major pieces of equipment consisted of the fol-
lowing:
A. Specimen holder for transient heat transfer ex-
periments. See Figure 4.1.
B. Leeds and Northrup Precision Potentiometer
Model 8686, Serial No. 1581952
Accuracy 1 0.03% of reading + 3 microvolts with-
out reference junction
C. Leeds and Northrup Recording Potentiometer, two
pens
Model G, Serial No. 866-752270-1—1

Range 60°F to 260°F, Copper—Constantan Thermo-

couples

Accuracy 3 0.3% of full scale

40

Figure 4.1. Specimen
holder with elec-
tric heating unit
and black glass
foam insert

Figure 4.2. Specimen
holder with red
silicone rubber
heat source and
microswitch (black)

Figure 4.3. Equipment.

during a test.

From left to right:
recording potenti—
ometer, specimen
holder, autotrans-
former, and record—
ing potentiometer

 

41

 

Figure 4.4. Elastic modulus test equipment. From top
to bottom: dial gauge, load cell (below hori-
zontal bar), and parallel plates with potato
section in place

 

Figure 4.5. Heat sources: electric heating element
with steel cylinder and silicone rubber cylinder

A‘K

 

42

D. Honeywell Recording Potentiometer, two pens
Model Electronik 17, Serial No. F5731475001
Range O°F to 250°F, Copper-Constantan Thermo-
couples
Accuracy 1 0.25% of full scale
E. Mettler Analytical Balance
Type A, Serial No. 34021
Range 0 to 200 gms.
F. Testing Machine for applying and sensing force
on potato sections (Finney, 1963). See
Figure 4.4.
G. Universal Amplifier
Model RD 5612 00
H. Moseley Autograf X-Y Recorder
Model 135, Serial No. 2138
The specimen holder was designed to hold a heat
source and a potato section in intimate and uniform con-
tact with each other for the duration of an experiment,
Figure 4.2. Each half of the specimen holder was made from
a 3 in. length of standard 6 in. diameter steel pipe. The
stationary half of the holder was welded to channel iron.
A flat base plate and angle iron rails were also welded to
the channel iron. V-grooved wheels mated with the angle

iron rails maintained accurate alignment in all planes be-

tween the movable and stationary halves. The longitudinal

displacement of the V-grooved wheels from each other

 

43

facilitated the rapid installation of the movable half onto
the rails. During the experiments a constant pressure was
maintained at the heat source-potato section interface by
rotating the specimen holder 90° and supporting the holder
by the channel iron, Figure 4.3.

A microswitch and its trip lever were fastened to
the stationary half and movable half respectively, Figure
4.2. When the halves of the specimen holder were brought
together for an experiment, the microswitch completed a
circuit for an electric interval timer and for an indexing
pen on each recording potentiometer. The microswitch was
adjusted to close the circuit when the heat source and po-
tato section made contact. A separate series circuit con-
sisting of a dry cell, light, and metal plates (to simulate
the heat source and potato surfaces) were used to adjust
the microswitch. Adjustment was correct when the light
and indexing pens operated simultaneously.

The insulation for the specimen holder was a poly-
urethane type (Dow Chemical Co., QX—3851.1) with a thermal
conductivity of approximately 0.16 Btu. in.»/(hr. ftaL °F).
A 4 in. length of insulation was machined to a snug fit
in the bore of each half of the holder. Mating grooves
were machined into the halves of insulation to minimize
any air currents and convection heat losses. A hole,

31/32 in. diameter and 1 in. deep, was machined into the

face of the insulation of the movable half of the specimen

44

holder; the potato sections were installed in the hole for
the experiments. A hole of the same dimensions was machined
into the face of the insulation for the stationary half

of the specimen holder; a silicone rubber heat source was
installed in the hole for the experiments, Figure 4.2.

When an electric heating element was used for the heat
source, the temperatures were too high for the stability

of the polyurethane insulation; a glass foam insert was

made to go between the heating element and the polyurethane
insulation, Figure 4.1.

For some of the lower temperature experiments, a
heated cylinder of silicone rubber was used as a heat source,
Figure 4.5. Cylinders of silicone rubber 61/64 in. diam-
eter and 1 1/32 in. long were cut from a cured slab of sili-
cone rubber; General Electric Co., SE-3604U. When not in
experimental use, the cylinders were kept at the desired
temperature in an oven.

Most of the experiments were performed with a steel
cylinder and an electric heating element as the heat source,
Figure 4.5. The 1 in. diameter and 1 in. long steel cylé
inder was continuously heated by a 37.5 watt soldering iron
heating element. Power to the heating element was con—
trolled by an autotransformer. A thermocouple was silver

soldered to the face of the steel cylinder.

The Leeds and Northrup Model 8686 Precision Potenti-

ometer was used to check the calibration of the two recording

 

 

45

potentiometers. The recording potentiometers were cali-
brated within the manufacturers' tolerance. The instru—
ments were within the manufacturers' tolerance at the com-
pletion of the experiments. The precision potentiometer
was also used to calibrate the thermocouples.

The recording potentiometers were used to record
simultaneously the temperatures at the following locations:

1. heat source contact surface,

2. potato section contact surface,

3. X=L of the potato section, and at

4. X: infinity of the potato.

The analytical balance was used to weigh the potato
sections before and after heat treatment. For specific
gravity determinations, a suspension system was used on
the scales to obtain the weight of the potato section in
water; see Figures 4.6 and 4.7.

For elastic modulus determinations, the testing
machine consisted of:

1. air motor

2. load cell, BLH Type U-lB, 50 1b. capacity

Accuracy 1 0.25% with a maximum nonlinear—
ity of I 0.10% valid for both
tension and compression

3. parallel plates

The double—acting pneumatically driven air motor

had a 4 in. stroke and a hydraulically controlled piston

 

 

46

Figure 4.6. Weighing potato
section in air

 

Figure 4.7. Weighing potato
section in water

 

 

47

speed in both up and down directions. The speed of the
loading piston was independent of the applied force (or
constant) within the force range from O to 150 lbs. The
load cell sensed the force applied to a potato section
located between the 1 1/8 in. diameter parallel plates,
Figure 4.4.

The force signal from the load cell was amplified
and fed into the Y—axis of the X-Y recorder. A constant
pen travel time of 2.09 sec./in. was fed into the X-axis
of the X—Y recorder. Thus the compression of a potato
section was recorded as force (1b./in. of chart) vs. pen
speed (sec./in. of chart). The force scale of the X—Y
recorder was calibrated before each series of tests with
a weight of 10.050 lbs. suspended from the upper parallel
plate. The gain of the amplifier was adjusted to give a
pen deflection of 1 in. on the graph paper.

A dial gauge, Figure 4.4, accurate to i 0.001 in.,
was used to determine the downward speed of the air motor
piston. Just prior to the compression of a potato section
between the parallel plates, a stOp watch was used to meas—
ure the time required for the piston to travel 1 inch.

Thermocouples were made from No. 30 gauge copper~
constantan wire. The junctions were silver soldered after
the wires had been cleaned of insulation and had been
twisted together. The junctions were trimmed to a length

of 1/16 in. or less. Distilled water was used to calibrate

 

48

the thermocouples at temperatures of melting ice, 74°F,

157°F, and boiling water. The maximum average error of

any thermocouple was less than 0.75% of the known temper-

ature.

4.3 Experimental Procedure

4.3a Flow Chart of Experimental Procedure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 potato weight of weight of compression
sections ‘—'"‘ sections “—1” sections ’ test
in air in water
compression weight of heat heat
test n—‘ section ‘——‘ transfer source
in air test

 

 

 

 

 

 

 

 

4.3b Heat Sources

1.

Silicone Rubber

a.

The cylindrical section of rubber was heated

and kept in a controlled temperature oven.

b. When preparing for a heat transfer and

thermal properties test, the rubber cylinder
was placed in insulation at room tempera-
ture and transported 8 ft. to test room and
specimen holder. (Insulation for transport~
ing rubber cylinder was machined to mate

the insulation of the specimen holder.)

The rubber cylinder was dropped into the
specimen holder with a minimum exposure to

the ambient air.

 

 

49

d. The thermocouple was inserted into exposed
end of the rubber cylinder.

e. After each test, the rubber cylinder was
returned to the oven.

f. No rubber cylinder was used more than once
in an 8 hr. period as a heat source for the
potato section.

2. Steel Cylinder

a. The power to the heating element was turned
on a few hours prior to any experiments.

b. The power level was adjusted with the auto—
transformer to maintain the desired temper-
ature of the steel cylinder.

c. After each experiment the steel cylinder
was allowed to equilibrate to the desired

temperature.

4.3c Potato Sections

1. A 0.953 in. diameter cylindrical section was
removed from a potato. The cylinder was cut
perpendicular to the least curved surface of
the potato, Figure 4.8.

2. An aluminum ring and single-edged razor blade
were used to remove a section from the potato
cylinder.

a. The section was removed from the central

area and just below the vascular ring.

50

 

Figure 4.8. Potatoes and cutting equipment. From left
to right: aluminum ring assembly 1 1/32 in. long,
potato cylinder and ring for cutting potato section
to proper length, and boring tool for removing cy-
lindrical section from potato

 

Figure 4.9. Semi—infinite portion of potato in specimen
holder with thermocouple at X = L

 

10.

ll.

51

b. The 0.953 in. inside diameter aluminum ring

was 0.238 in. thick (length to diameter ratio

of l to 6).
Excess surface moisture was removed from the
potato section with a clean paper towel.
The potato section was weighed in air and in
distilled water, Figures 4.6 and 4.7.
Excess surface moisture was removed from the
potato section with a clean paper towel.

The potato section was used immediately for

elastic modulus determinations.
The remaining potato cylinder was placed in

a welded aluminum ring assembly and trimmed

to a length of 1 1/32 in., Figure 4.8.
Another potato section adjacent to the first

was removed from the 1 1/32 in. potato cylinder.

The aluminum ring of 2b above was used.
Excess surface moisture was removed from the

potato section and cylinder with a clean paper

towel.
The potato cylinder was placed in the movable

half of the specimen holder. The potato cyl-

inder became the semi-infinite portion of the

potato, Figure 4.9.

The X ~ L thermocouple was placed on top of

the semi-infinite portion of the potato.

 

 

 

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

52

The potato section was weighed in air and in

distilled water.
Excess surface moisture was removed from potato
section with a clean paper towel.

The thickness of potato section was measured

with calipers.
The potato section was placed on top of the

X = L thermocouple in the movable half of the

specimen holder.

The X = 0 thermocouple was placed into the po-

tato section.

After the heat transfer test, the potato sec—
tion and semi-infinite portion were placed
together in a plastic bag and sealed.

The plastic bag was placed in front of the room
air conditioner for rapid cooling to room con—
ditions.

After the potato section and semi-infinite por-

tion had equilibrated to room conditions for

a few hours, the pieces were replaced in the

specimen holder for an additional 3 min. heat
treatment at a maximum temperature of 160°F
at X = 0 of the potato.

The potato section was reweighed in air.

The thickness of the potato section was re-

measured.

 

 

22.

23.

53

The diameter of the potato section was measured
at the X = 0 surface.

The potato section was placed between the par-
allel plates of the testing machine with the

X = 0 surface next to the upper parallel plate.

4.3d Elastic Modulus Determinations

l.

The amplifier was turned on at least one hour
prior to calibration and use.

The X—Y recorder was turned on approximately
15 min. prior to calibration and use.

The calibration of the load cell, amplifier,
and X-Y recorder was checked at the beginning
and end of each day.

To minimize any horizontal components of shear,
a film of light oil was placed on the parallel
plates of the testing machine.

The air motor was energized to force downward
the piston, load cell, and upper parallel plate.

A stop watch was started when the dial gauge

indicated 0.000 in.

When the dial gauge indicated 1.000 in. the
stop watch was stopped and time recorded as
sec/in.

The X—Y recorder pen was energized just before

the upper parallel plate contacted the potato

section.

 

54

The air motor and X-Y recorder pen were turned
off when the load cell reached its limit or
when the potato section ruptured.

For each experiment the elastic modulus curve
for both the raw and heat treated potato sec—

tions were recorded on the same sheet of X-Y

recorder paper.

Transfer and Thermal Diffusivity Tests

As soon as the thermocouple was inserted in
the rubber cylinder, the two halves of the
specimen holder were pushed into contact. As
the surface of the rubber cylinder contacted
the potato section, the microswitch completed
the electrical circuit to the interval timer
and to the indexing pen on each recording

potentiometer. The specimen holder was ro—
tated 90° so that the potato section was above
the rubber cylinder and the axis of the cyl—
inders was in the vertical plane, Figure 4.3.
Thermal contact at constant pressure between

the rubber cylinder or steel cylinder and

potato section was maintained for the desired

length of test.

 

55

4.4 Discussion of Experimental Techniques
4.4a Potatoes

Excel potatoes grown on the Michigan State Univer-
sity Farm, Lake City, Michigan, were used for the tests.
The Excel variety is known to have consistent cooking qual—
ities. The potatoes were harvested in 1965 and stored at
40°F until the tests were performed in July, 1966. Stored
potatoes are normally more uniform in physical character—
istics than freshly harvested potatoes.

The potatoes were removed from storage approxi-
mately 24 hr before use and equilibrated to the testing
room temperature of 76°F. The equilibration of the pota-
toes to the testing room temperature and the performance
of all procedures in the constant temperature testing room
insured an initial condition of uniform temperature dis-
tribution in the potato specimen as required for the ther—
mal diffusivity tests.

Only firm potatoes without defects were used for
the tests. Cylinders cut from soft potatoes were not uni-
form in diameter and the diameter was less than the 0.953
in. specified for the tests. The elastic modulus of a raw
specimen from a soft potato was found to be approximately
100 psi higher than the elastic modulus of a raw specimen
from a firm potato. Ten replications were made at each

test condition.

56

4.4b Heat Transfer and Thermal Diffusivity Tests

To minimize thermocouple conduction errors, the
lead wires were placed across the face of the heat source
and wound partly around the circumference of the heat source
before entering the insulation of the specimen holder (Fig-
ure 4.1). The same method was used for placing thermocouple
leads at X = 0, X = L, and at X =00 (Figure 4.9). The
thermocouple at X =00 was silver soldered to a thin copper
wafer which held the thermocouple in proper position at
all times.

One of the boundary conditions required the tem-
perature at X =cw to be constant during the interval of
determining thermal diffusivity. The recorded temperatures
at X =<x>showed that the boundary conditions prevailed for
at least 2 1/2 min. for every test. Therefore, a data time
of 100 sec. or less was chosen for all tests.

To satisfy the conditions of one dimensional heat
transfer, a potato section length equal to 1/6 of the sec-
tion diameter was chosen. This was a compromise between
edge heat losses and convenient size potato sections.

To attain one of the objectives of the research,
the thermal diffusivity had to be determined for a potato
section before and after heat treatment. The boundary con-
ditions restricted thermal diffusivity data to the first
one hundred seconds of each test, which was satisfactory

for determinations on a raw potato section.

57

Because thermal diffusivity data could not be taken
at the end of a heat treatment, the heat treated section
and its semi-infinite portion were removed from the speci—
men holder, stored in a sealed plastic bag, and equilibrated
to the testing room temperature. After attaining the de-
sired initial condition of uniform temperature distribution,
the potato section and its semi-infinite portion were re-
placed in the specimen holder and given a 3 minute heat
treatment with a maximum temperature of 160°F at X = 0.

The first one hundred seconds of data from the second heat
treatment was used to compute the thermal diffusivity of
the heat treated potato section.

When silicone rubber cylinders were used for a heat
source, a thermocouple junction approximately 1/32 in. long
was bent perpendicular to the lead wires and was placed
in a small slit in the surface of the rubber. Thus the
longitudinal axis of the junction coincided with the long-
itudinal axis of the cylinder. The same technique was used
for the placement of a thermocouple at X = 0 of the potato
section. The average temperature of the two thermocouples
was used as the temperature at X = 0.

A thermocouple was silver soldered in a small de-
pression in the surface of the steel cylinder. Lead wires
were laid in the groove across the face of the cylinder.
The thermocouple junction was soldered in the plane of the

surface of the cylinder and made direct contact with the

 

58

X = 0 surface of the potato section. Therefore, a separate
thermocouple at X = 0 in the potato section was eliminated
and the thermocouple on the steel cylinder measured the
temperature at X = 0.

A length of l in. was chosen for the steel cylinder
to insure uniform heating at the surface in contact with
the potato section. To check for variations in surface
temperature, a thermocouple was placed at several positions
on the surface of the steel cylinder. No variations in

temperature were found.

4.4c Specific Gravity Tests

 

When a section was cut from a potato, moisture ac—
cumulated on the surfaces. Prior to any weighing opera-
tions the excess moisture was removed with a paper towel.
The potato sections were weighed in grams accurate to the
third decimal place. Removal of moisture other than excess
surface moisture may have introduced some error in the spe-
cific gravity determinations. But the ten replications‘
for each test condition should have averaged out any such

random errors.

4.4d Elastic Modulus Tests

The velocity of the air motor and piston on the
testing machine was not uniform from one operation to the
next. An error in the velocity of the piston would cause

a large error in the calculated strain and the resulting

 

S9

elastic modulus of the potato section. By determining the
velocity of the piston for a one inch displacement preced—
ing the contact of the upper parallel plate with the potato
section for each individual test, this error was minimized

to + 1%.

 

5. RESULTS AND DISCUSSION

Finite difference methods have been adapted to com-
puter use for solving heat transfer equations. The magni-
tude of the errors introduced by the estimation process
are frequently less than the magnitude of the errors in
the data. This is shown in Table 5.1 where many of the
root mean square values are less than 0.5°F. The record-
ing potentiometers had a permissible error of 0.6°Fo

All data calculations were done by the Control Data
Corporation 3600 Computer at Michigan State University.

All curve fittings were done with a least squares computer
program identified as E2 UTEX LSCFWOP.

The heat transfer methods used in the experiments
combined with the finite difference method of data analysis
had the advantages of speed, simplicity, ease of applica-
tion to other products and accuracy. Depending upon test
duration, approximately four heat treatments could be com—
pleted in an hour. No difficult laboratory preparations
or techniques were involved. Other biological products
could be adapted to the specimen holder and large masses
were not required. Random errors were cancelled by the
finite difference method, but a continuous error of +1°F

in temperature measurement was found to cause an error of

60

 

61

 

 

 

 

 

mav.o mao.o a¢¢.o omm.o mmmmum><
mmm.o mom.o 646.0 mmm.a mam ma mas
mmm.o mom.o mmv.o aaa.a cam oa was
mam.o «mm.o mmm.o mma.o mam a can
Hmm.o amm.o omm.o HmH.H mma ma ems
Hoo.o amm.o Hmm.o omm.a mma oa awe
mam.o som.o Ram.o Ram.o aka 0H Has
mam.o mma.o omm.o moa.o moa 0H mos
.smov Tamas Amos hence Amos panes

6mm om u u umm ooa u u umm om n p umm OOH u u o u x pm umme .oz mmwumm

oumuom Umumom oumwom 3mm .QEmB ESEHXMZ mo cumcmq umma

mmSHm> mHMSUm and: uoom

 

mucoumm ooa paw monoumm om umumm UmuMHSUHmo mmHuH>HmSMMHo HmEumcu
Eoum mcauHSmmu mmudumquEmu mo modam> mumsvm CmmE noon mo conflumdeou .H.m magma

62

—0.5% or less in the value of the thermal diffusivity. As
indicated in the literature reviewed, errors of 5% were
not uncommon in the determination of thermal properties.
Some of the terms used in the tabulations and in
the discussions to follow are clarified. The value for the
diffusivity of a "raw" potato section was determined from
data taken during the first fifty seconds of heat treatment.
(Data were originally taken for one hundred seconds but
changed to fifty seconds for reasons explained in the next
section.) "Heated potato" sections received a specified
heat treatment, were cooled to desirable initial thermal
conditions, and were reheated for a short time at a low
temperature. The only purpose of the reheat was to obtain
data for an additional fifty second interval to determine
the diffusivity of the potato section after the desired
heat treatment. Thus an assumption was made that the re-
heat had no effect on the thermal or physical properties
of the heat treated potato section. The same reheat treat-
ment was given to all heat treated potato sections.
Complete data on all tests and replications is in
Appendix B. The tabulations and graphs in “Results and
Discussion” contain the averages of ten replications for

each test.

5.1 Thermal Diffusivity_
Temperatures of the potato sections at X = 0, X = L,

and X =€O were read from the recorded charts in 10 sec

 

63

intervals from time t = O to t = 100 sec. An assumption
was made that the thermal properties of the raw potato sec-
tion were constant during the first one hundred seconds

of any heat treatment and would not influence the value

of thermal diffusivity. This assumption was investigated
by computing the thermal diffusivities at t = 50 sec and

at t = 100 sec. An inspection of Table 5.1 shows that for
all raw potato diffusivities, the average root mean square
value of the difference between the calculated temperatures
and the measured temperatures was higher for the t = 100
sec determinations than for the t = 50 sec determinations.
The average values were 0.980°F for t = 100 sec and 0.447°F
for t = 50 sec. In contrast, small differences occurred
between the rms values at t = 100 sec and t = 50 sec for
the heat treated sections of potato.

As the severity of the heat treatment was increased,
with maximum temperatures of 195°F and above at X = 0, the
rms values for raw potato sections increased to above 1°F
for t = 100 sec. This was not true for the raw potato sec—
tions for t = 50 sec. The agreement in rms values for both
raw and heat treated sections at t = 50 sec was good and
the averages were nearly the same. There were no consis-
tent trends of individual values.

Thus the larger errors in the t = 100 sec data were
due to the changing properties within the potato. Starch

begins to gelatinize in the range of 147°F to 160°F (Talburt

 

64

and Smith, 1959), with moisture movement and evaporation
occurring. The higher temperatures accelerated the changes.
This also accounts for small increases in the rms values

at the higher temperatures after only 50 sec. On this
basis, the t = 50 sec diffusivity data were used for all
subsequent correlations between parameters.

The plot of thermal diffusivity in Figures 5.2 and
5.3 shows the data of the 714 test series to be much higher
than any of the other points. The data was rechecked but
no errors or inconsistencies were found. The rms values
for the thermal diffusivity temperatures of the 714 test
series were comparable to the rms values of other tests.
The 714 test series data were evaluated in two ways: as-
suming the data to be in error, and assuming the data to
be indicative of some unusual change. To give credence
to the 714 test series data, other tests should be performed
with slightly different times and temperatures.

The thermal diffusivity of the raw potato sections
was found to be of the same order of magnitude as some
other fruits and vegetables. Parker and Stout (1963) de-
termined the thermal diffusivity of tart cherry flesh; 5.00

-3

x 10 ftg/hr to 5.20 x 10_3 ftg/hr. Kethley, Cown, and

Bellinger (1950) gave values for fruits and vegetables that

3 ftg/hr.

ranged from 5.35 x 10—3 ftg/hr to 6.15 x 10-
Hurwicz and Tischer (1956) experienced increasing

and decreasing values of thermal diffusivity for different

 

 

65

combinations of time and temperature when processing canned

beef. A maximum critical point was also noted.

5.2 Elastic Modulus

 

Data for elastic modulus determinations was obtained
from the X—Y recorder charts by constructing a tangent to
the first linear portion of the curve following the initial
deformation of the potato section, Figures 5.7, 5.8, and
5.9. The slope of the tangent was used in the calculation
of the elastic modulus.

Because the methods of obtaining data for elastic
modulus determinations involved a destructive test, two
sections were removed from each cylinder cut from a potato.
The section next to the vascular ring was used for raw po—
tato elastic modulus determinations. The heat treatment
of the other potato section was followed by the elastic
modulus determination. Thus an assumption was made that
the elastic moduli of the two raw sections were equal.

No information was found that invalidated the assumption.

After the elastic modulus was computed for all tests
and replications, the results showed more variation in elas-
tic modulus between the raw potato replications (a minimum
of 51 psi) than between the averages of the tests (a max-
imum variation of 39 psi). Thus the elastic moduli of the
heated potato sections were used for the correlations and
the assumption that the elastic moduli of the two raw sec—

tions were equal became unnecessary.

 

66

5.3 Specific Gravity_

Specific gravity was determined on both raw potato
sections; one used for raw elastic modulus tests and the
one used for heat treatment tests. The standard equation
(5.1) was used. The temperature was maintained at 76°F

for all tests.

weight in air (5 1)
weight in air - weight in water °

Specific Gravity =
The potato section used for the elastic modulus
test was located nearer the vascular ring than the section
used for the heat treatment tests. For all tests and rep-
lications, the specific gravity for the outer section aver-
aged 0.976% higher than the specific gravity of the inner
section. These results agreed with the findings of Whit—
tenberger and Nutting (1950) and Sharma E; El: (1958).
Correlations between specific gravity and the other
parameters were attempted but none were found to exist.

Also, the specific gravity did not show any pattern of

change over the 15-day testing period.

5.4 Heat Exposure
When using a temperature—time relationship in this
study, the area under the heating curves was considered a
parameter and correlated with thermal diffusivity and elas-
tic modulus. For the purposes of this research, such an
area was denoted as heat exposure with units of °F-min.

No information was found in the literature as to

 

67

the individual effects of temperature and time on biolog-
ical products. One intuitively assumes that exposure to
a 1°F temperature difference for l min at 200°F would have
more influence on a biological product than an exposure
of 1°F temperature difference for 1 min at 100°F. In the
absence of any precedent on the subject, a base of 160°F
was chosen; only temperatures above 160°F were used in the
measurement of the area under the heating curve. The area
was measured with a planimeter. A base temperature of
160°F was chosen for the following reasons:
1. Starch begins to gelatinize in the range of
147°F to 160°F.
2. The maximum temperature of the second heat
treatment on each potato section was 160°F
or less and therefore did not contribute to
the area.
In the correlations of the parameters, the heat
exposure with units of °F-min was used as the independent

variable.

5.5 Correlation of Parameters

 

5.5a Thermal Diffusivity and Storage Time

 

The thermal diffusivity tests were conducted dur-
ing a 15-day interval from July 9, 1966, to July 24, 1966.
An unexpected variation of thermal diffusivity with the
storage interval was found. Figure 5.1 is a plot of the

thermal diffusivity of the raw potato sections against the

 

68

mm

 

ummu mo oumo cam >ua>am3mmwo Hmeuonu cmm3umn dacwcoaumHom

$2 52. s .28 a:

mw _N m. N. 9 2
_ 4 L T a «

.H.m musmwm

l on

 

a on

 

 

 

om Mwsnmo Iowa“

m
U:

( .

Z

69

test dates. The diffusivity decreased linearily with time
according to the relation

3

04 = 6.327 x 10" - (1.126 x 10"4

x test date) (5.1)
The root mean square value of the relation was 4.08 x 10-4
ftg/hr. Specific gravity and elastic modulus did not show
any correlations with the storage interval. Why the thermal
diffusivity decreased with storage interval is not known.
One can surmise that the change was due to small physiolog—
ical changes that are not detectable with the usual macro-
physical tests.

The variation in thermal diffusivity due to the
storage interval was larger than the variations caused by
heat treatments. Thus for subsequent correlations, the

change in diffusivity from the raw section to the heat

treated section was used for the parameter.

5.5b Thermal Diffusivity_and Heat Exposure

Data from Table 5.2 was used to plot the upper curve
in Figure 5.2. As noted in Section 5.5a, the ordinate for
the curve is the change in diffusivity from the raw section
to the heat treated section. Assuming the 714 test series
point to be valid, it may have been a critical point or a
Point of maximum influence of heat exposure on thermal dif-
fusivity. Also, the point may have been due to the rupture

of the cell walls and other physical changes that were not

complete or uniform throughout the section. The extent of

cooking is indicated in Figure 5.4 by the depth of the black

QWM'Tirfimaw '3 Tim

7O

 

 

 

 

 

 

 

 

 

00.600 060.6 600.0 000 00 006 00:00u0
00.n06 000.0 000.6 000 00 600 00I6Hu0
00.000 000.0 060.6 000 6 000 00-0010
00.000 660.6 000.0 000 00 600 00:60:»
00.000 000.6 000.0 000 00 005 00:00-0
00.000 005.0 006.0 000 00 000 00:00-0
00.00 000.0 000.0 000 00 000 00u0u0

x006 u 0.0 Aunxmww0nofix0 Aun\m000u00x0 10.0 10060

mudmomxm oumwom Umpmmm oumwom 30m 0 n x no #009 mo .02 mmflumm mpmo
000m >00>0000000 000>0000000 .0600 essaxmz 000000 0000

 

mHSmOQXm 0003 cam >00>HmSMMHU

Hmeumcu mo mmsam> mmwum>m spa: ompmasnmu mummp mo coaudfluummo cam muma

.N.m OHQMB

Modulus (psi)

Elastic

Change in Thermal Diffusivity (H0335?)

71

 

.1
W
.1
fl
.1

 

 

 

 

 

CY”
T _
7'7 7?.l
GO 0 0724
7n
709 78
o 4 _l 1 l l _L
4“) ’T’ I 1 I ”cf 1

07“

 

300*

200—

 

O 1 L 1 l 1 A
0 ICC 200 300 400 500 600
Heat Exposure (°F-mm)

Figure 5.2. Parameters of thermal diffusivity and elastic modulus
versus heat exposure

 

 

700

 

72

ring (associated with enzyme activity) below the X = 0
surface; the depth of the ring increased with cooking.

The heat treated sections of the 714 test series were soft
at X = 0 and firm at X = L. The heat treated sections of
the 719 test series were soft at both surfaces and appeared
more uniform in physical appearance. Note that the 719
test series had the most severe heat exposure and the low-
est thermal diffusivity.

The correlation curve shows that the thermal dif-
fusivity increased as heat exposure was increased up to
350 °F-min. Above a heat exposure of 350 °F-min diffusiv-
ity decreased. The correlation was given by

4 6

=<.= 1.031 x 10‘ + (2.528 x 10‘ x HE) —

9

[3.628 x 10‘ x HE2] (5.2)

where: HE = heat exposure (°F — min)

4

The correlation had a rms value of 4.91 x 10- ftg/hr.

5.5c Thermal Diffusivity and Maximum Temperature at X = L

 

Because the thermal diffusivity of the potato sec-
tions was determined at X = L, a correlation with the max-
imum temperature at X = L was made. The correlation was

given by

2 4

c(_= -l.962 x 10‘ + (2.617 x 10' x T) - (8.500

x 10"7 x T2) (5.3)
where: T = maximum temperature at X = L (°F)

The rms value of the correlation was 5.00 x 10-4 ftg/hr.

73

The curve in Figure 5.3 is similar in shape to the
thermal diffusivity vs. heat exposure curve in Figure 5.2.
According to the correlation curve, thermal diffusivity
was a maximum for a temperature of 155°F at Xy= L. But
as in the previous correlation, the 714 test series had
the maximum values for the curve at an average temperature
of 165°F at X = L. Having the maximum diffusivity occur
in the 155°F to 165°F range suggests that the maximum dif-
fusivity was related to the starch gelatinization of the
potato. A maximum physical and/or chemical change in the
potato may have contributed to the maximum value of thermal
diffusivity. Talburt and Smith (1959) did not discuss the
factors that may influence the temperature at which gelat—
inization occurs.

An examination of Table 5.3 and Figure 5.3 shows
that the maximum temperatures at X = L differed by only
4°F for the 717 and the 711 test series. Correspondingly,
the diffusivities changed very little; 0.327 ftg/hr and
0.297 ftg/hr, respectively. This reaction may be compared
to the differences of 2°F between the 724 and the 714 test
series. The diffusivities changed from 0.322 ftg/hr to
0.792 ftg/hr. This analysis indicates that the 165°F tem-
perature may be the critical point for reactions within
the potato section.

The results of the correlation between thermal dif-

fusivity and maximum temperature at X = L Show the following:

 

A u x um musumuodemu EDEmea
0:» 0:0 Mu0>003mwflo Hmsumcu :0 mmcmcu an» cmmzumn dacmCOHumamm .m.m madman

Coibnx .0 820.0068. 606:0:

74

o:

02

09

OS

 

 

0:0

_

SN

6~mu

J

4|

 

 

 

 

0.

(

0m Amysnmg (auuaul u! abuoqg

M
Q”:

75

 

 

 

 

 

 

 

0000.0 00.000 00.000 000.0 000 m0m 00 000
0000.0 00.00N mm.00¢ mm0.0 000 00m 00 000
0000.0 00.00m 00.000 0mm.0 N00 NON 0 000
0000.0 00.00m 00.000 mmm.0 000 000 00 0N0
0000.0 00.000 00.000 mwm.0 000 000 00 0N0
0000.0 00.000 00.000 00N.0 000 000 00 000
0000.0 00.000 00.00 000.0 000 N00 00 000
00000 1000 u 0.0 A000000.005 00.0 10.0. 00060
000000 000000 000000 000000 00000000 000>0000000 q u x 0 n x 0000 mo .02
>u0>0uw 0305002 000m 80 mmc0nu 00 .0809 00 .0808 £00800 000umm
00000000 0000000 8:80x02 8:80x02 0008
0000080000

020 mo 00:00> 00000>0 £003 000003000 00000 mo 80000000000 080 mu0o .m.0 0090B

 

76

1. Thermal diffusivity increased as the maximum
temperature was increased to 155°F.

2. Thermal diffusivity decreased for temperatures
above 155°F.

3. The lowest and highest temperatures changed

the thermal diffusivity by the same amount.

5.5d Elastic Modulus and Heat Exposure

 

The lower curve in Figure 5.2 shows that the ini-
tial influence of heat exposure was to increase the elas-

tic modulus or to make the potato section less stiff and

 

more "rubbery." Additional heat exposure made the potato
sections softer. These results are comparable to the find-
ings of Tuomy E; El, (l963) with respect to the influence
of heat on meat; as heat treatment increased the toughen—
ing increased. Tenderness was shown to be dependent on
both time and temperature.

The decrease in elastic modulus with increasing
heat exposure began in the area of the 711 and the 717 test
series. A comparison of the data in Table 5.3 for these
tests shows that a long time and low temperature (10 min
and 179°F) had the same influence on elastic modulus as
a higher temperature and short time (4 min and 212°F).
Note that the heat exposures are similar, being 186.73
°F-min and 198.70 °F-min, respectively. Similar compari-
sons can be made for the 714 and the 724 test series; the

temperatures and times were different but the heat exposures

77

and the resulting elastic moduli were equivalent.

The relationships between elastic modulus and heat
exposure are shown more vividly in Figures 5.5 and 5.6.
The rupture of a 719 test series potato between the paral—
lel plates is shown in Figure 5.5. Heat exposure increased
from left to right on the potato sections in Figure 5.6.
Elastic modulus tests on the potato sections in Figures
5.4 and 5.6 resulted in the plots shown in Figures 5.7,
5.8, and 5.9. In the latter figures, the first break in
the slope of the force-time line coincided with the initial
rupture of the potato section. Approximately half of the
heat treated potato sections of the 721 test series exhib-
ited broken force—time curves. All of the heat-treated
potato sections of the 714, 719, and 724 test series ex-
hibited broken force-time curves. In general, the break
occurred with decreasing values of force as the heat ex-
posure was increased.

The correlation between the elastic modulus and
heat exposure was given by:

2

E = 3.568xlO + (1.14c1x10"l

x HE) - (5.786xlO-4

x H82) (5.4)

where: E elastic modulus (psi)

HE heat exposure (°F-min)

The rms value of the correlation was 36.53 psi.

 

Figure 5.4. Representative
heat treated potato
sections and corres—
ponding semi-infinite
cylinders. Test
series number s are ,
from left to right,
717, 714, and 719.

Figure 5.5. Rupture of heat
treated potato sec-
tion representative
of test series number
719

 

Figure 5.6. Representative
ruptured heat treated
potato sections. Test
series numbers are,
from left to right,
717, 714, and 719.

 

79

 

mmflnmm ummu has mo mm>usu mawulmuuom 0>Humucmmwummm

 

.h.m masons

 

 

 

     

 

 

    

m Auomv veep
v m e
mal ¢|_ ILA\I4 _ _ N 00
.cmacew
Io.
L8
.lom
22cm. Swims

uo.om: m
In;
n.0m

_ It! _ t

 

 

 

 

(‘q|) 33103

80

 

nmflumm away was no mm>usu meulmuuom m>HumucmmmHQmm

 

 

228
E8:

  

 

3mm. mes.

.m.m mucosa

 

 

0.

cm

on

oc

on

 

 

(’ql) 33103

8].

£4

 

mm unow man mo mo>usu mElemuuom m>HbmuC®moummx

a... 2.:

 

 

w
_

 

.m.m

‘

@HZU

[Harm

 

 

tic.

I48

 

S

at at
c
(‘qn 93105

 

 

82

5.5e 'Thermal Diffusivity and Elastic Modulus

The plot of thermal diffusivity and elastic modulus
against a common parameter of heat exposure in Figure 5.2
indicates that diffusivity and elastic modulus have simi-
lar behaviors with respect to heat exposure. As heat ex—
posure was increased, diffusivity and elastic modulus in-
creased a small amount and then decreased. The initial
rapid decrease in the elastic moduli of the potato sections

was accompanied by the maximum increase in thermal diffusiv—

ity.

5.6 Application of Results

The thermal diffusivity and the elastic moduli of
the heat treated potato sections are plotted in Figure 5.2
to indicate a unique application of physical and thermal
properties. Elastic modulus was a measure of the degree
of cooking or heat treatment of the potato. Therefore,
a potato processor could specify a desirable elastic modu-
lus for his product. An engineer could use the curves in
Figure 5.2 to select the required heat exposure for the
product. A value for heat exposure would permit an engin-
eer to select the most desirable combination of temperature
and time with respect to such factors as energy sources,
equipment capacity, production rates, and costs of opera-
tion.

From the chosen point on the elastic modulus curve,

a vertical line would be extended to the thermal diffusivity

 

83

curve. Predetermined values of density and specific heat
of the potato would be used with the value of thermal dif—
fusivity to calculate the thermal conductivity of the po—

tato. Fourier's heat conduction equation

dT
where: q = heat requirements (Btu/hr)
would be used to determine the energy requirements of the

process. The advantages of determining the energy require—

ments of the process were discussed in chapter one.

 

6. CONCLUSIONS

1. The finite difference method of calculating
the thermal diffusivity from temperature history data pro—
vided less variability than the guarded hot plate method
and the Cenco-Fitch apparatus used by other researchers.

2. The thermal diffusivities calculated for the
potato sections at time equal to 50 seconds had lower root
mean square values than the values calculated at time equal
to 100 seconds.

3. The thermal diffusivity of Excel potatoes
decreased during a lS-day storage at 40°F. The lS-day
storage had no influence on other parameters.

4. The specific gravity of the raw potato sections
was not related to any of the determined thermal or phys-
ical property parameters.

5. The thermal diffusivity of the potato sections
was related to the maximum temperature at X = L. As tem-
perature increased, the thermal diffusivity increased up
to a maximum and then decreased with higher temperatures.

6. The thermal diffusivity of the potato sections
was related to heat exposure. As heating increased, ther—

mal diffusivity increased up to a maximum and then decreased

with additional heating.

84

85

7. The heating of the potato section initially
increased the elastic modulus. As cooking progressed, the
elastic modulus decreased rapidly.

8. A sudden decrease in elastic modulus of the
potato sections was accompanied by the maximum increase
in thermal diffusivity.

9. The maximum thermal diffusivity was associated

with the starch gelatinization of the potato section.

7. RECOMMENDATIONS FOR FUTURE WORK

The results of this research have indicated an exi-
gency to investigate the following areas:

1. Determine the relationships between time and
temperature for the heat exposure of food products. Derive
a standard definition for heat exposure that would have
universal application and acceptance.

2. Determine the individual contributions of ther—
mal conductivity, density, and specific heat to the varia-
tions of thermal diffusivity with respect to processing
food products from the raw state to the cooked state.

3. Investigate the existence of critical points
or points of maximum change in the thermal properties of
food products.

4. Define the cooked state of food products in
terms of elastic modulus or by standard engineering tests.

5. Determine whether or not meats, fruits, and
vegetables have similar curves for relationships between
thermal prOperties and physical properties.

6. With respect to vegetables, investigate the
variation of thermal diffusivity with time in storage and

relate the variation to some defined parameter.

86

REFERENCES

Ball, C. Olin, and F. C. W. Olson (1957). Sterilization
in Food Technology. McGraw—Hill Book Co., New
York, N.Y. 654 pp.

 

Beck, James V. (1963). Calculation of thermal diffusivity
from temperature measurements. Transactions of
the ASME, Journal of Heat Transfer, Series C, 85:
181—182.

Bennett, A. H., W. G. Chace, Jr., and R. H. Cubbedge (1962).
Estimating thermal conductivity of fruit and vege-
table components—-the Fitch method. ASHRAE Jour-
nal, 4, No. 9:80-85.

Bennett, A. H., w. G. Chace, Jr., and R. H. Cubbedge (1964).
Thermal conductivity of Valencia orange and Marsh
grapefruit rind and juice vesicles. ASHRAE Trans—
actions, 70:256-259.

Carslaw, H. 5., and J. C. Jaeger (1959). Conduction of
Heat in Solids. Oxford University Press, London,
England. 510 pp.

 

Crafts, A. S. (1944). Cellular changes in certain fruits
and vegetables during blanching and dehydration.
Food Research, 9:442~452.

Charm, Stanley E. (1963a). The Fundamentals of Food Engin-
eering. Avi Publishing Co., Westport, Conn. 592

PP0

Charm, Stanley (1963b). A method for experimentally eval-
uating heat-transfer coefficients in freezers and
thermal conductivity of frozen foods. Food Tech—
nology, 17:1305-1308.

Dyner, Henri, and August L. Hesselschwerdt, Jr. (1964).
Temperature-time characteristics during food pre—
cooling. ASHRAE Transactions, 70:249-255.

Eckert, E. R. G., and Robert M. Drake, Jr. (1959). Heat

and Mass Transfer. McGraw-Hill Book Co., New York,
N.Y. 530 pp.

87

 

88

Eucken, A. (1940). Allgemeine gesetzmassigkeiten fur das
warmeleitvermogen verschiedener stoffarten und
aggregatzustande. Forsch. Gebiete Ingenieur.
Ausgabe A, ll(l):6—20.

Evans, H. L., and P. W. Board (1954). Studies in canning
processes. I. Effect of headspace on heat pene-
tration in products heating by conduction. Food
Technology, 8:258-262.

Evans, H. L. (1958). Studies in canning processes. II.
The effects of the variation with temperature of
thermal properties of foods. Food Technology, 12:
276-280.

Finney, Essex Eugene, Jr. (1963). The viscoelastic behavior
of the potato, solanum tuberosum, under quasi—static
loading. Thesis for degree of Ph.D., Mich. State
Univ., East Lansing. (Unpublished.)

 

Gurney, H. P., and J. Lurie (1923). Charts for estimating
temperature distributions in heating or cooling
solid shapes. Industrial and Engineering Chemis-
try, 15:1170-1172.

Hurwicz, H., and R. G. Tischer (1952). Heat processing
of beef. II. Development of isothermal and iso-
chronal distributions during heat processing of
beef. Food Research, 17:518-542.

Hurwicz, H., and R. G. Tischer (1956). Heat processing
of beef, part VI. Thermal diffusivity and "slopes"
of heating and cooling curves for the high temper-
ature process. Food Research, 21:147-155.

Kaczmarzyk, Leonard M., O. Fennema, and William D. Powrie
(1963). Changes produced in Wisconsin green snap
beans by blanching. Food Technology, 17:943-946.

Kethley, T. W., W. B. Cown, and F. Bellinger (1950). An
estimate of the thermal conductivities of fruits
and vegetables. Refrigerating Engineering, 58:
49-500

Kramer, Amihud, and Bernard A. Twigg (1962). Fundamentals
of Quality Control for the Food Industry. Avi Pub-
lishing Co., Westport, Conn. 512 pp.

 

Kreith, Frank (1958). Principles of Heat Transfer. Inter—
national Textbook Co., Scranton, Pa. 553 pp.

:lTl: 17'“

0k“

89

Lentz, C. P. (1961). Thermal conductivity of meats, fats,
gelatin gels, and ice. Food Technology, 15:243-
247.

Long, R. A. K. (1955). Some thermodynamic properties of
fish and their effect on the rate of freezing.
Journal of the Science of Food and Agriculture,
6:621-633.

Lujan, Lauro, and Ora Smith (1964). Potato quality, XXIV.
Objective measurement of mealiness in potatoes.
American Potato Journal, 41:244-252.

Maxwell, James Clerk (1891). A Treatise on Electricity
and Magnetism. Dover Publications, Inc.4Tl9547.
New York, N.Y.; Vol. 1, 506 pp.; Vol. 2, 500 pp.

 

 

Melnick, Daniel, Melvin Hochberg, and Bernard L. Oser (1944).
Comparative study of steam and hot water blanching.
Food Research, 9:148-153.

Miller, Herbert L., and J. Edward Sunderland (1963). Ther—
mal conductivity of beef. Food Technology, 17:
490-492.

Moline, S. W., J. A. Sawdye, A. J. Short, and A. P. Rinfret
(1961). Thermal properties of foods at low temper-
atures. I. Specific heat. Food Technology, 15:
228—231.

Nicholas, R. C., and I. J. Pflug (1961). Over- and under-
pasteurization of fresh cucumber pickles. Food
Technology, 16(2):lO4—108.

Olson, F. C. W., and J. M. Jackson (1942). Heating curves--
theory and application. Industrial and Engineer-
ing Chemistry, 34:337-341.

Parker, Rayburn E., and B. A. Stout (1966). Thermal prop-
erties of tart cherries. American Society of Ag-
ricultural Engineers Paper No. 66—337. Saint
Joseph, Michigan. 22 pp.

Personius, Catherine J., and Paul F. Sharp (1938). Ad—
hesion of potato-tuber cells as influenced by tem-
perature. Food Research, 3:513-524.

Porter, W. L., T. J. Fitzpatrick, and E. A. Talley (1964).
Studies of the relationship of specific gravity
to total solids of potatoes. American Potato Jour-
nal, 41:329-336.

9O

Riedel, L. (1951). The refrigerating effect required to
freeze fruits and vegetables. Refrigerating Engin—
eering, 59:670-673.

Schneider, P. J. (1955). Conduction Heat Transfer. Addi-
son-Wesley, Inc., Reading, Mass. 395 pp.

Sharma, M. K., D. R. Isleib, and S. T. Dexter (1958). Spe-
cific gravity of different zones within potato
tubers. American Potato Journal, 35:784-788.

Sharma, M. K., D. R. Isleib, and S. T. Dexter (1959). The
influence of specific gravity and chemical composi-
tion on hardness of potato tubers after cooking.
American Potato Journal, 36:105-112.

Short, Byron E., and Luis H. Bartlett (1944). The specific
heat of foodstuffs. University of Texas, Bureau
of Engineering Research Bulletin 4432. 39 pp.

Short, Byron E., and Horace E. Staph (1951). The energy
content of foods. Ice and Refrigeration, 121:
No. 5 (Nov.), pp. 23—26.

Short, Byron E., W. R. Woolrich, and Luis H. Bartlett (1942).
Specific heats of food stuffs. Refrigerating En-
gineering, 44:385—388.

Siebel, E. (1892). Specific heats of various products.
Ice and Refrigeration, 2:256—257.

Simpson, Jean 1., and Evelyn G. Halliday (1941). Chemical
and histological studies of the disintegration of
cell-membrane materials in vegetables during cook-
ing. Food Research, 6:189-206.

Staph, Horace E. (1949). Specific heats of foodstuffs.
Refrigerating Engineering, 57:767—771.

Staph, Horace E., and W. R. Woolrich (1951). Specific and
latent heats of foods in the freezing zone. Re-
frigerating Engineering, 59:1086-1089, 1114.

Talburt, William F., and Ora Smith (1959). Potato Process-
ing. Avi Publishing Co., Westport, Conn. 475 pp.

 

Tressler, Donald K., and Clifford F. Evers (1957). The_
Freezing Preservation of Foods. Vol. I,_Freezing
of Fresh Foods. Avi Publishing Co., Westport,
Conn. 1214 pp.

 

 

 

91

Tuomy, J. M., R. J. Lechnir, and Terrance Miller (1963).
Effect of cooking temperature and time on the ten-
derness of beef. Food Technology, 17:1457—1460.

Walters, Roger E., and K. N. May (1963). Thermal conduc-
tivity and density of chicken breast muscle and
skin. Food Technology, 17:808—811.

Weier, T. Elliot, and C. Ralph Stocking (1949). Histolog—
ical changes induced in fruits and vegetables by
processing. Advances in Food Research, 2:297-342.

Whittenberger, R. T., and G. C. Nutting (1950). Observa-
tions on sloughing of potatoes. Food Research,
15:331-339.

Wing, P., and C. J. Monego (1959). Thermal insulation
measurements on textiles--a comparison of two
methods. ASTM Bul., 241:29—33.

Zaehringer, Mary V., Helen H. Cunningham, Duane J. Le Tourneau,
and Joyce T. Hofstrand (1963). Standardization of
a cooking method for objective evaluation of potato
texture. Food Technology, 17:1321—1323.

 

 

 

APPENDIX A

Thermal Diffusivity Computer Program

FTN5.11

(100110030???)

98

10

99

?n

23
21

2?

08/17/66

PROGHAH wonnr¢

FIND THEFHAL )IF‘URIVITY IN A FINITE WALL or A sent-INFINITE POTATO HHERE
NTIH I N0. HF INPUTS. TIM I TIMES OF INPUTS. TIER I TEMP AT X I O

TIL I TEVP AT x s L. TXINF a TEMP AT x I INFINITY, UT 1 TIME STEP.

VMAx I LENGTH OF CALCULATION. ALP I ASSUHED ALPHA, SMINFL I SEMI-INFINITE
LENGTH. TBFO : INITIAL TFHP, MN I NO, or NODES. JL I THERHOCCUPLE
POSITION AT T = L. INDEX I COUNTER. TT I STARTING TIME. Tnov I TIME JUMP
neTHEEM Tun MFASURFD TEMPS, vAxc I couATER, PL I LENGTH OF POTATO SLICE
AT x I L. JJ : MlnnLF NODE. Tx I TIME STEP. T I CALCULATED TEMP.

x I CALCULATED DISTANCE

NI NUHDEF 0F TESTS IN THF PROGRAM

DIHEMSION Tt5I), TZtVISOO). TXL(300I. TXINF(50). TIHTSO). 1(50). T

1ESTNO(50). PI(50). TFEGTSL)

READ 99. NTI*.MN.JL.PT.YNAX.ALP.~

FOQHAT (3'1U13r10I73!10’

PRINT 10

FORMAT (/(1FNJU. INPUTS.5x.9HNO. NODES.SX.AHXIL NODE.5x.2HDT.SI.¢H

1vnax.5:.sHALP~A.6x.12HN0. or TESTSII

PRINT 99. NTIW.MN,JL.DT.YMAX.AIP.N

FORMAT (bx.12.1?X.12.10X.12.7X.‘5.2.4!.F4.O.5X.F5.3.RX.13)
READ 110. (TITCI‘). IA=1.NTI")

FORMAT (Er1n.TT

PRINT )1

FORMAT (1(Hx.15HTIHES 0b INPUTST)

pRlN‘ Sir. ‘Ti”(l‘)0 IA.1DVTIH)

FORMAT (PFIG.J)

n0 6 ItloN

FORMAT (I. F1‘.3. 10510.3)

FORMAT ($10.1.1x.10710.3)

roanzT TITn.rTH.9.)FTS.J.2‘15.?I

ITFRI1

ALvsP,nos

READ 2n, TESTIO(I).PI(II.TXINF(|T

FORMAT (JFTF.$)

Tr (TESTTU(1)’ 506025

PRINT 91. YESTUCII)

FORMAT {/(HHTEST NO..FR.6)I

PRINT ?2. poIT

ronHAT (l(Hx,24HPOTATO LENGTH AT KIL Tc ,Fn,3,1x,6HlNCHES))
READ 111' (Tfku (In): [9:10 LII")

FORMAT (rr1(.~v

PRINT T?

F0~HAT (1(Ri.IQNTEM9tRATUHtS AT X=O))

PRINT 111. ('[F+([H). 18:1. ‘71")

FQJHAT (EFIn.2)

READ 11,0 (“I..(l"‘). (H2105'11V)

FouMAT (Ar1n.3)

PRINT 16

FORMAT {/(sy,;9~TEMDIRATURES AT X=L))

pRlNI 11*, 47(L(IH,. 1H31,‘Y[H)

FOQMAT (EF16.2)

PRINT 14. Tx'ILTT)

roeMAT (1(Hx,)JATFMQIRATURt AT X=1NFINITY IS.F7.7))
TREG(I):TXIN‘(I)

PRINT 15

FORMAT tI/‘bx'QHTILqAT[0N,4x,11flUIFFUSIVITV))

93

FTN5.11

201

278
21?

20?

203

303

22?

94

08/17/66

PRINT 314. ITER.ALP
FORMAT (Ex.12.5x.F15.8)
INDEisf
TTI TIH()NDEY¢1)
INDEI:INDE¥¢1
TMOVI TTF(IN0El)-TIN(INDFX-1)
THOVPITNCv-.0001
MAXCI 10.0
SLTI 0.0
PMI0.0
SCLT= 0.0
no 200 (:1,50
X(K)=TREC(I)
T(K):Ta&n([)
XMNIHN
SMINrLgsoPLII)
OXISHINFL/XHV
XMI(DXID¥/(ALJIUT))I25.0
XMMI XV-5.0
XHPI xvoj,n
MNP: HHIT
ALDM8 (ALPID.0001I
ALpe= ALP. (o.uun1IAIP)
xntstanFX/(ALPE-DTI)025.0
HRMI XNE-1.0
HRPI XME*1.U

RESIN ODD PASS
TXIO.0
G0 TU 21?
TX! TX¢0.5
T(1)=(TXITM0V)-(TZE4(INDEXI-TZER(INDEX-1)).TZER(INDtX-1)
T(HNP):(TX/TM0VII(TXINF(INDEXI-TXINFTINDEX-1))ITXINI(INDEX-1)
D0 203 K'32IMN
T(KK)= (T(KK-1)+T(KK*1)OXMMOT(KK))/XMp
CONTINUE
X(1)I T(1)
X(MNF)= T(VNP)
00 5C3 KI:?.”N
X(KK):(X(KK-T)‘k(KK¢1)+HRM9X(KK))/HRP
CONTINUE

FIND SUMMATION
IF(T¥-TNOVM) 226.222.222
ELT=IxtJI)-T<JL))/ALPN
CLTzTXL(INDhi)°T(JL)
PM: LMo(CLTII2)
SCIT: SCLT‘(CLTIELT)
5LT! SITI(FLTIFLT)
PRINT 10$. TT.(T(ID).ID=1.9)
PRINT 10r.TT.(XIID). 1031.9)
PRINT 10?. JL.TXL(INDEX).ELT.CLT.SCLT.°LT
INDEX: IFDFX¢1
TMOVI TIH(INU:X)-TI*(INDFX-1)
TMOVM: TMOV-.?”L1
TT= TT+ aesitTMUV)
IF(TT-VMAX)206.706.205

"IF‘TTN EVEN pASS

95

FTN5.11 06/17/66

?06 TX: 0.O
no To 914
226 TXI Tqu.b
214 T(1)chx/TMOVI-ITZFRTINDEXI-TZERIINDEX-1))ITZERCINDEx-1)
T1M~P>zTTxxTWOVIITTxINF<INUEXT-TXINF1INDFx-111oTx1~r¢1~oex-1)
Do 204 Kr=9.MI
K3:H~-ug.9
TTK31: (7(K3-1)OT(KJ¢1)9XHMIT(K3,) / AMP
2n4 COVTINHE
“1)8 1(1)
X(MNE): 7(MN“)
00 314 K?:9.N~
K38HL-V202
X(K3): (h(K3-1)¢X(K5¢1)¢HHMIX(KJ))/HRP
304 COJTINHE
IF(T)-TMOVM) 32“.?50.230
C VINO SOrMATIOv
230 FLTsthtJL)-7(JLIT/ALPH
CLTITXI(IN0E¥1-I(JL)
RH. PM0(CLTOOI)
QCIT: QCITIICLTILLT)
SLY: <IT¢(ELTIILT)
PRINT 103. IT,1I([n).ID=1.9)
PRINT 10'.TT,(X(ID)I 10:1.9I
PRINI 102. JL.T;L(INFEXI.ELT.CLToSCLT.¢LT
INOE>= INDFYoI
TMOV: TITTIuhsz-TINTINDFx-I)
TMUV': TFUV-.0001
TT: TT. AB§$(TWUV)
IF(TT-v4:x) 201,2n1.2nb
205 CONTINUE
C Flu” UA
DAI SUIT/SIT
RALP: VA/ALP
HMS: SQRTF(H“/(INHFX 11
PRINT 2)
25 FORMAT 1/(RHwO‘E N0..1X.11HUIFFUEIVITY.2!.11HDELTA ALPHA.3X.13HDEL
TTA A/ALP»A.bx.on~M< VALUE))
RRIA1 907. J'.LL”.UA.H‘LP.Q”5
207 FOHMRT (115.6‘1‘.H)
IF (ITLR-MATCI 206.708.211
208 IF (AHQFTHAlp)--.UOUU5) 211.211.210
210 ALR: AIP¢DA
ITEHIITE~II

(30 TO ‘7
?11 GO TO 101
6 COITIMNE
FNI

Although this program has been used by the author,
no warranty, expressed or implied, is made as to the ac-
curacy and functioning of the program.

APPENDIX B

97

 

 

 

 

 

 

.noa H wo humusuow ovuméaumo cm m>mc muasmmu umOu wcu .mmmoauza mcauomcwmco mom
No.mmo amvo.a wmmo.a Km.mv~ Ho.nam Ohm.o mmm.o oom.m NHh.m NNH OHN ma Olmah
n.mmo memo.a amoo.a mo.mmm mm.man w~w.o mom.o obn.m nwm.m mn.swa mm.ma~ ma mlman
ma.moo mamo.a ammo.a mm.ama 00.3mm mmv.o nmm.0 mv~.v mmw.m m.moH HAN ma Vlmah
va.mmo vmmo.~ omvo.a mo.mom mm.Vnm nmm.0 >mv.o mmm.m Hmm.v mm.¢na mam ma mlman
ms.wao mmwo.b ammo.~ mv.mwi Nv.vvm was.o 060.0 vma.v mam.m na.~ma m.aa~ ma mlaaa
an.man mono.4 kmko.a mo.mma mm.mmm HVm.o Hmo.o Noa.m was.m 34H m.mam ma Human
mv.wow momo.a nm\).~ oo.mvm mm.mom OH~.0 «hm.o mam.v mm~.v m.m¢a NAN v Halhaw
mn.ODm mOmD.H nooa.a mo.mmm mm.nvm OHN.O mvm.o vm®.v bmm.¢ mud Nam v oalnan
wa.oma mmm>.a mmn3.m mn.amm Ha.vmm omm.0 mw~.0 bmm.m oma.n mva NAN v minds
m4.ma~ Himo.s mi\3.a am.osn “n.3mm Ham.o mmm.o omm.m .vk.v «an mam v tukaa
n..9ms vkva.s Hang.b wa.smm o\.vmm mm¢.o mmm.3 voa.m moa.m mad HAN e snags
ab.nna own).a aoiw.a ma.¢nm mm.mnn “0).? mma.3 amm.v Hwa.v n.5ma mam ¢ nlias
In.amw 4).).4 oq.;.z sa.vmm om.aem mmm.o ~am.3 oao.m oem.v sea mam v ansas
n.1md _qn..s on a.H on.mam mh.mom nm~.o can.o can.m ovo.m nva Adm q mnkan
“4.0ma via).a Nnoa.H am.on mn.~nm mam.) amk.o qso.m mna.m n.vea Ham v mnnan
nw.y>~ an...4 flzna.a 41.nna mv.0nv mam.o \vm.o nvm.m mas.m med mam a finish
1H.n3¢ uxn).a ammv.a mp.mbm mv.mmm mad.) 5mm.0 m)«.o Nmn.v sod m.oam DH malvat
N..nir 04-1.A Nun).a mo.mmw wa.nmm nom.a na¢.o vws.o min.v mm.qoa m.oam 0H manage
om...\,,).v wa¢72~ “Awaia mm.§vm MITQOM baa.) mph...) manna. 044.1 nDH HAN OH aHIvan
wa..3: on}... mn13.~ md.nnw fiv.oon rma.o am..: amm.m Lom.v om.oJH n.94m 3H «Tana
N. In}. “1.4).4 nnn1.a ".m..r.«,m Hw.0mn oma.) OVN.) fiom.m 361.01.? moa m.mam 3M slfafi»
1-..“? .,i).. wo...~ qw.nmw mo.amm was.) 43v.o moo.o H~3.n 16H cam 3H ones”
9.x“: .r:..« 0....H no.,mk mi.arm wkv.o awn.o mem.m mom.a mofl m.aam on quark
nw.w~« )tn).w an.w.4 m,.o~w Hm.>om qu.) Hfio.o mmm.m noo.m nN.©bH I.nom 3H mlwaw
nw.nnv wt”..a Ann).« ow.nkw “v.amn awn.) v\¢.o Aqm.v mvm.m 404 mm.0am DH mlva»
un.mvv msn).a MOOQ.A H4.Haw Wm.nan 0»n.3 «m3.a mmm.v mmm.v m.m04 m.m3m QM “Teas
o~.naa wdw).~ HJCJ.M um.mvn a\.oom \Lw.3 oo~.o mva.o amm.m m.oea m.tsa 0H malaan
DH.¢na nw.).« men).~ 1n.ovm mm.ram hum.3 Nam.3 nma.o mnw.v mvH Q.mmH DH Dalaan
ab.oaa mw«1.H Lm1).~ n0.~nn no.5mn Non.) was.) chm.m Hmm.v m:.m¢a m.mma OH mlaan
qw.3a~ 3H-).H Hts).a m7.mmm mn.qnm Hmm.o Nov.) msv.m mao.m mn.mva m.mna 9H mlaah
.r.wiq aqru.s or-.s «n.3,w 1m.¢um mon.o Ava.o mms.m vmk.m ova am.isa as Luann
«v.0.a many.“ ann>.4 3m.1>m Dv.t¢n nnn.3 mam.) amc.m mmo.m «VA mm.L\H 0H blaas
m4.mwa hmvw.a wq-,.H mm.bav ms.omm ncv.0 0mm.o DOD.D mmm.v “VA O.mia OH VIHHN
vm.) « movu.a nn17.H Vn..mm ha.mwm ham.o BHH.9 ma_.m von.v mm.ova mw.mma 3H mlaan
mm.H>w wa>.H )010.H Mb.n3m mv.>an n37.o man.) nnm.m mmo.m nva ma.wma OH mlaan
vn.wnw wwwd.H nnau.. wm.i n nw.mnm \r\.J xMw.) ®LO.m mma.n Wfia hm.wma 0H Hagan
av.n nan).a avg).a mm.amm mn.nan mwn.o mmW.O Nao.n nmm.v AMA nN.mnH OH Ollo
«m.wm un«3.~ NM.>.4 v-.mam mfl.ovm n»H.3 5mm.) mom.m m 0.7 mn.mma mm.mma 0H mToH>
m1.Io v1wo.a mov1.H «m.v n m..w¢m ,wN.) mid.) 01 .1 mam.n n.0ma nm.moa 0H Vloan
mn.nm wmno.H amp).u .1.nvm Jb.vwm www.o msfl.q mwa.m mvm.m mma mw.aba OH mloan
m3.vu wana.a aawu.d wm.wmn vm.mmm mmw.0 Dun.o nom.v mav.m n.mma m.qba OH NIQHN
av.nv mvmo.~ anva.a mo.amm nm.mvm mov.o 1am.w mam.v ma\. nm.nMM mm.¢pa OH aloau
mo.ma mwmo.fl .wn).a nt.n0m or.nmm mma.o sad.» mmo.m mmm.n m.mma 5m.904 04 mumom
wa.mw smm0.H Hm0.4 «n.mmm vv.03m nnm.n O.H.) nma.» ”33.7 nm.mma ma.woa o vlmoe
av.nn 00a1.a .wwd.u 1w.shm ow.wwm me.u mma.® nam.n amo.n m.nna n0.m«a OH mimon
na.sv nsmo.. o.mo.4 em.,nm .n. ma van.o rqm.o mugs nco.m mnna x Hmm.m m.wms mm.qoa oH mumon
acre 1 :1 Adam. 1H.m, “not 1.0, iucxmuti lucxmuwc Amos «not Asses
.Aumumwu {Raqucmm unoa .4.m ohmuoi 0;. on Oumsol poudwx numjo. ram auduoi abou0m 4 u x pm 0 n K um umdk us .02
amp: nan nvmu Umrmww 36m mcowumumum Nuu>nmwmex Dunno: 2mm .orv; .QEOB zuacwq unmk
manomnoa 3m: Ln InHwUOL ufl-mmam Hmeuoce Soum mcfiuurmox mufi>flnsmuso Hmsumre .xmz .xc:
mbw>mub Oabflnuy mouvumuvaamm pmumfidufldu

62m Hmucucduonx» cmmzuwm
:ocmnkuwo no mwfiam> mum

mnasmvo tcm camp no xumsezm .mH.m magma

98

.10a I no hum4suum UODMEqumw cm m>mc muasmwu ummu ecu

+

.momoaujd ocauwmcamco uom

 

 

 

 

>uu>muw oflufluoam

mODSDMHOQEOB UmumazuHmU
ocm Hancoehumaxm cwvzumm
mocmumwwqo mo wwnam> mzx

E"

 

 

muasmmu ocm sumo mo xumeesm

 

o..iin mmno.s onto.a :..xim at..om mm... mnw.o «sa.q mmm.m m.voH ms.mma ma canvms
no.1). mq.3.4 «0.3.A am..4~ .q.ovm mmm.o mmm.o sma.v oma.m m~.¢oa mm.¢ma mH muema
.N.A.7 «mm..s “moo.s L~.mom aa.num mmo.o ama.o Nem.q moa.¢ n.moa mos ma muvmp
v~.3~n Hmco.fl kn.o.s u..mem oo.wom mom.o mmm.o ama.q ~HN.V mod m.mma ma RIVNA
u».uom mmqo.~ amoo.z aw.Hkm a man Nam.o imm.o mwa.n mam.m nm.ao~ m.vma ma oqua
an.wam mmos.H nora.a cv.m.a cm.mkm ham.a mmq.o nma.v mmm.m med m.wm~ ma muams
-v.n3n Ammo.a «Ano.a om.ovq mm.nqn oav.o Ha..o mmn.m Hmm.m eon mod ma quvma
mm.owm ovqn.~ nmvo.H n1.urm an.osw www.o syn.o soo.v mmw.m mba m.mmH ma mlvmn
oo.mn¢ mmno.H omoo.H mm.mm~ om.anm mmn.o mmm.o 1.9.4 oqa.m ma.ooa mm.moH ma Nuvma
ms.qmv .Hmo.d havo.s ms.mam nm.mmm 040.3 mmq.o mmm.m vok.m mod mN.mmH ms anma
mi.mmm mmwo.a mm.o.~ q:.mmm 14.3HA mam.o oao.o m»~.q mod.v m.nma mh.¢ma oH NHIHNA
am.wmn omna.~ kooo.a an.mmm HA.¢NM mmo.o Hmo.o mov.v qao.v n.6ma ms.mma OH HHIHNA
mo.mfim mama.a mooa.a Tm.mm~ Hm.mom omm.o vmm.o omm.v oom.m m.mma ms.mma on oauams
nm.mwm mmm9.H ammo.s ma.mmm mm.~mm aao.o mon.o vam.m Nmm.m ems was OH anamn
Am.mam Hivo.fl momo.H ms.mam 4m.vmm mom.o ¢q\.o mam.m mfia.m m.omH man as muams
ma.swm Novo.s cams.a 91.3mm «H.9mm 4.1.9 «36.0 Him.« omm.m mma m~.mmH oH slams
4m.ooq mama.a mmoa.H mm.nom 06.0mm moo.o kmo.o om~.v kms.m m.ama n..mma 0H ousma
mm.msm imma.a maoo.a ns.oflm em.~vm 545.0 omm.o bom.v mmm.m m.¢ma m.oma oa muams
95.6Hm ammo.a mmoo.~ mfl.mmm oo.hmm Ham.o mom.o Hmm.m mkm.m mma was oa NIHNR
Nb.nmm wmvp.H nano.s om.¢mm 46.9mm nmv.o 4H4.o mam.m moq.m and mm.«ma 0H HIHNF
mm.mzk ,mon.i mms:.a m~.4ms us.omm Lam.o mmm.o a H.v qao.¢ ma.moa mm.¢sm ma canons
mm.nm. a1ma.a kmvo.a ma.kma on.msm mmm.o muo.o mno.v o-.v «\H n.aam ma anode
va.rmo mmva.fl ammo.a oo.mcs o~.aem mmo.o ono.o mms.v Nmm.m NAM m.oa~ ma muss“
mm.mmw coma.a maoo.s mk.om~ mH.mnm vmo.o mkm.o muss x Hom.m muoa x mmo.¢ mm.maa m.qa~ ma suaak

1:42 1 mos .Ammw “ammo Amos Amos AAEVMOCV iuc\auuc Amos Amos Aches

musmoamfl medumo: naps .E.m Canned abouom Outbom ombmm: Cumuom 3mm oumuom Oumuoa 4 u x um o u x um umwe mo .02
umo: MOM own: owumm: 36m chHDMIODH mub>wmnuufla ovummz 30m .meme .QEOB cuocmq ance

mwOumuum 3cm uo wraaooz Uwummam ameuwca Eouu ocauasmmm >ua>am5wwflo HMEuch .xm: .xoz

.na.m OHDMB

99

 

 

 

 

 

 

.TJH N we moansuum UOOMSaunm cm w>vc nuarmou DmOD ozu .mmwoausa mcHHOOCHocw mom
mm.i\u mm.-.” w-.o.a ofia.o mom.3 ovo.o 9q3.v com.m asa mam ma man wolmann
am. Mr unla.H ow.v9m mun.o wmm.o mw.3 mon.n oaw.v moH on OH van bolvdlm
an.m d NM->.M 00.nam rum.n mvm.o mmm.o Mma.n owm.v mva mam 6 gas wolnaln
on.n0m mmwo.a o) .vm mmm.o Hmm.o 0mm.3 ¢v3.v mmn.m Mba mma ma vmn omuvmln
om.mHm unva.a m>.Hmm mvm.o Hom.o me.o oma.¢ mun.m mmH mma OH awn molamlh
mn.oma vamo.H mv.wom nmm.o mom.o ham.o mon.m mbv.m ova and 0H AHA QOIHHIB
mw.mm mnmo.H H~.mmm mica x mv~.o mam.o 0mm.o MIJH x Ham.m mica x moa.m mma Nod OH mon mmimnn
2nd,. ABEL... 2.3 C... 2:: u“, 25 9.: E.,, C: 22.9;
m LII .IINII
m .x >u4>muc nuanooz Hua>flw3mwnn Qumuoi oeumvm Ouduoi 30m Cucuoi Dumbom A u x um O n x um page mo .02 mums
ham: :4 04440036 Uaummau Hmiuocz ncoabmuwua >DH>Hn5mafla omumm: 36m .QEOB .QEOH cuwcwq mmaqmm
ozcme CH chm;w HdinCB aoqu mEADaSmmm >ua>flmswwflm ameuwcg .xmz .xm; umoe
mwusumquEOI owxoasuamu
ocm HmucmenuvmxI cmuzuwm
woswuvawfla «o mosam> m_m
nuasmmu ocm mumo mo mosam> womuo>m «o xumeesm .m.m manna

INDEX

Agar gel, 25
Area, under a heating
curve, 27, 28, 67
Assumption, constant thermal
prOperties, 37, 62
affect of reheat, 62
elastic modulus, 65
one dimensional heat
transfer, 37

Ball, C. Olin, 12
Bartlett, Luis H.,
Beck, James V., 36
Beef, model of, 18
tenderness of, 28
Bellinger, F., 6, 16,
Bennett, A. H., 4, 8,
Blanching, 2
Board, P. W., 23, 27
Boundary conditions,
56

15, 16

64
10

22,
9.

35, 37

Calibration, potentiometer,

45
thermocouple, 45,
X—Y recorder, 47

Calorimeter, 15—18
Carslaw, H. S., 34
Cenco-Fitch apparatus,
8, 10, 13
Chace, W. G., Jr.,
Charm, Stanley E.,
Computer program,

fitting, 60

finite difference,
Conduction equation, 34,
Cooking, extent of, 69
Correlations, elastic modulus

with heat exposure, 76
thermal diffusivity with

heat exposure, 69, 72
thermal diffusivity with

maximum temperature at

48

3, 4.

4, 8, 10
12, 19
curve

93
35

X = L, 72
Crafts, A. 3., 2
Cown, W. B., 6, 16, 22, 64
Cubbedge, R. H., 4, 8, 10
Cunningham, Helen H., 29
Curve fitting, 60

101

Index
Data analysis, 60
Density, 1
cherry flesh, 12
Dexter, S. T., 30,
Dial Gauge, 47
Drake, Robert M., Jr., 6
Dry substance content, 17,
18, 20
Dyner, Henri,

31

25

6
1:

Eckert, E. R. G.,
Elastic modulus,
26, 32, 38
application of, 82
correlation with heat
exposure, 76
determination of,
65
discussion of results, 65
experimental procedure,

2, 21,

39, 45,

53, 58
potato, 55
relationships with, 33
test equipment, 41
Energy balance, 1, 3, 34, 35
Energy requirements, deter-

mination of, 83

Enzymes, 2

Equation, conduction, 34, 35
finite difference, 35
Fourier's, 83

Equipment, photograph of, 40
used in research, 39

Errors, discussion of, 60

Eucken, A., 5, 6, 8

Evans, H. L., 23, 27

Evers, Clifford F., 2

Experimental techniques,

discussion of, 55
Fat content, 17
Fennema, O., 2, 28
Finite differences, 4, 6O
equation, 35
Finney, Essex Eugene, Jr.,
2, 31, 32

Fitzpatrick, T. J., 31
Fourier's equation, 83
f-value, 21

 

102

Gelatin gel, 7, 8

Guarded hot plate, 3, 4, 7,
9, 10, 13

Gurnie, H. P., 6, 22

Halliday, Evelyn G., 2

Heat exposure, 4, 14, 21, 38
application of, 82
correlations, 66, 69, 72,

76
definition, 27
determination of, 39, 67

discussion of results, 66
effect of, 29, 76
potato section, 39
variations in, 28
Heat source, 38, 42
photograph of, 41
silicone rubber, 44
electric heating element, 44
Heat transfer, experimental
procedure, 54
one dimensional, 56
Heat treatments of potato
section, 62
Heating element, description

of, 44
heat source procedure, 49
Hesselschwerdt, August L., 25
Hochberg, Melvin, 2

Hofstrand, Joyce T., 29
Hurwicz, H., 22, 23, 27, 64

Initial conditions, 37, 57

Insulation for specimen
holder, 43

Isleib, D. R., 30, 31

J. M., 21

J. C., 34

Jackson,
Jaeger,

Kaczmarzyk, Leonard M., 2, 28

Kethley, T. W., 6, 7, 16, 22,
64

Kramer, Amihud, 31

Kreith, Frank, 6

Least squares, 36
Lechnir, R. J., 28
Lentz, C. P., 7, 8

Index

Le Tourneau, Duane J., 29
Load cell, 45, 47

Long, R. A. K., 5, 6
Lujan, Laura, 31

Lurie, J., 6, 22

May, K. N., 4, 11
Maxwell, James Clerk, 5,
Melnick, Daniel, 2
Microswitch, 43
Miller, Herbert L., 3,
Miller, Terrance, 28
Moisture content, 11,
fruits, 16, 17
vegetables, l6, l7
Moline, 5. W., 18
Monego, C. J., 4

6,8

10, 11

13, 20

Nicholas, R. C., 28
Nodal points, 35
Node, 35-37
Nutting, G. C., 30, 66
Objectives, 38

Olson, F. C. W., 12, 21
Oser, Bernard L., 2

Parallel plates, 45, 47
Parameters, rupture, 31
thermal and physical, 38

Parker, Rayburn E., 12, 20,
25, 64

Personius, Catherine J., 2

Pflug, I. J., 28

Physical properties, 1-4, 38
.application of, 82
fruit juices, l7

Planimeter, 67

Porter, W. L., 31

Potato, cylinders, 32
elastic modulus, 32
heat treatments, 62
rupture, 77
rupture parameters, 31
section, 39, 42
section used for elastic

modulus, 65

semi-infinite cylinder, 38
slices, cooking, 29

temperature of, 32, 33, 55

 

103

Potato, total solids, 31

uniaxial compression test, 32

zones, 30, 31
Potatoes, elastic modulus of,
55
used for research, 55
Potato section, description
of, 49
experimental procedure, 50
weighing of, 46
Potentiometer, 39
calibration of, 45
Powrie, William D., 2, 28
Pressure, constant, 10, 14, 43
Procedure, experimental, 48
Replications, number of, 55,
62
Results, application of, 82
averages of, 70
Riedel, L., l7, l8
Rinfret, A. P., 18
Root mean square values,
64, 69, 72, 77
Rubber, for heat source,
48
silicone, 9
Rupture of potato, 77

60—

44,

Sawdye, J. A., 18
Schneider, P. J., 3, 6, 34
Sharma, M. K., 30, 31, 66
Sharp, Paul F., 2
Shear press, 28, 31
Short, A. J., 18
Short, Byron E., 15, 16
Siebel, E., 14, 15, 16, 20
Silicone rubber, 9
description of, 44
for heat source, 44, 48
Simpson, Jean 1., 2
Smith, Ora, 31, 73
Soluble solids, 12,
20, 26
Specific gravity, 1,
correlations, 66
determination of, 45, 58, 66
discussion of results, 66
equation for, 66
of potatoes, 30, 31
relationships with, 30, 31

13, 17,

6, 13, 38

,

Index

Specific heat, 1, 3, l4
beef model, 18

cherry flesh, l2
foods, 14, 15, 18, 19
frozen codfish, l9
frozen meat, 19
fruits, 15, 16, 18, 2O
ham, 15

juices, 17

shrimp, 15

sugar solutions, 15
variations with temperature,
17, 21
vegetables, 15-18, 21
Specimen holder, 39
description of, 42
photograph of, 40
Staph, Horace E., 15-17, 19
Starch, gelatinization, 63,
67, 73
Steady state process, 3, 15
Stocking, C. Ralph, 2
Storage time, 67
Stout, B. A., 12, 20, 25, 64
Sunderland, J. Edward, 3, 10,
11

Talbert, William F., 73
Talley, E. A., 31
Temperature, correlation with
thermal diffusivity, 72
histories, 38, 39
of heat source, 57
of potato, 32, 33, 35
of testing room, 55
recording of, 45
variations with, 17,
32, 33
Test dates, 69
Test interval, 67
Testing room, temperature of,
55
Thermal conductivity, 1, 5
beef, factors influencing,

21-26,

11
chicken breast muscle and
skin, 11

cherry flesh, 12
codfish, 12

fish muscle, 6
frozen material, 12

Thermal conductivity,

fruits, 4-10

gelatin gels, 8

ice, 7

meat, 3, 4, 7, 8, 10

metals, 3

relationship with moisture
content, 10

relationship with specific
gravity, 10

silicone rubber, 9

variations, l3

vegetables, 4, 6, 7, 14

Thermal diffusivity, l, 3, 4,

6, 21, 38

agar gel, 25

application of, 82

bean—bentonite mixture, 24

beef in cans, 23

cherry flesh, 12, 25, 64

correlation with heat ex-
posure, 69, 72

correlation with maximum
temperature at X = L, 72

correlation with storage
time, 67

determination of, 56

discussion of results, 64

experimental procedure, 54

factors affecting, 22, 23,
26

Index

Thermal diffusivity,
finite differences, 36
fruits, 22
function of temperature-
time exposure, 27
raw potato section, 62, 64
water, 24
variation with temperature,
23-26
vegetables, 22
Thermal properties, 1-4, 38
application of, 82
Thermocouples, calibration
of, 47
conduction error, 56
description of, 47
placement of, 56, 57
Tischer, R. G., 22, 23, 27, 64
Transient process, 3, 4, 6, 15
Tressler, Donald K., 2
Tuomy, J. M., 28, 76
Twigg, Bernard A., 31

Walters, Roger E., 4, 11
Weier, T. Elliot, 2
Whittenberger, R. T., 30, 66
Wing, P., 4

Woolrich, W. R., 15, 16, 17

X — Y recorder, 42, 47

Zaehringer, Mary V., 29

 

          

   

    

MICHIGAN STA

III III

312IL

T

E UNIV. LIBRRRIES
IIIIIIIIIIIIWIIIIIIIIIHIIIHIIIIIII
102392283