TRANSIENT COOKING RATES OF GROUND
BEEF WITH INFRARED HEATING

TIxulx In! NH Dogma of DII. D.
MICHIGAN STATE UNIVERSITY
Frank Donald Borsenik

1964

 

..‘ I ”w

”mu. :Jfll'u'v‘n
t

u . ,0. n '
THESIS I. ' 3

TRANSIENT COOKING RATES OF GROUND BEEF

WITH INFRARED HEATING

BY

Frank Donald Borsenik

AN ABSTRACT OF A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1964

ABSTRACT

TRANSIENT COOKING RATES OF GROUND BEEF
WITH INFRARED HEATING

By Frank Donald Borsenik

The objectives of this study were to investigate
(l) the influence of infrared source temperatures. and (2) the
effects of various infrared heat fluxes on the transient
processing rates of ground beef. In addition, several
related topics were examined. These were: (1) the effect
of enclosed processing chamber reradiation on processing
rates; (2) product volatile losses: and (3) product volume
changes.

Ground beef was selected because it is fairly
homogeneous and it normally represents the average com—
position of beef products. The average fat content of the
product was 20%.

Three electric infrared heat sources were used to
provide wave lengths from 1.233 to 3.164 microns, the quartz
lamp, the quartz tube and the calrod unit. These heat
sources were selected because of their flexibility in
obtaining different heat source temperatures and various
radiant energy fluxes.

Samples of ground beef. 3 inches wide. 6 inches long

and one inch deep were used. The samples were placed in an

Frank Donald Borsenik

insulated container with a 3 inch by 6 inch surface exposed
to the heat source. All samples were heated from approxi-
mately 45 to 170 F.

The processing rates of samples in an enclosed
high emissivity volume were not significantly different from
those in non-enclosed volumes. Samples were processed in
non-enclosed chambers.

Five radiant heat source temperatures were used
for processing, 4230.0, 3465.0, 2260.0, 1864.5 and 1648.7 R.
A range of heat fluxes was used at each of the heat source
temperatures. It was found that: (a) a linear relation—
ship exists between surface heat flux and the average
surface temperature; (b) a linear relationship exists
between volatile loss and time at a given surface heat
flux; (c) the rate of volatile loss can be represented by
the Arrhenius equation, for first order chemical reactions:
(d) a linear relationship exists for values of h(t - ti)/qs"
vs. a‘t/s2 for various k/hs parameter values, within the
following temperature ranges: above freezing to 122 F, 122
to 140 F, 140 to 157 F, 157 to 170 F; (e) a procedure is
given to determine processing times; (f) decreasing the
radiant heat source temperature from 4230 to 2260 R de-
creases processing times at the same heat flux, with a
further reduction of heat source temperatures to 1648.7 R
not essentially affecting the processing time: (9) the
maximum total product losses occurred with a heat source

temperature of 2260 R, the losses at other heat source

Frank Donald Borsenik

temperatures were not significantly different for the same
heat flux; (h) the volume change was only significant be-
tween the 4230.0 and the 1648.7 R heat source temperatures.
From these results, it is recommended that a heat
source temperature of 1864.5 R should be used for the

radiant heat processing of fresh ground beef.

Approved w M W
#74 t/

TRANSIENT COOKING RATES OF GROUND BEEF

WITH INFRARED HEATING

BY

Frank Donald Borsenik

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1964

ACKNOWLEDGEMENTS

The author expresses his sincere appreciation for
the counsel, guidance, and interest of Dr. C. W. Hall,
under whose supervision this work was accomplished.

He is also indebted to Dr. A. W. Farrall, Chairman
of the Department of Agricultural Engineering, Michigan

tate University, for his support which made it possible

to carry out the investigation. A special note of
appreciation is expressed to Dr. S. E. Thompson and Dr.
J. W. Thompson, Assistant Director and Director of the
School of Hotel, Restaurant and Institutional Management.
respectively, and to Henry Ogden Barbour, present Director
of the School of Hotel, Restaurant and Institutional
Management, Michigan State University, for their encourage-
ment and financial aid during the course of the study.

Appreciation is expressed to Dr. J. L. Newcomer,
former Director of the Food Service Research Industry
Center, Michigan State University, and to Dr. A. M. Dhanak.
Department of Mechanical Engineering, Michigan State
University, for their sympathetic understanding and helpful

suggestions during the course of the study.

ii

VITA
Frank Donald Borsenik

Oral Examination: May 6, 1964
Dissertation: Transient Cooking Rates for Ground Beef
with Infrared Heating
Outline of Studies:
Major Subject: Agricultural Engineering
Minor Subjects: Mechanical Engineering

Statistics

Biographical Items:
Born: October 19, 1933, Saginaw, Michigan
Undergraduate Studies:
Michigan State University, 1951—55
BSAE, 1955
Graduate Studies:
Michigan State University, 1955-58
MSAE, 1958
1958—1964
Experience:
1952-1955: part time engineering aid during under—
graduate studies for H. J. Heinz Co..
Michigan and Indiana
1955-1956: Graduate assistantship, Department of
Agricultural Engineering, Michigan State
University.

iii

1956-1957: Research Assistant, Department of
Agricultural Engineering, Michigan
State University.

1957-1964: Instructor, School of Hotel, Restaurant
and Institutional Management, Michigan

State University.

Membership in Organizations:
American Society of Agricultural Engineers
The Society of Sigma Xi (Scientific Honorary)
The Society for the Advancement of Food Service
Research
Sigma Pi Eta (National Hotel, Restaurant and

Institutional Management Honorary)

iv

TABLE OF CONTENTS

INTRODUCTION 0 o o o o o o o o o o o o o o o s o 1"].

REVIEW OF LITERATURE . o o o o o o o o o o 9 o o 2-1

2.1 The thermal properties of beef 2-2
2.1.1 The specific heat of beef 2-2
2.1.2 Thermal conductivity of beef ' 2-7
2.1.3 Thermal diffusivity of beef 2—8
2.1.4 Latent heat factors in the

processing of beef 2-11

2.1.5 The emissivity of beef 2-12

2.2 The factors that affect beef processing 2-16
2.3 The infrared and the conduction heating

theories 2-19

2.3.1 The infrared theory 2-19

2.3.2 The conduction heating theory 2—26

2.4 Electric infrared heat sources 2-30

EXPERIWNTAL APPARATUS o o o o o o o o o o o o 0 3‘1

PROCEDURE 0 o o o o o o o o o o o o o o o o o o 4"].

4.1 Electrical energy characteristics of the

heat sources 4—1
4.2 Physical measurements of the three heat

sources 4—1
4.3 Heat flux measurements 4-2
4.4 Effect of surrounding walls and reradiation 4-3
4.5 Transient processing rates of ground beef

with infrared heating 4—6

RESULTS, CALCULATIONS AND DISCUSSION . . . . . . 5-1

5.1 Calculation of the specific and latent

heats of ground beef 5-1
5.2 Calculation of geometrical angle factors 5-3
5.3 Determination of the sample size for

statistically equal heat fluxes on the

sample surface 5-10

5.4 Electrical energy characteristics of
the three heat sources

5.5 Calculation of the radiant heat outputs
of the three heat sources

5. l Quartz lamp source
5. .2 Calrod heat source
5 3

5
.5. Quartz tube heat source

Heat flux measurements
Fitting of third degree polynominals to
heat flux calculations for various
distances between the sample surface
and heat source units
5.8 Effect of surrounding walls and reradiation
5 9 Transient processing rates of ground
beef with infrared heating

mm
\10

SUMMARY AND CONCLUSIONS . . . . . . . . . . . .

6.1 Calculated and measured heat fluxes

6.2 The effect of environment wall re-
radiation on processing time

6.3 The effects of heat source temperature
and surface heat flux on processing
times and weight losses

6.4 General recommendations

APPENDIX . O O O O O O O O O O O O O C O O O 0
EXAMPLE CALCULATIONS . . . . . . . . . . . . . .
REFERENCES 0 O O O O O O O O O O O O O O C O O 0

vi

5.2.

5.4.

LIST OF TABLES
Page
The composition of various meat cuts . . . . 2-4

Surface heat fluxes used in the processing
of ground beef at different source
temperatures . . . . . . . . . . . . . . 4-13

Calculated specific heats of ground beef of
average composition in various temper—
ature ranges and the latent heats of
fusion at the transition temperatures . . 5-3

Geometrical angle factors between single unit
heat sources and a parallel centered
18 sq in surface at different perpen-
dicular distances . . . . . . . . . . . . 5-8

Equivalent geometrical angle factors between
single heat sources and a parallel
centered surface with an equivalent
surface area of one sq ft using an 18
sq in surface as a basis at different
perpendicular distances . . . . . . . . . 5-8

Combined geometrical angle factors between
a group of three similar heat sources
and a parallel centered 18 sq in
surface at different perpendicular
distances . . . . . . . . . . . . . . . . 5—10

Combined equivalent geometrical angle
factors between a group of three
similar heat sources and a parallel
centered 18 sq in surface at different
perpendicular distances . . . . . . . . . 5—10

Geometrical angle factors for various sample
widths (c) and lengths (b) at a
distance of four inches. The values
in the table are F/dA (sq ft‘l) . . . . . 5-14

Analysis of variance of F/dA of the various
rows and columns of one quarter of a 5 in
by 10 in surface reduced to elemental
finite areas . . . . . . . . . . . . . . 5-16

Comparison of manufacturers data and calculated

watt inputs, based on volt and ampere
averages, for the 1600 watt quartz lamp . 5—17

vii

5.15.

5.16.

5.17.

5.18.

Comparison of manufacturers data and
calculated watt inputs, based on volt
and ampere averages, for the 1000 watt
calrod unit . . . . . . . . . . . . . . .

Calculated heat balances of the quartz heat
lamp at different voltages . . . . . .

Comparison of calculated percent radiations
from a 240 volt quartz lamp rated at
1600 watts at different voltages to the
manufacturers data . . . . . . . . . . .

Calculated heat balances of the calrod unit
at different voltages . . . . . . . . . .

Comparison of calculated percent radiations
from a 1000 watt, 240 volt calrod unit
at different voltages to the manu-
facturers data . . . . . . . . . . . . .

Comparison of calculated radiant heat fluxes
to measured radiant heat fluxes for
different voltages and distances for
one quartz lamp . . . . . . . . . . . . .

Comparison of calculated radiant heat fluxes
to measured radiant heat fluxes for
different voltages and distances for
three quartz lamps . . . . . . . . . . .

Comparison of calculated radiant heat fluxes
to measured radiant heat fluxes for
different voltages and distances for one
calrod unit . . . . . . . . . . . . . . .

Comparison of calculated radiant heat fluxes
to measured radiant heat fluxes for
different distances for a 120 volt,

550 watt quartz tube . . . . . . . . . .

Results of orthogonal polynominal curve
fitting to surface heat flux calculations
for the equation: qs" = A+Bd+Cd2+Dd3.
Maximum deviations are also indicated . .

Ground beef samples processed at 170 F at
946 Btu per sq ft-hr and A of 1.194u
in an open room and in an enclosed
volume . . . . . . . . . . . . . . . . .

viii

Page

5-27

5—31

5-38

Table

5.20.

5.21.

5.25.

5.26.

Page

Analysis of variance of percent yields
for enclosed volume vs. non-
enclosed volume samples at 946 Btu
per sq ft-hr and A = 1.194 u . . . . . . 5—40

Analysis of variance of percent drippings
for enclosed volume vs. non-enclosed
volume samples at 946 Btu per sq ft-hr
and k = 1.194 u . . . . . . . . . . . . . 5-40

Analysis of variance of percent volatile losses
for enclosed volume vs. non-enclosed
volume samples at 946 Btu per sq ft-hr
and X = 1.194 u . . . . . . . . . . . . . 5-40

Analysis of variance of relative processing
time (60 to 170 F) for enclosed volume
vs. non-enclosed volume samples at
946 Btu per sq ft-hr and A = 1.194 u . . 5-41

Polynominal constants for the fitting of time
vs. temperature at the one in. depth for
ground beef at 946 Btu per sq ft-hr and
1 of 1.194 u in an open room and in an
enclosed volume. (Y=A+BX+CX2, Y is the
temperature in F at the one inch sample
depth and X is the time in minutes) . . . 5—43

Analysis of variance of (A) constants in the
fitted polynominal equation of temperature
vs. time at the one inch depth for ground
beef at 946 Btu per sq ft—hr and at a
A of 1.194 u in an open room and in an
enclosed volume . . . . . . . . . . . . . 5—44

Analysis of variance of (B) constants in the
fitted polynominal equation of temperature
vs. time at the one inch depth for ground
beef at 946 Btu per sq ft-hr and at a
A of 1.194 u in an open room and in an
enclosed volume . . . . . . . . . . . . . 5—44

Analysis of variance of (C) constants in the
fitted polynominal equation of temperature
vs. time at the one inch depth for ground
beef at 946 Btu per sq ft—hr and at a k
of 1.194 u in an open room and in an
enclosed volume . . . . . . . . . . . . . 5—44

ix

Table

5.28.

5.32.

5.33.

Convective, radiative and apparent co-

efficients of heat transfer from the
surface of the sample to the room for
various room temperatures and sample
surface temperatures for each of the
tests . . . . . . . . . . . . . . . . .

Correlation of temperature vs. time distri-

bution patterns for various surface heat
fluxes from a source temperature of
4230.0 R, k = 1.233 u. Y = A+BX repre-
sents the linear regression equation

of aT/52 (Y) vs. k/hs (X) at a constant
h(tl—tO)/qs". R is the correlation of
Y on X and the standard error is $1 . .

Correlation of temperature vs. time distri-

bution patterns for various surface heat
fluxes from a source temperature of
3465.0 R, A = 1.505 u. Y = A+BX

represents the linear regression equation

of GT/SZ (Y) vs. k/hs (X) at a constant
h(tl—to)/qs". R is the correlation of Y
on X and the standard error is 31 . . .

Correlation of temperature vs. time distri—

bution patterns for various surface heat
fluxes from a source temperature of
2260.0 R, k = 2.308 u. Y = A+BX repre—
sents the linear regression equation of
GT/SZ (Y) vs. k/hs (X) at a constant
h(tl—tO)/qs". R is the correlation of
Y on X and the standard error is sl . .

Correlation of temperature vs. time distri-

bution patterns for various surface heat
fluxes from a source temperature of
1864.5 R, k = 2.797 u. Y = A+BX repre—
sents the linear regression equation of
OLT/s2 (Y) vs. k/hs (X) at a constant
h(tl-to)/qs". R is the correlation of

Y on X and the standard error is sl . . .

Correlation of temperature vs. time distri-

bution patterns for various surface heat
fluxes from a source temperature of
1648.7 R, A = 3.164 u. Y = A+BX repre-
sents the linear regression equation of
Orr/s2 (Y) vs. k/hs (X) at a constant
h(tl-to)/qs". R is the correlation of

Y on X and the standard error is 51 . . .

X

Page

5—59

5-60

Table

5.34.

5.38.

Percent volatile and dripping losses and
volume change in length and width for
ground beef processed at 170 F at
various radiant heat temperatures and
at different heat fluxes . . . . . . . .

Analysis of variance of total processing
losses for the different heat source
temperatures . . . . . . . . . . . . . .

Summary of "t" tests for comparing the per-
cent total losses for each of the heat
source temperatures . . . . . . . . . . .

Analysis of variance of percent volume change
for the different heat source temper-
atures O I O O O O O O O O O O C O O O 0

Summary of "t" tests for comparing the
percent volume changes for each of the
heat source temperatures . . . . . . . .

Processing results of ground beef,
processed to 170 F . . . . . . . . . . .

xi

Page

LIST OF FIGURES
Figure Page

2.1 Q, Btu/LB,and temperature relationships
for 100% beef fat and beef with 20%
fat . . . . . . . . . . . . . . . . . . . 2—6

2.2 10 mm and one mm water absorption and wave
length, microns, relationships; Ekb x
105/0T5 and wavelength, microns,
relationships for various black body
surface temperatures (R) . . . . . . . . 2-6

2.3 Hottel's geometrical model for determining
the geometrical angle factor between a
differential surface and a parallel
finite surface . . . . . . . . . . . . . 2-25

2.4. Surface element heat balance . . . . . . . . 2—25
4.1. Heat source and pyrheliometer arrangement . . 4—4
4.2. Product, copper container, insulated box

and heat source arrangement . . . . . . . 4—4
4.3 Experimental apparatus arrangement . . . . . 4-10

5.1. Relationships of a, b and c for determining
the geometrical angle factor between a
differential surface and a finite
rectangular surface parallel to it . . . 5—7

5.2. Relationships of a, b, c for determining the
geometrical angle factors from a heat
source to a finite surface . . . . . . . 5-7

5.3. Relationships of c and a for determining the
geometrical factors from a group of three
heat sources to a finite surface (b re-
lationships same as in Fig. 5.2) . . . . 5—7

5.4. Relationships of c and b and distances for
determining sample surface area . . . . . 5-13

5.5. (F/dA) values for surface elements from
Fig. 504 o o o o o o o o o o o o o o o 0 5-13

xii

Figure Page

5.6. Relationships of tS (average product
surface temperature) and qs" for
ground beef 0 o o o o o o o o o o o o o o 5‘47

Mo _ M T_1 —3
5.7. Log -——M——— and (1/TS) x 10
0

relationships ground beef . . . . . . . . 5-47

5.8. h(tl - tO)/qs" and aT/s2 relationships at
various k/hs values for ground beef
(C = 0.75) and a radiant heat source
temperature of 4230.0 R. tl (maximum)
= 122 F . . . . . . . . . . . . . . . . . 5-62

5.9 h(tl - 122)/qs" and OLT/s2 relationships at
various k/hs values for ground beef
(C = 0.80) and a radiant heat source
at 4230.0 R. tl (maximum) = 140 F . . . 5—62

5.10. h(tl - l40)/qs" and aT/s2 relationships at
various k/hs values for ground beef
(C = 0.74) and a radiant heat source
at 4230.0 R. tl (maximum) = 157 F . . . 5-62

5.11. h(tl - 157)/qS" and (47/52 relationships at
various k/hs values for ground beef

(C = 0.80) and a radiant heat source
at 423000 R o o o o o o o o o o o o o o 0 5-62

5.12. h(tl — tO)/qs" and err/s2 relationships at
various k/hs values for ground beef
(C = 0.75) and a radiant heat source
at 3465.0 R. tl (maximum) = 122 F . . . 5-63

5.13. h(tl - 122)/qs" and CIT/52 relationships at
various k/hs values for ground beef
(C = 0.75) and a radiant heat source
at 3465.0 R. tl (maximum) = 140 F . . . 5-63

5.14. h(tl - l40)/qs" and aT/s2 relationships at
various k/hs values for ground beef
(C = 0.74) and a radiant heat source
at 3465.0 R. tl (maximum) = 157 F . . . 5-63

5.15. h(tl - 157)/qs" and CIT/s2 relationships at
various k/hs values for ground beef

(C = 0.80) and a radiant heat source
at 346500 R o o o o o o o o o o o o o o o 5'63

xiii

5.17.

5.18.

5.19.

5.20.

5.21.

5.23.

5.24.

5.25.

h(tl - tO)/qs" and (IT/s2 relationships
at various k/hs values for ground
beef (C = 0.75) and a radiant heat

source at 2260.0 R. tl (maximum)

h(tl - 122)/qs" and OL'r/s2 relationships at
various k/hs values for ground beef
0.80) and a radiant heat source
at 2260.0 R. tl (maximum)
- l40)/qs" and GT/SZ relationships at
various k/hs values for ground beef
0.74) and a radiant heat source
at 2260.0 R. t1 (maximum)
h(tl — 157)/qs" and 07/82 relationships at
various k/hs values for ground beef
0.80) and a radiant heat source at
2260.0 R

h(tl - to)/qs" and OLT/s2 relationships at
various k/hs values for ground beef
0.75) and a radiant heat source
at 1864.5 R. tl (maximum)
h(tl - 122)/qs" and OL'r/s2 relationships at
various k/hs values for ground beef
0.80) and a radiant heat source
at 1864.5 R. tl (maximum)
1 - l40)/qs" and GT/SZ relationships at
various k/hs values for ground beef
(C = 0.74) and a radiant heat source
at 1864.5 R. tl (maximum)
— 157)/qs" and OLT/s2 relationships at
various k/hs values for ground beef
(C = 0.80) and a radiant heat source
at 1864.5 R .

h(tl - tO)/qs" and aT/s2 relationships at
various k/hs values for ground beef
(C = 0.75) and a radiant heat source
at 1648.7 R. (maximum)

h(tl - 122)/qs" and OL'c/s2 relationships at
various k/hs values for ground beef

0.80) and a radiant heat source

at 1648.7 R. (maximum)

Page

Figure

5.26.

5.27.

h(tl — l40)/qs" and aT/52 relationships at
various k/hs values for ground beef
(C = 0.74) and a radiant heat source
at 1648.7 R. tl (maximum) = 157 F . . .

h(tl - 157)/qs" and OLT/s2 relationships at
various k/hs values for gnaund beef
(C = 0.80) and a radiant heat source
at 1648.7 R . . . . . . . . . . . . . . .

h(tl - 157)/qs" and Cit/s2 relationships at
k/hs = 0.6 for ground beef (C = 0.80) at
different radiant heat source temper—
atures, R . . . . . . . . . . . . . . . .

Product (tS - to) and time, min, relation-
ships at different surface heat fluxes,
Btu per sq ft-hr, and heat source
temperatures, R. ts, product surface
temperature, F. to, initial product
temperature, F . . . . . . . . . . . . .

Volatile loss, percent of initial product
weight, and time, min, relationships
at different surface heat fluxes, Btu
per sq ft—hr, and heat source
temperatures, R . . . . . . . . . . . . .

Product (t1 - to) and time, min, relationships
at different surface heat fluxes, Btu
per sq ft-hr, and heat source tempera-
tures, R. t1, product temperature, 1 in
depth, F; to’ initial product tempera-
ture, F . . . . . . . . . . . . . . . . .

h(tl - to)/qs" and dT/52 relationships at
four experimental k/hs values for
ground beef (C = 0.75) and a radiant
source at 3465.0 R. tl (maximum) =
122 F . . . . . . . . . . . . . . . . . .

XV

Page

7-4

w m IV » 3’ >

OOU‘WWW

mbol

F

= b/a

= c/a

NOMENCLATURE

a. Simple Latin Letter Symbols

Quantity

Area, surface and cross-sectional
Element designation

Element weight in a mixture

Orthogonal polynominal constant

Distance between two radiating surfaces
Ratio of length (b) of a finite rectangle
surface to the distance (a) between the
rectangle surface and another radiating
surface

Element designation

Element weight in a mixture

Orthogonal polynominal constant

Length of one side of a rectangle
Orthogonal polynominal constant

Surface area of a rod extending from

a heat source

Ratio of length (c) of a finite rectangle
surface to the distance (a) between the
rectangle surface and another radiating
surface

Planck constant

Planck constant

Specific heat

Length of one side of a rectangle surface
Perpendicular distance between two
radiating surfaces

Orthogonal polynominal constant

xvi

Unit
sq ft

lb

in

in
lb
in

sq ft

cm4 per
hr-sq ft

cm per R

Btu per
lb—F

in

in

Symbol

x/D

y/D

(hC/kA)

surface coefficient of heat transfer h,

(km—h)/(km+h)

Quantity

 

Element designation

Element weight in a mixture
Perpendicular distance between two
radiating surfaces

Diameter

Emissive power factor

Geometrical angle factor

Equivalent angle factor

Incident radiant energy on a surface

Coefficient of heat transfer

Thermal conductivity

Length

Latent heat of vaporization or con-
densation

Characteristic surface length

Ratio of the length (x) of a finite

rectangle surface to the distance (D)

between the rectangle surface and another

radiation surface

Ratio of length (y) of a finite

rectangle surface to the distance (D)

between the rectangle surface and
another radiating surface

1/2 A quantity composed of the

the thermal conductivity k, the
circumference C, and the cross—
sectional area A

Product weight

thermal conductivity k, the surface

coefficient of heat transfer h, and the

quantity m

xvii

A quantity composed of the

Unit

lb

in

ft

Btu

sq ft-1
Btu

Btu per
sq ft-
hr F

Btu per
ft-hr F

in
Btu per
lb
ft

ft—
lb

Symbol

qS

defiamm

ba*< k: K >< x >< 2 :2 <

Quantity
Heat capacity

Rate of heat flow

Surface heat flux

Correlation coefficient

Distance between the centers of two
radiating differential surfaces

Standard error estimate

Depth

Temperature in the absolute scale
Temperature in the international scale
Average temperature in the absolute scale
Average temperature in the international
scale

Volatile loss from product

Condensing or vaporizing weight

Weight of a mixture of elements

Time in the orthogonal polynominal

Length of a finite surface

Length of a differential volume
Temperature in the orthogonal polynominal
Width of a finite surface

Width of a differential volume

Depth of a differential volume

b. Simple Greek Letter Symbols
Thermal diffusivity

Radiation absorptivity
Radiation emissivity
Temperature excess over a fixed
reference temperature

Wave length of radiation

Density
Radiation reflectivity

xviii

Unit
Btu
Btu per hr

Btu per sq
ft—hr

in

ft

'11

F
gm
lb per hr
lb
mhl
in
ft
F
in
ft
ft

sq ft per
hr

CHI

lb per
cu ft

Symbol Quantity Unit

0 Stefan — Boltzman constant Btu per
2‘: 5%4
Time hr
Radiation transmissivity .....
® Angle of incidence = angular deviation
from normal direction .....

xix

1.0 INTRODUCTION

The use of infrared radiation for heating has been
somewhat limited in food processing. The primary use of
infrared radiation has been in the drying and dehydration
of food products. Asselbergs, §;_al (8), Krupp (35) and
Pollak (47) have reported on the radiant heat processing
of various food products. They report two advantages of
radiant heat processing over regular convection processing
of similar products. These advantages are: fast heating
response; generally shorter processing times. Krupp and
Pollack attributed the faster processing times to the heat
penetration effects of the electromagnetic waves. Asselbergs
measured the heat penetration in apple tissue and found
that heat penetration was dependent on the heat source temp—
erature and the intensity of radiation.

The fundamental laws of radiant heat transmission
require the following factors in order to evaluate heat
transfer by radiation: (a) the temperature of the heat
source; (b) the emissive properties of the source; (c) the
surface area of the source of temperature; (d) the trans-~
mittance of the media between the source and the heated
surface; (3) the reradiation properties of the media:

(f) the geometrical arrangement of the source and receiver,

sometimes called the geometrical angle factor; (g) the

1-2

absorptivity, reflectivity and transmitivity of the receiver:
(h) the emissivity of the receiver: (i) the surface temper-
ature of the receiver: (j) the area of the receiver. Krupp
amd Pollak did not report information of this nature.
Asselbergs' work contained many of the above factors for
some of the processed products, but it was incomplete for
other products.

The thermal properties of the heat source can
normally be found in the literature. DeWerth (19) presents
a rather complete work on surface emissivities for non-food
items. The other radiant heat transmission factors of the
source and the media between the source and the product
surface can normally be calculated from radiant heat theory.
However, the radiant heat properties of food products are
generally unavailable.

After the heat is absorbed by the surface, several
factors influence the heating of the product at a given
depth. Some of these factors are: (a) product environment
temperature; (b) product surface heat convection: (c) pro-
duct surface heat radiation loss, if applicable; (d) product
surface moisture loss; (e) the thermal properties of the
product: such as conductivity, specific heat and diffusivity:
(f) product changes, such as chemical or biological; (g) in-
ternal heat generation or absorption; (h) product thickness:
(1) convection of liquids within the product: and (k) time.

A homogeneous product simplifies many of the above factors.

1—3

The surface heat losses or gains, other than
radiation to the surface, can normally be calculated by the
generally accepted equations for convection and radiation.
However, the product surface temperature is generally not
known, unless it is measured, as the surface temperature is
dependent on the above listed parameters. The product
moisture loss was found to be a linear function of time, at
given high temperature environments by Lowe (37), McCance
and Shipp (43). Jakob (33) handled the surface moisture
loss by using an apparent coefficient of heat transfer.

The thermal properties of food products are normally
difficult to find in the literature, and most of these
data have been reported in the past ten years. This could
indicate that the need for this information is becoming
more apparent, as research is expanding for foods.

It has been generally recongized that chemical
changes take place when a food is heat processed. The
exact nature of these changes as well as the heat require--
ments to cause the changes are essential if food processing
is to be completely analyzed.

If a food product can be considered basically
homogeneous, various solutions of the Fourier conduction
equation may have applications for limited boundary conditions.
Heisler (26), Carslaw and Jaeger (13) have solved the Fourier
equation for a radiation boundary condition with a surface
heat loss to an environment. Heisler has also presented a

graphical solution for the equation for various parameters.

1—4

Some authors have indicated that, for a moist
product with surface moisture losses, the spectral
absorption properties of water act as a limiting factor
for radiant heat absorption. If this hypothesis is true,
a critical examination of the critical region of moisture
absorption should be performed. Also, equivalent radiation
intensities should have similar effects on the heat
processing of food products.

The above two hypotheses lead to the objectives
of this study. The objectives are:

1. To investigate the influence of infrared source
temperatures, within the critical spectral absorp-
tion wave lengths of water (one to three microns),
on the transient processing rates of ground beef.

2. To investigate the influence of infrared heat
fluxes on the transient processing rates of ground
beef.

Ground beef was selected because it represents a

fairly homogeneous meat—type moist food product.

2.0 REVIEW OF LITERATURE

The use of infrared radiation as a source of heat
for food processing has been limited (8). Infrared energy
has been used for the drying of macaroni (7), the blanching
of celery and apples prior to freezing (9), and the peeling
of apples (10). Asselbergs, EE.§l (8) have blanched peas,
asparagus, corn, beans, turnips, and carrots. They also
prepared french fried potatoes and braised meat for beef
stew.

The widest use of infrared radiation has been in
drying and dehydration (6, 19, 25, 49, 54, 55, 58). It
was thought that infrared radiation would offer many advan—
tages over hot air drying because of the penetrating effect
of the electromagnetic waves.

Shuman and Staley (55) points out that an evaluation
of the uses of infrared should include fundamental studies
on the types and properties of the heat sources and on the
absorption and heat conducting characteristics of the product.
Asselbergs, E£._£ (8) revealed that such fundamental
studies were lacking in a review of available literature.

Chase (15) has reported that the application of
infrared heating to food processing is a matter of placing
enough heat source elements into an oven to obtain acceptable

Processing times. He also reports that product color can

2—2

be changed by adjusting the heat source temperature.

In an attempt to correlate the various factors that
affect the infrared or radiant heat processing of food and,
in particular, ground beef, a review of literature on the
subject will be covered in four general areas. These areas
are: (a) the thermal properties of beef: (b) the factors
that affect the processing or cooking of beef: (c) the basic
infrared and the conductive heating theories; (d) the

electric infrared heat sources.

2.1 The thermal properties of beef

The basic thermal properties of beef are: specific
heat, conductivity, diffusivity, latent heat, emissivity and

absorptivity.

2.1.1 The specific heat of beef

Sibel (52) first reported the specific heats of
foodstuffs. He concluded that since most foods were composed
of water and solids the specific heat would be between 0.2
and 1.00 Btu per 1b—F. The 0.2 value was used as the
Specific heat of the solid portion of the food and 1.00
was the specific heat of water. The water weight fraction
added to the solid weight fraction multiplied by 0.2 gives
the specific heat of the product. These figures were
accepted until 1942, when Short, §t_§l (53) measured the

Specific heat of various foodstuffs and found large deviations

between their results and Siebel's. This was particularly

2—3

true in specific temperature ranges. Many authors (4, 5,
60) have listed the specific heat of food products but
they did not define the temperature ranges.

Awberry and Griffiths (11) presented a graphical
relationship between the percent water in meat and the
specific heat of meat, for the temperature range of 18 to
48 C. They reported a specific heat of 0.375 Btu per lb
F at 0% water and 1.00 Btu per lb F at 100% water, a
linear relationship existed between the two points.
Mannhiem (39) also suggested that the specific heat of
foodstuffs is directly related to the percent water in the
product.

Daniels and Alberty (18) state that the specific
heat of a product or a mixture of products is the weighted
average proportion of the constituents which make up the
product multiplied by the specific heat of each of the
components. This concept has been generally accepted.

If this concept is applied to food products and in parti—
cular meat, all that is required is the composition of meat
and the specific heat of each of the elements that make

up the meat.

Chatfield, gt a1 (16) have reported the composition
of various cuts of beef in terms of four basic constituents,
realizing that each constituent is made up of similar sub-
constituents. The four basic constituents are: water,
protein, fat and ash. The various cuts of beef and their

percentages of each of the constituents are shown in Table 2.1.

2-4

 

 

 

Table 2.1. The composition of various beef cuts.
Beef cut Protein, Water, Fat, Ash,
percent percent percent percent

Chuck 18.6 65.0 16.0 0.9
Flank 19.9 61.0 18.0 0.9
Loin 16.7 57.0 25.0 0.8
Rib 17.4 59.0 23.0 0.8
Round 19.5 69.0 11.0 1.0

2 55.0 28.0 0.8

Rump 16.

 

Schweigert and Payne (50) gave the average composi-
tion of beef, including chuck, flank, loin, rib, round and

rump cuts. They reported the following:

 

Constituent Percent
PIOtein 18.05
Water 61.00
Fats 20.17
Ash 00.78

100.00

The American Meat Institute Foundation (3) reports
that the specific heats of protein, water and ash are 0.44,
1.00 and 0.12 Btu per 1b-F, respectively. The Foundation
also points out that fat is unstable in meat. Generally,
triglycerides predominate in meat fats. The natural fats
in beef are a mixture of triglycerides, monoglycerides
and diglycerides, all of which are chemically quite homo-
geneous. The triglycerides will exist in two forms, the

unstable a-form and the stable B-form. The a-form exists

2-5

in the solid state for the temperature range, freezing to
121.8 F. Its specific heat is 0.295 Btu per 1b-F. The
a-solid changes to d—liquid at 121.8 F, with each pound of
fat absorbing 68.76 Btu at this temperature. The specific
heat of the d—liquid is 0.527 Btu per 1b—F. The a—liquid
changes to S-solid at 139.1 F and releases 24.3 Btu per

lb during the transition. The specific heat of the B-solid
is 0.266 Btu per 1b—F. The B—solid changes to B-liquid at
156.4 F and the fat absorbs 96.84 Btu per 1b during the
transition. The specific heat of B—liquid is 0.527 Btu
per 1b-F.

A graphical plot of fat heat content vs fat temper-
ature is shown in Fig. 2.1.

If the above values of specific heat are used for
protein, water, adi and fat in different temperature ranges,
in the Daniels and Alberty specific heat equation the
average specific heats should be fairly realistic. These
values should also replace the values given in literature,
which are not based on this or a similar method. The total
heat content of beef, of average composition, is also
shown in Fig. 2.1. The total heat content assumes that the
specific heats of water, ash and protein are constant.
However, in general the specific heat should vary with
temperatures, as it does for water, but only single values

have been reported for protein and ash.

' :zQ LLJQHJIL

g-

 

11014.13; lit! _

_CL_‘.L

B'Solid *8 ~ Li uid

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

|9=’“9“!"| 8*Solid I 8- Liquid
200 11
I | '
no i l
.. I
|
MO ,L
l
EEIZG f "
, m I I
at p,,—" .",
o 41/ /
w I,
g; ow 1
50
‘ e
B“ ‘ | l
40 “ ‘/ i i
.AV ( Fo‘ I I
20 1 .13“ Ad"
.7 l T
o LN ”’7‘ I I L
40 60 80 I00 I20 l40 I60
I, F
Fig. 2.1 Q, Btu/1b, and temperature relationships for 100% beef fat

and beef with 20% fat.

 

 

 

 

 

Adsorption , Percent

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EA; x l05

ch’

   

20 15 10 15 £0 15

Wavelength, microns

Fig. 2.2 10 mm. and one mm. water absorption and wave length, microns, relation-
ships; Exb x 105/0 T5 and wave length, microns. relationships for

various blackbody source temperatures (R).

2 ’1
I

2.1.2 Thermal conductivity of beef

Information on the thermal conductivity of meats
and related animal fats is very limited and often conflict-
ing. Often the composition of the product is not specified
and if the thermal conductivity has been experimentally
determined, the temperature range for the determined value
normally is not given. Because of the importance of freeze
dried products in the past ten to fifteen years, most of the
information is basically limited to temperatures below
freezing.

Awberry and Griffiths (11) gave a thermal con-
ductivity of beef of approximately 0.92 Btu—ft per sq
ft—hr-F. However, they omitted the temperature or temper-
ature range. They were primarily concerned with low
temperatures. They also indicated that the thermal con-
ductivity of horsemeat was 0.254 Btu-ft per sq ft-hr—F
above its freezing temperature.

Tappel, §£.§L (57) have reported the thermal con—
ductivity of freeze dried meat as 1.3 Btu-ft per sq ft-hr—F
for frozen meat at the beginning of drying to about 0.02
when the meat is dry. In "Advances of Food Research" (1)

a similar value is used for the freeze dried product.

In addition the following statement is made, "In general,
little change would be expected in thermal conductivity
from one meat sample to another, even with different kinds

of meat." Again this statement does not indicate a

2-8

temperature range, or if the product is fresh, frozen
or dried.

Cherneeva (17) reported that thermal conductivities
of fat beef, lean beef and pork of moisture contents 74.5%,
78.5% and 78.8%, respectively, were identical at tempera—
tures of 32 F and above. The thermal conductivity was
0.276 Btu—ft per sq ft—hr-F. Lentz (36) has also reported
the same value for various meat products in the temperature
range of 32 to 50 F. Lentz had measured the value in
accordance with ASTM standards and also calculated the
value using the Maxwell—Eucken formula. However, this
formula assumes knowledge of the conductivities of fat
free beef and beef fat. Lentz also reported that the
thermal conductivities of meat products above freezing
were about equal and about 10% below the established value
for water. Sayles (48) recommended that the 0.276 Btu-ft
per sq ft—hr-F value be used in the analysis of heat transfer
in meat processing.

Cherneeva, Lentz and Sayles all agree on a thermal
conductivity value, but they do not state what happens to
the conductivity if or when moisture is lost from the sur-
face of the product, a phenomenon that occurs in the

processing of meat.

2.1.3 Thermal diffusivity of beef

The thermal diffusivity of beef has been given

considerably more attention than the thermal conductivity.

2-9

Since diffusivity is dependent on thermal conductivity,
specific heat and density, conflicting data appear in the
literature.

Awberry and Griffiths (11) reported that the dif—
fusivity of beef was about 0.0147 sq ft per hr in the
temperature range of -40 to 80 C, for a density of approxi-
mately 73 lb per cu ft. Hurwicz and Tischer (29) reported
in 1952 that the apparent diffusivities of solid pieces
of shoulder clod beef, canner and cutter grades, were
approximately 0.0067 and 0.0073 sq ft per hr at 225 and
255 F, respectively. Hurwicz and Tischer (30) also had
found, in 1956, for solid pieces of beef rounds, that the
apparent diffusivities were approximately 0.0163 and 0.0176
sq ft per hr for the temperature ranges, 225 to 261 F
and 279 to 315 F, respectively. The diffusivities were
significantly different in these two temperature ranges.
They obtained the diffusivities from can processing heating
and cooling curves. They failed to report the densities
of the meats in both papers.

Evans (21) has reported that the diffusivity of
most non-water constituents in food is lower than for water
and would not be expected to vary greatly with temperature:
therefore, the diffusivity of foods will be slightly less
than those of water at similar temperatures, and will be
expected to undergo a smaller variation with temperature,

perhaps 5 to 20% less than for water.

2-10

Jackson (31) has classified food products depending
on whether they exhibit conduction or convection heating
.curves and then subclassed by moisture content. Jackson
states the following products will exhibit conduction
heating curves throughout a canning process and will have
thermal diffusivities close to that of water: these products
include: solidly packed meat and marine products, such as
corned beef, chicken loaf, minced clams, cod fish, sand-
wich spreads and spiced hams; meat and cereal mixtures,
such as dog food and some meat loaf products. He also
states that some products will exhibit convection heating
curves but have thermal diffusiVities considerably less
than that for water, these include a few meat products
with a low moisture and high fat or oil content.

Olson and Schultz (45) have reported a diffusivity
value of 0.005 sq ft per hr for spiced ham and that most
meat products have a diffusivity similar to the spiced ham
value. They also indicated that the 0.005 value is most
frequently used in the canning industry for meats that
exhibit conduction heating curves.

It is interesting to note that if the specific
heat values as found by the Daniels and Alberty formula
for the average composition of beef, and the recommended
value of thermal conductivity are used with a boneless,
basically homogeneous beef product, the result is a dif-

fusivity close to that recommended by Olson and Schultz.

2-11

2.1.4 Latent heat factors in the processing of beef

Lowe (37) Lukianchuk (38), McCance and Shipp (43)
all report that during processing of meat there is a loss
of moisture and fat. Lowe, McCance and Shipp report that
the volatile loss of a meat product consists of water vapor,
while the dripping losses are primarily water and fats with
small amounts of salts. McCance and Shipp first reported
that the volatile loss of a beef product was a linear
function of time. This was verified, at a later date, by
Lowe. Lowe has also reported that higher final product
temperatures result in a larger volatile loss. This latter
statement would naturally follow if the previous remarks~
are correct, because a higher product temperature indicates
a longer processing time, at equivalent processing rates.

If the volatile product loss is water and if the
product surface temperature is known, the latent heat of
vaporization can be found from steam tables.

In section 2.1.1, the latent heats of triglycerides
were given for various a- and B-transitions. These latent
heats could then be applied to the fat changes within beef.

Lowe (37) also points out that protein denaturation
probably occurs at 140 F, which is an endothermic process.
The American Meat Institute Foundation (3) states that
denaturation caused by thermal energy occurs at the same
temperature. They suggest that thermal energy causes

the rupture of intra—anuiinterchain hydrogen bonds and this

2—12

results in the unfolding of certain protein chains, called
peptide chains, and the reaction is an irreversible endo-
thermic process. At about the same temperature, 140 F,
a-form liquid fats change to B-form solid fats and energy
is released in this process. This is probably why the
product temperature rise is not accelerated during the
exothermic latent heat process.

The American Meat Institute Foundation has indi- ~
cated that there is not a statistically significant loss of
amino acids under commercial methods of processing or
cooking. The Institute indicates that the degree of fat
dispersion is a function of product surface area and total
fat mass and somewhat dependent on the degree of swelling,
shrinkage or disintegration of the collangenous fibers
in beef. Also, the elastin proteins in beef are not

appreciably changed during processing.

2.1.5 The emissivity of beef

Absorption data of foodstuffs are almost non—
existent. However, Hall (25) has made the following general
statements concerning products heated by infrared:

2.1.5.1 The absorptivity of non—conductors or

insulators increases as the wave length
of electromagnetic radiation in the infra-
red region is increased, that is, the

temperature of the emitter is decreased.

2-13

2.1.5.2 Most hygroscopic materials have a low
absorptivity in the range from 0.5 to
3 microns and a high absorptivity beyond
3 microns.
2.1.5.3 The maximum absorptivity of water occurs
at 3, 6 and above 15 microns wave length.
2.1.5.4 Generally, as the temperature of a product
increases the absorptivity decreases.
2.1.5.5 As the moisture content increases the
absorptivity increases.

Infrared energy may be reflected, absorbed or
transmitted through a body, both the absorpiton and trans-
mittance are of primary importance in the processing of beef.

DeWerth (19) has reported that the surface color
of a product has an effect on absorption, with lighter
colored surfaces having lower absorption. He also found
that the radiant heat source temperature had a critical
effect on absorption. With high heat source temperatures,
the surface color greatly influenced absorption rates,
while low heat source temperatures reduced the differences
in surface color effects. Hienton, §t_al (27) report
that grey, green, brown and red colors have absorptions
in the range, 0.65 to 0.75, while the lighter colors such
as light green, yellow and white have absorptions in the
range, 0.40 to 0.55. Hall (25) reported that the absorption
of infrared energy by sand is a function of the percent

of water in the sand, with higher water percentages

2-14

leading to higher absorptions.

Shuman (54) reported the absorption and wave length
curve for orange juice solids, which indicated a maximum
absorption at about 3.6 microns. He also stressed the
importance of matching the wave length characteristics of
the radiant heat source with the absorption properties of
the product.

Schroeder (49) reported a linear correlation between
initial moisture content and infrared drying rates, which
were significant at the one percent level for four varieties
of rice. Shuman (54) has reported that researchers have
had disappointing results with infrared heating because of
popular misconceptions about the energy and a lack of
fundamental knowledge concerning the absorption of infrared
energy.

Asselbergs, §t_§1_(8) reported on the heat pene-
tration into apple tissue after five minutes exposure to
three types of infrared radiators. These radiators were a
quartz lamp, a quartz tube and a calrod, the electromagnetic
wave lengths at maximum energy emission were 1.16, 2.35
and 2.65 microns, respectively. They found that by in-
creasing the surface heat flux at each of the above wave
lengths that the heat penetration increased. The heat
penetration and surface heat flux relationship was basically
linear in a given time period. Lastly, they reported that
the infrared absorption characteristics of apple solids

became important only during the advanced stages of dehydration.

2—15

However, they did not indicate how they defined these
advanced stages of dehydration.

DeWerth (l9) and Shuman (54) gave the spectral
transmittance and absorption of various thicknesses of water.
Some of these are reproduced in Fig. 2.2. Plotted in the
same figure are various black body energy distributions at
different source temperatures, these are plotted in accordance
with Planck's law of energy distribution (46). From Fig. 2.2,
it can be seen that lower source temperature radiations
are almost totally absorbed by surface layers of water.
Therefore, if a moist meat product has volatile losses
during processing, this indicates that water is on or very
close to the surface of the product and the absorption
spectrum of such products could then be similar to that of
water.

Sevick and Sunderland (51) reported in 1962 on the
emissivity of beef. This is probably the first article to
appear in literature on the measurement of emissivity of
food products. Chase (14) and DeWerth (19) had assumed
values close to that of water for their work. Sevick and
Sunderland stated that the emissivity of lean beef muscle
was 0.74 and 0.73 at 70 and 95 F, respectively. A linear
relationship exists between these values. They also
reported values of .780 and .775 for beef fat between the

temperatures given above.

2-16

2.2 The factors that affect beef processing.

Lowe (37) states that when meat is processed or

codked the following changes may occur:

1. Color of meat
2. Weight
3. Volume contraction

4. Fatty tissue

5. Structural proteins or connective tissue

6. Muscle fibers

7. Flavor

Most of these factors have already been discussed.

However, her remarks on volume contraction are particularly
interesting. She states the volume does not basically
change until a temperature of 140 F is attained, then from
140 to 158 F, a high volume reduction occurs. The volume
continues to decrease but at a much lower rate in the 158
to 248 F temperature range. In most cases the length and
width are decreased but the product depth is increased.
In all cases the reduction of volume is less than the total
weight loss of the product. Lowe's statements are in general
agreement with other researchers. For example, Meigs (44)
found little volume change below 104 F, McCance and Shipp (43)
indicated very small volume changes below 140 F. The
American Meat Institute Foundation (3) found that collagenous
fibers, first swelled, then shrank, and finally disintegrated

for well done beef (about 170 F). They also indicated that

2-17

shrinkage due to coagulation, or extensive protein de-
naturation is nearly complete at approximately 152 F.
Lowe (37) also suggests that the time required for
processing or cooking is dependent on:
1. The method of processing
2. The processing temperature
3. The weight, surface area and maximum depth
4. The final product temperature
5. The composition of the meat
6. The degree of post mortem changes
7. The initial temperature of meat

Six of the seven above items normally appear in heat
transfer equations for product temperature determination at
a specific depth and time. Only the sixth item does not
appear, although this factor is probably indirectly involved
with product thermal properties, such as conductivity,
specific heat, diffusivity and emissivity.

Product heat penetration rates, in minutes per
degree temperature rise, or time-temperature curves are
reported by Lowe (37), Towson (59) and Lukianchuk (38).

An analysis of the heat penetration rate or curves indi-
cated four definite rates or linear relationships within
the temperature ranges given for the various d- or B-forms
of fat in beef. The temperature ranges were: from the
initial temperature, above freezing, to about 122 F; 122

to 140 F; 140 to 157 F; and above 157 F.

2-18

Chase (14) discussed surface heat flux effects on
cake quality and found that 550 Btu per sq ft-hr was an
optimal surface heat flux. He also stated that changes
of 50 Btu per sq ft-hr from the optimal value of 550 re-
duced the quality of the cake. But, he did not take surface
moisture evaporation into account in his calculations. If
the latter factor had been determined, his surface heat
flux rates would have probably increased. In addition, the
energy requirement to cause the cake rising reaction was
not considered. Therefore, the optimal value was probably
higher than he indicated.

Pollak (47) has processed meat to a center temper—
ature of 150 F, with a conventional convection type oven,
with infrared radiation and with a microwave type cooker,
utilizing the magnetron. He measured all product changes
with each heat source and reported the results as percent
heat source input and heat absorbed by the product ratio.

He only indicated that the conventional oven temperature
was set at 325 F and that the infrared device was placed
three inches from the product. Electrical wattages of the
elements, surface heat fluxes, product surface temperatures
and other heat transfer information were not given.

Lowe(37) reported on the effects of various oven
temperatures and final product temperatures on weight
losses. Keating (34) reported similar information for forced
convection processing of meat and other products. Chase (14)

stated that when data are presented in the above manner,

2-19

heat transfer analysis is very difficult and in some cases
impossible because of the lack of essential information.
Chase is only one of the few authors, except for those con-
cerned with canning processing, who attempted to analyze
the mechanisms of heat transfer and correlate data on these

results.
2.3 Infrared and the conduction heating theories

2.3.1 The infrared theory

The total radiant energy emitted per unit time per
unit area is defined as the total emissive power and is
often denoted by E (24). The amount of energy emitted by
a body generally varies with wave length or frequency.

The variation is often defined by the monochromatic emissive

power E which is the amount of energy emitted in the

x!
spectral range A to dk and is generally defined by Exdk,

so E = J(00 Ekdk.
o

If radiant energy were incident upon a surface of
finite thickness, the energy could be absorbed, reflected
and transmitted. Total monochromatic absorptive, reflective
and transmitive powerscan be defined as above. From these,
the absorptivity a, reflectivity p, and transmissivity T,

can be defined. The absorptivity (a) is defined as follows:

00
-1
a—Gf GAGAd?‘

O

2-20

Where G is the incident radiant energy, Gk is the spectral

distribution of G; GA is the fraction of the monochromatic
incident energy absorbed and k is the wave length. It would
follow that a + p + T = 1.

Kirchhoff established the following relationship:
for radiation at the same wave length and temperature, the
ratio of the emissive power to the absorptivity is the same

for all bodies. The importance of Kirchhoff's law is

indicated when one considers a black body. A black body

is a body which absorbs all incident radiation (d 1).
If a black body is a radiator no other body could radiate
more heat than it. If Ekb is the monochromatic emissive

power of a black body, then the monochromatic emissivity,

Ek’ of a non-black body is:

ex = Ek/Ekb

The total emissivity, 6, could then be defined as
the absorptivity was defined above. If Kirchhoff's law
is employed and if one of the bodies is a black body, the

following relationship exists:

Ci.A = €%’ and G = e

Kirchhoff's law specifies that these relationships exist
at one temperature. If the behavior of a body can be
approximated by considering ax = 61 = a = e for all wave
lengths and temperatures, these bodies are called gray

bodies.

2-21

Most radiation theory is developed on a black body
basis or by assuming monochromatic properties. It is
generalized from the monochromatic to the total spectral
properties, and finally in some cases further generalized
for gray bodies.

The Stefan-Boltzmann law relates the total emissive
power of a black body to the absolute temperature of the
same body, it is:

4

Eb = O AlT

Where Al is the black body surface area of a finite
depth (P), o is the Stefan—Boltzmann constant (0.174 x 10—8
Btu per hr-sq ft — R4 (33)), and T is the absolute tempera-
ture, R.

Wein's displacement law states, if a wave of length
%2 at T2 is displaced from that of length ll at T1’ such
that A2T2 = le1,

these two wave lengths are directly proportional to the

the monochromatic emissive powers of

fifth power of the absolute temperatures. The relationship
indicates that the maximum value of Ek/TS occurs when AT =
5215.6 micron - R. If the temperature of a black body source
is known, the wave length of maximum energy emission can be
solved for this value and is frequently used in literature
(19, 25, 33, 48, 54).

Wein developed an equaticn for the spectral distri-
bution of energy which was accurate for wave lengths up to

two microns. Rayleigh and Jeans also developed an equation

2—22

for the spectral distribution of energy, but it failed at

low wave lengths. Planck (46) then proposed a law which
fits experimental data, and was also consistent with the

Stefan-Boltzmann law. Planck's law is as follows:

-5
c
E =1:

Ab eC2/KT_l

This equation is particularly useful for plotting the
spectral energy distributions of black bodies, gray bodies
and other bodies with known monochromatic properties at
given temperatures.

The radiant energy exchange between surfaces is
dependent upon the emission, absorption and reflection
characteristics, which were discussed above. It also
involves the geometrical surface arrangements and the
media between the surfaces. If air is the media between
surfaces, it can generally be considered opaque (28).
However, if it contains water vapor the absorption and
emission of water vapor must be considered. If the satur-
ation level and partial pressure of water vapor is low,
the emission of energy from it is generally low and is
often neglected in the radiant energy exchange between
bodies (24, 28, 42, 48). A similar situation applies to
carbon dioxide gas (24, 33). Only the case of diffuse
radiation through a non—absorbing medium will be con-
sidered.

Jakob (33) gives a crude approximation for the

net heat exchange by radiation between a completely convex

2-23

body which radiates diffusely to a completely concave

enclosure at a lower temperature; it is:

q net = 610 Al (T — T ),

Where the subscripts 1 and 2 refer to the inner
body and enclosure, respectively. Jakob also assumed that
Lambert's law is valid and derived a general equation for
diffuse radiation between two surfaces. He considered two
differential surface elements, separated by a distance (r)
at arbitrary angles to each other, the angle (¢) was de-
fined as the angle between (r) and the normal to the surface.

The differential radiation from dAl to dA2 would be:

dE = e OT 4 cos¢l cos¢2 dAldA2
(ledZ) 1 1 2

III

 

= 6 CT 4 dA cos¢l cos¢2dA2

A2 'Wrz

 

He then defined the geometrical angle factor F(d as

1)2
that fraction of the energy emitted from dAl which directly

strikes the area A2:

F = cosdl cosd2
(d1)2 Trr2
A2

A similar procedure is followed for dE(d2)(dl):

4 cos¢ cos¢ dA dA
= 2
dE(d2)(dl) 62 0 T2 1 2 l

2
tr

2-24

and dA would be:

The energy exchange between dAl 2

dq net = dE(dl)(d2) — dE(dz)(d1)

cosd)l cost2 dAldA2

2
tr

0(T4—T4)

 

If F12 is the geometrical angle factor of Al versus A2,

the geometrical angle factor is:

cos¢ cos¢ dA dA

 

F = l 1 2 l 2
12 Al nrz
A1 A2
so q net = e e F <3A (T 4 — T 4) if F is constant
’ l 2 12 l l 2 ’ (dl)2

over the surface Al'

Hottel (28) then applied the general geometrical
angle factor equation to a specific situation. He found

F for a differential area radiating heat to a finite

(d1)2

parallel surface area, Fig. 2.3 represents the geometry.

For parallel surfaces: cos¢l = cos¢2. The distance D is

the perpendicular distance between surfaces, (r) is the

distance drom dAl to dA2,

is the width of A2 and L1 = x/D, L2 = y/D, he then inte—

equation of Jakob. The result is:

x is the length of A and y

2

grated the F
(cal)2

 

 

F =-—l— L2 sin.l Ll
(d1)2 2w (L22 + l)1/2 (1+L22 + Ll2)1/2

 

 

 

 

1‘ /dA2
dx
dy y
/l
I .
’ l
I
D 4% 2 L|:-%r
V :L
// L2 0
/
[37
AA.

Fig. 2.3 Hottel's geometrical model for determining the
geometrical angle factor between a differential
surface and a parallel finite surface.

aqs

 

 

 

 

 

 

 

§+
=nq=0
‘ nx
ax
Mr
”'0 ' Aqsux’cp
oq,

Fig. 2.4 Surface element heat balance.

2-26

McAdams (42) presented a graphical solution to the

equation, as did Jakob. However, Jakob used different

symbols, a, b, c, B and C for D, x, y, L1 and L2, respectively.
Having determined the geometrical angle factors

and knowing the surface emissivities, areas and tempera-

tures, the radiant heat exchange between the surfaces can

be determined. For the heated surface, subject to a high

heat source temperature, with the heated surface being much

lower in temperature, a constant surface heat flux (Btu

per sq ft-hr) may be used according to Heisler (26).

2.3.2 The conduction heating theory

The Fourier differential equation of heat conduction

without heat sources (23) is:

t d2t dzt dzt
X2

Q

=C(,"""—+——— __

d

El

The equation assumes constant thermal properties of
a homogeneous substance, also heat is not generated or
absorbed by the body.

The equation can be simplified, and heat flow
restricted to one direction if an infinitely wide surface
area is used. Jakob (33) suggests that if an infinitely
thick plate is used, its length and width may be finite
if it is perfectly insulated around the edges, in which
case the heat flow will be perpendicular to the surface.

Many solutions to the Fourier equation for dif-

ferent boundary conditions are given in the literature on

2-27

the subject (13, 26). However, before a solution can be
determined for a particular problem, boundary conditions
must be specified. To best indicate possible boundary
conditions for processing meat, by high temperature
radiant energy sources,a heat balance should be attempted
for an element of the material. Fig. 2.4 represents a
surface element of the product, with uni-directional heat

flow. Aqs represents the incident radiant heat on the
surface, only Aqs" will be absorbed. Aqr is the radiant
heat loss from the surface to the environment, if the
temperature of the environment is lower than the surface
temperature. ch represents the surface convection heat
loss to the environment, if the environment is again at a
lower temperature. AqL is a latent heat loss, or product
volatile loss which can be represented in units of heat loss.
Aql is the heat transferred through the product. Aqs
is the heat stored within the product, this indicates a
transient heat transfer problem, in contrast to a steady
state problem. Finally, AqF is the heat absorbed or released
in product changes. In the case of beef processed above
121.1 F this qF would represent the various changes of
state for the a- and B—form fats. The a in the Fourier
equation is thermal diffusivity, not to be confused with
d—form fats within the meat product.

Heisler (26) solved the Fourier equation for a

similar boundary condition, but he did not include the qF

term above. His solution was for the induction heating of

2-28

metals, at given cycles per second and for given penetrations
into the surface of the metal. He also assumed the product
had a finite thickness and it was heated from both sides

by similar surface heat fluxes. Jakob points out that a
product that is perfectly insulated at some depth, can be
considered a product of finite thickness, with a depth of

one half of the finite thickness situation. Heisler's

final solution is:

t(m1X) "tb
qs”/h

. 2
(Sin wk)(cosnwk)exp (—wk X)

 

 

,_.
I
N
I-‘MB

wk + (Sin wk)(cos wk)

Where n indicates the relative position in the
body; X = (GT)/L2, L is the depth, a is defined above,
T is time; qs" is the surface heat flux; h is the coefficient
of surface heat loss; t is the initial product temperature,

b

which is constant at T = 0; wk is taken from : nw = cot w,
where w is an integer. He also gives an approximate solution
for values of X < 0.2. The solutions of these equations are
given on his familiar Heisler charts, instead of Go/Gi he
uses 1-h(80—0i)/qs" as one of the parameters, the other
parameters are unchanged for XL> 0.2. On his chart for

X < 0.2 the parameter h(G - ei)/qs" is used instead of

l - e/ei. Except for the qF heat term, this is a solution
for the particular radiant heating problem. If qF is
considered at definite temperatures, which are known,

perhaps charts similar to Heisler's could be plotted within

various temperature ranges, with the qF temperatures acting

2-29

as a parameter temperature for each temperature range.
However, one of Heisler's boundary conditions should be
checked if experimental data is to correspond with his
solution. The particular boundary condition is that a
final uniform product temperature is assumed to be qs”/h)F
above the original product temperature.

The surface heat transfer coefficient depends on
three types of heat transfer; they are radiation, convection
and a latent heat of vaporization. The first two heat
losses are easily handled by generally accepted heat
transfer equations. Jakob (33) discusses the latent heat
case, stating that if the weight of the vaporizing product
is known (m), its latent heat of vaporization is known (L),
then this can be equated to an apparent coefficient of
heat transfer (hL), the environment temperature (te) and
the surface temperature (ts), thus:

mL = h (t - t )

L s e

mL/(ts - te).

hL

The use of the apparent heat transfer coefficient

is only valid if the rate of 1255 per unit of time is
constant.

Carslaw and Jaeger (l3) discuss the case of an
infinitely wide plate of finite thickness, with a
radiation boundary condition, and heat loss from the sur-
face. They give, the solution for this surface temperature,
temperature at the center and the average product temperature.

Their solutions correspond to Heisler's.

N
I
m
(D

2.4 Electric infrared heat sources

The three most common electric heat sources are
quartz lamps, quartz tubes and calrods.

The quartz lamp consists of a coiled tungsten
filament enclosed by a fused quartz envelope. The common
electrical consumption of the lamp is 100 watts per linear
inch of coiled filament length. At its rated voltage, the
filament will operate at about 4500 R (12). The filament
temperature is then reduced at voltages less than rated.
The lamps can be made at alnost an infinite number of
lengths. At reduced voltages, the emissivity of tungsten
is reduced (40) as well as the temperature, hence radiant
heat outputs are greatly reduced (12). In addition, the
transmittance properties of fused quartz are also affected
by different filament temperatures, generally the trans-
mittance is decreased at lower temperatures (12). Fused
quartz approaches a black body condition for a radiation of
five microns and longer (12). The fused quartz then absorbs
energy and reradiates heat at lower temperatures and at
reduced intensities. The difference between the absorbed
heat and the reradiated heat of the quartz envelope is
either lost by convection to a lower temperature environ—
ment or conducted to the ends of the cylinder—type envelope,
and the heat is lost by convection, radiation or conducted
to the electrical terminal. At ordinary room air temper-
atures, the terminal may have an equilibrium temperature of

about 200 F, under extremely high environment temperatures

2-31

the terminal may attain a temperature of 625 F, which is the
maximum design terminal temperature (12).

The quartz tube consists of a coiled chromnickel
filament, enclosed by a fused quartz envelope. The normal
operating temperature of the filament is 2260 R at rated
voltage. The chromnickel emissivity is a function of
temperature, generally decreasing at lower temperatures
(19). The general properties of fused quartz were given
above and apply equally well for the quartz tube. The
quartz tube end losses are similar to those indicated for
the quartz lamp, except for a higher end or terminal temper—
ature (12).

A 1600 watt, 240 volt quartz lamp has a 16 inch
filament and an 18 inch fused quartz envelope. The 550
watt, 120 volt quartz tube has a 17 inch filament and an
18 inch fused quartz envelope. The quartz lamp and tube
ends can be treated as short rods, transfering heat to
an environment.

The calrod or radiant rod consists of an electrical
resistance filament, which is covered by insulation, and the
insulation is covered by a thin wall metal sheath. Heat
is primarily transferred by conduction to the metal sheath
which attains a temperature of about 1960 R under rated
voltage and wattage. For example, a 240 volt, 1000 watt
calrod will maintain a metal sheath temperature of about
1960 R when operated at ordinary room temperatures (19).

This rod will be approximately 17.5 inches in length. The

2-32

actual length of the surface at the 1960 R must be deter—

mined or measured (12). The remaining surface, or the
ends of the rod could then be treated as rods of medium
or short length with a source temperature of 1960 R (at
240 volts).

Jakob (32) suggests the following equation for the
heat loss of a not very long rod protruding from a heat

source:

- 2L
_ 1/2 l-pem
qO - (KhAC) l + pe-mZL 90:

Where qO is the heat loss from the rod, K is the

 

thermal conductivity, h is the surface heat transfer co-
efficient, A is conducting cross section area of the red:

C is the rod surface area, p is defined as (Km -~h)/Km + h),
m is defined as (hC)/(KA) 1/2’ L is the rod length, 90 is
the temperature difference between the source and the
environment. Jakob also suggests the following equation

to determine the temperature distribution on the surface

of the rod at various distances (x) from the source of heat:

9
9 = o (e-mx + pe-mZL emx)

1 + pe—mZL

Where 9 is the temperature difference at the distance

 

I

(x) and the environment, the other terms are defined above.

3.11

3.12

3.13

3.14

3.0 EXPERIMENTAL APPARATUS

Steel rule, accuracy 1 1/64 inch

Vacuum tube voltmeter, accuracy 1 5 volts AC

Ammeter, i_0.05 amperes AC

Brown Electronik Recording Potentiometer, accuracy
i.1 F in the range of the experiments, : 4 F in the

O to 600 F range, both accuracies with iron constantan
soldered thermocouples

Weighing scale, 1 0.05 grams

Mercury in glass thermometer, accuracy 1 0.5 F

Variac transformer

Eppley radiation pyrheliometer, maximum transmittance
of crystal 12 u, heat flux range (unknown, but the
instrument is primarily used for solar radiations)
Leeds-Northrup manual potentiometer with room temper-
ature compensation setting, reading accuracy 1

0.03 millivolts

Stop watch, accuracy : 0.005 minutes

Micrometer, accuracy 1 0.001 inches

Copper sample container, 1" (depth) X 3" (width) X 6"
(length)

Insulated box, 8" (depth) X 6" (width) X 10" (length)
Relative weighing volatile loss scale, with vibrator,

reading accuracy 1 1 unit (the scale had a linear-unit

3—2

vs weight removal relationship)

3.15 Paper distance scale between heat source and sample

surface, reading accuracy i 0.03 inches

 

4.0 PROCEDURE

4.1 Electrical energy characteristics of the heat sources

The electrical energy requirements of the three heat
sources (quartz lamp, quartz tube and calrod) were measured
by a voltmeter and ammeter. Voltage was controlled by a
variac transformer. Three ampere measurements were made
at each voltage increment of 20 volts for the quartz lamp

and calrod, while only 120 volts were used for the quartz

tube.

4.2 Physical measurements of the three heat sources

The diameters and lengths of the three heat sources
were measured using a micrometer and measuring rule. Ten
measurements were made of each of the diameters and lengths.

The filament diameters of both the quartz lamp and
quartz tube were measured by a micrometer. The same
instrument was used to measure the external shell diameter
of the quartz lamp, quartz tube and calrod. Inside calipers
‘were used to measure in interior diameter of the calrod
steel shell. The filament measurements were made on
only one lamp and tube, while at least three different units

*were used for external shell and length measurements.

4.3 Heat flux measurements

Heat flux measurements of the specific heat sources
(quartz lamp, quartz tube and calrod) were made at different
electrical voltages for the quartz lamp and calrod and for
the normal operating voltage (120 volts) of the quartz
tube. The heat flux measurements were also made at three
distances from the heat source.

A variac transformer was used to regulate the
voltage of the heat sources. The voltage was measured by
a voltmeter. Heat flux measurements were made with a
radiation pyrheliometer connected to a manually operated
potentiometer. Voltage increments of 20 volts were used
for the quartz lamp and calrod unit. To the quartz tube,
120 volts were applied. Heat fluxes were measured at six,
nine and twelve inches from the center of the heat sources.
One and three heat source unit fluxes were measured at the
above voltages and distances for the quartz lamp. A one
unit heat source was used for the calrod and quartz tube.

All heat flux measurements were made in a non-
enclosed volume at normal room temperature. The wire leads
from the pyrheliometer to the potentiometer were shielded
from the heat source by highly reflective metal foil.

Room temperatures were measured by a mercury in glass
thermometer. A room temperature compensation was made
on the potentiometer. In all cases the exposure time of

the pyrheliometer was at least three minutes. A ten minute

4-3

minimum time period was used for the calrod to allow the
heat source to approach its equilibrium temperature.

The pyrheliometer was placed perpendicular to the
center of the heat source and similarly to the center-unit
for the three unit source. The three units were parallel

and were spaced one inch on centers. See Fig. 4.1.

4.4 Effect of surrounding walls and reradiation.

Six samples of ground beef from the same mass were
cooked to determine the effect of reradiation from surround—
ing walls. The samples were one inch in depth, three inches
wide and six inches long. The sample was placed in a copper
container of the same size. The copper container was
placed in an insulated container that provided at least two
inches of insulation on the sides and bottom of the sample
container. The top of the insulated container was flush
with the top of the sample container, thus a three inch
by six inch surface area was exposed (Fig. 4.2). The top
of the insulated container was arranged parallel to a
quartz lamp heat source. The sample container center was
arranged perpendicular to the center of the heat source,
with the six inch length parallel to the length of the
heat source.

A constant lamp voltage (220 volts) and a constant
distance from the center of the lamp source to the insulated
container surface were maintained. This yielded a heat

flux at the sample surface of 946 Btu per sq ft-hr at a

4-4

/Heat Source \
- f 1

Heat Flux
g/Meosuring Distance--\‘N

‘L—r—r/f Pyrheliometer\~r_/I_1L

r fl 1

W WW

 

flF

 

 

 

 

 

 

Fig. 4.1 Heat source and pyrheliometer arrangement.

  
    
  

Heat Source

Product in

/ Copper Container

 

 

lnsquted Box

/

 

 

 

 

 

 

 

Fig. 4.2 Product, cooper container, insulated box and
heat source arrangement.

4-5

maximum energy wave length of 1.194 u. The samples were
processed until the temperature at the one inch sample
depth was 170 F. The following data were obtained: one
inch sample depth and sample surface temperature at one
minute intervals; the initial weight of the sample: the
container weight: the final sample weight, including
drippings; the dripping weight. The difference between
the initial weight and final and dripping weights was
determined as the volatile weight loss.

The three remaining samples were processed in a
similar manner, except that the processing volume was
totally enclosed. The enclosure was 36 inches by 48 inches
by 48 inches. The insulated container and quartz lamp
were located approximately in the center of the enclosure.
The inside of the plywood enclosure was painted blackboard
black. Various enclosure wall temperatures were measured
and a shielded thermocouple was placed in the enclosure.

The sample surface temperature was measured by a
thermocouple, which was soldered to a one inch square thin
copper plate which was painted lamp black on the side
exposed to the radiant heat source. The plate was
fastened to the sample surface by fine wire staples
driven into the sample. All thermocouple leads were
shielded by highly polished metal foil. All thermocouple

junctions were soldered.

4-6
4.5 Transient processing rates cf ground beef with infra-
red heating

Samples of ground beef were processed at different sur—
face heat fluxes and at different source temperatures.

The ground beef was purchased at one time from the same
initial mass and packaged in one and three pound packages and
frozen to 0 F on the same day it was ground. The beef* con—
sisted of 160 pounds of lean beef and 40 pounds of beef fat.
The frozen samples were removed from the freezer 24 hours before
use and placed in a 35 F cooler, whereby defrosting could take
place at a uniform rate for all samples. The samples were
packaged in freezer paper (wax-coated on the side adjacent to
the ground beef), to keep moisture losses to a minimum during
storage and to prevent surface dehydration (freezer burn).

Five heat source temperatures were selected, namely:
4230.0 R, corresponding to the quartz lamp filament temperature,
and operated under 200 volts AC; 3465.0 R, corresponding to
the quartz lamp filament temperature, operated under 120
volts AC; 2260.0 R, corresponding to the quartz tube
filament temperature, operated under 120 volts AC; 1864.5
R, corresponding to the calrod shell temperature, operating
under 220 volts AC; 1648.7 R, corresponding to the
calrod shell temperature, operating under 180 volts AC.

These source temperatures would then be equivalent to the

maximum energy emission from a black body at 1.233 u

 

*The beef, a mixture of choice grade cuts,was ground
with first medium (5/16”) and then fine (1/8”) meat cutter

blades.

4-7

1.505 u; 2.308 u; 2.797 u and 3.164 u, respectively,
according to Wien's Displacement Law.* The above wave
lengths cover the critical portion of the water absorption
spectrum, DeWert (19).

Generally surface heat fluxes are not reported in
the literature, only oven or autoclave temperatures. See
Lowe (37), Lukianchuk (38), Chase (14) and others. How-
ever, Chase (14) had calculated surface heat fluxes from
some of Lowe's earlier experiments and found some products
of rather low moisture content had an optimum heat flux
rate of about 550 Btu per sq ft-hr. Meats and especially
ground beef have relatively high moisture contents, so a
range of heat fluxes were used, starting with around 500
Btu per sq ft-hr to over 1000 Btu per sq. ft—hr, assuming
the product was a black body. The heat fluxes are shown
in Table 4.1.

A sample of ground beef was placed in a copper
container 1 inch (depth) by 3 inches (width) by 6 inches
(length). The copper container was then placed in an
insulated box, which provided at least four inches of
insulation on the bottom. The top surface, 3 inches by
6 inches, was left exposed and the ground beef sample was
flush with the top of the insulated box. The heat source

or sources were then placed parallel to the top surface

 

*Black body radiation is a function of AT. The
maximum of Ex/T5 occurs when AT = 5215.6 in R, where
Ex is the monochromatic emissive power. Giedt (24).

4-8

of the insulated box and the center of the heat source or
heat sources were placed perpendicular to the center of the
ground beef sample (1/2 width and 1/2 of the length). All
samples were processed in an air conditioned room (80 F).

The distance between the heat source and the sample
was varied to produce desired surface heat fluxes on the
sample. Table 4.1 shows the relationships between surface
heat fluxes and distances for the different sources, and
source temperatures as well as the corresponding wave
length, in microns (u), at which maximum energy emission
occurs.

All ground beef samples were taken from the 35 F
cooler and packed in the copper container, which had been
previously weighed. The sample and copper container were
then weighed. The weight of the ground beef samples ranged
from 312 to 330 grams, excluding the copper container.

The top surface of the ground beef was flush with the top
of the copper container. Two soldered iron constantan
thermocouples were placed on the bottom of the container,
approximately three inches apart and approximately 2-1/2
inches from the ends and at one half of the width of the
container, after the ground beef had been packed in place
and weighed.

An iron constantan thermocouple had been soldered
to one side of a one inch square copper plate, the other
side of which was painted lamp black. The plate was centered

on the ground beef surface and held in place by two staples

4-9

made of stiff fine wire. This plate was used to measure
the surface temperature of the ground beef.

The copper container was placed in the insulated
box, which was then placed on a weighing scale. The
weighing scale was attached to a vibrator, which could be
operated to minimize static scale error.

The thermocouple leads, which were attached to a
Brown Electronik Recording Potentiometer, were shielded
from the heat source or sources, by highly reflecting metal
foil. Room air temperature was also measured by the potentio-
meter.

The heat source or sources were attached to a
floating frame which could be adjusted to vary the distance
between the heat source and the sample surface. As the
product was being processed its weight was reduced by the
volatile loss and periodically (every five or twenty
minutes, depending on the heat flux) the difference between
the initial weight of the sample, copper container and
insulated box and the weight at that time was recorded
and a distance adjustment was made to compensate for the
decreased distance between sample surface and heat source.
The maximum distance deviation was 0.03 inches in any one
time increment.

Fig. 4.3 shows the arrangement of heat source,
sample and weighing scale. The device for measuring the
distance between the sample surface and the heat source is

also shown in the figure.

#xL /

Insulated
Bax /

4-10

Heat Source
or Sources

 

 

Producl\

 

I

 

'itli _ _

fl

__J

6"

 

 

 

 

 

 

 

 

 

‘ ‘Weiqht Scale

 

Fig. 4.3

 

 

Distance Scale (for maintaining a

constant distance between product

and heat source.)

Experimental apparatus arrangement.

4—11

All samples were processed until the temperature
at the one inch sample depth was 170 F, the linear average
of the two thermocouples at that depth.

The various sample temperatures were recorded every
minute on the recording potentiometer.

The voltage, hence source temperature, was main-
tained by a manual variac transformer and a vacuum tube
voltmeter. The amperes were measured by an AC ammeter.
When three heat sources were used simultaneously, each
heat source was regulated by individual variac transformers.

When the final processing temperature was attained
the heat sources were shut off and the product was allowed
to cool to at least 152 F, at the one inch depth, while the
ground beef container was still in the insulated container.
This cooling procedure is recommended by Lowe (37).

The thermocouples were removed from the ground beef
after cooking, and the cooper container and the ground beef
were weighed in grams. The difference between this weight
and the initial copper container and ground beef weight
was assumed to be the volatile weight loss of the product.
The ground beef sample was then removed from the copper
container and its width and length were measured. An
attempt was made at measuring the depth of the product, but
it was difficult to ascertain any change in height within
.1 1/16 inches, so depth changes were not indicated. The
copper container, along with drippings, was weighed in

grams. The difference between this weight and the initial

4-12

copper container was assumed to be the dripping weight.

The time-temperature relationships at the one inch
depth and at the surface were recorded from the potentio-
meter recording every five minutes, starting with the initial
time at which the heating started (time zero) to the final
processing temperature of 170 F at the one inch depth.

The times at 122, 140 and 157 F were also recorded, if
they did not occur at the five minute increments.

Summarizing, the following data were taken in each

of the tests:

4.5.1 Copper container weight, grams

4.5.2 Ground beef weight, grams

4.5.3 Voltage of the heat sources

4.5.4 Amperes of the heat sources

4.5.5 Distances between heat sources and sample surface,
inches

4.5.6 Time—temperature relationships, minutes

4.5.6.1 Product surface, F

4.5.6.2 One inch below the product surface, F

4.5.7 Time-relative sample weight loss relationship,
per five and twenty minute time period, grams

4.5.8 Final sample weight, grams

4.5.9 Sample dripping weight loss, grams

4.5.10 Sample volatile weight loss, grams

4.5.11 Sample length and width changes, inches.

 

Table 4.1.

4-13

beef at different source temperatures.

 

Surface heat fluxes used in the processing of ground

 

 

 

 

 

 

 

Quartz Lamp Quartz Lamp Quartz Tube ‘fi:
4230.0 R; A = 1.233u 3465.0 R; A = 1.5054 2260.0 R; A = 2.308u j
A B C D A B C D A B C D j

4s?
35 4.55 1124.01 1 10 5.14 1163.87 3 59 5.30 1151.82 3 '
34 4.73 1077.69 1 11 5.50 1077.48 3 63 5.60 1081.34 3
33 4.95 1024.06 1 12 5.81 1009.85 3 57 5.90 1016.45 3
32 5.20 967.05 1 13 6.19 934.40 3 58 6.25 947.25 3
l 5.50 903.57 1 36 6.38 899.23 3 69 6.55 893.41 3
2 5.81 843.72 1 14 6.56 868.11 3 60 6.90 836.52 3
3 6.19 777.33 1 15 7.01 797.34 3 62 7.30 778.42 3
4 6.49 729.93 1 16 7.61 716.54 3 66 7.75 721.09 3
5 6.75 692.37 1 37 8.00 671.65 3 61 8.25 666.42 3
6 7.13 643.27 1 17 8.33 637.57 3 68 8.70 624.24 3
7 7.69 580.94 1 18 9.19 562.60 3 65 9.30 576.10 3
8 8.06 545.35 1 38 9.95 507.88 3 67 10.00 528.96 3
9 9.00 472.90 1 64 10.75 484.86 3

A - test number

B - distance between heat source and ground beef surface, inches

C - surface heat flux, Btu per sq ft—hr

D - number of source units used at the indicated distance

to provide the indicated heat flux.

 

 

 

Calrod Calrod

1864.5 R; A = 2.797 1648.7 R; A = 3.164
A B C D A B C
55 7.15 1029.76 3 39 4.00 1281.52
56 7.55 955.46 3 52 4.25 1203.40
29 3.20 916.62 1 47 4.45 1144.89
54 7.80 913.90 3 46 4.75 1063.17
28 3.43 862.77 45 5.05 988.37
53 8.15 860.29 42 5.30 931.20
27 3.65 813.66 44 5.65 857.93
26 3.90 761.61 40 6.00 792.69
25 4.15 712.07 41 6.45 718.77
19 4.50 650.08 43 6.90 655.43
20 4.80 601.10 49 7.40 595.28
21 5.06 561.91 51 7.90 544.16
22 5.44 510.22 50 8.55 487.96
23 5.61 489.10 48 9.25 436.25
24 6.18 426.28
31 6.60 387.42
30 7.10 348.24

 

5.0 RESULTS, CALCULATIONS AND DISCUSSION

5.1 Calculation of the specific and latent heats of
ground beef

The average composition of beef, including the
following cuts: chuck, flank, loin, rib, round and rump,
is given below:

Protein 18.05%

Water 61.00
Fats 20.17

Ash 00.78

Total 100.00%

The specific heats of protein, water and ash are
0.44, 1.00 and 0.12 Btu per lb F, respectively (3). The
specific heats of the above three constituents vary slightly
with temperature in the normal processing ranges.

Since triglycerides predominate in meat fats,
although small amounts of mono- and diglycerides may be
present, they are chemically quite homogeneous (3). The
specific and latent heat properties of triglycerides have
been analyzed in normal processing ranges. The triglycerides
are known to exist in two forms, the d- and B—forms. The
a-form is generally considered the unstable form and the
B-form is recognized as a stable form of the fat. As the

a-form changes states in processing, d-solid to a—liquid,

5-2

heat is absorbed and as the unstable G-form is changed to
the stable fi-form heat is released. Then the stable B—form
changes from the solid to liquid state, again requiring
heat. The Specific and latent heats for the a— and B—forms
and state changes were given in the review of literature.

As the specific heat of fat varies over a temper-
ature range, its effects on the combined specific heat of
meat should be considered. The average specific heat of
meat, which consists of four definite substances of known
specific heats is given by Daniels and Alberty (18). The
equation follows the general form:

A B C CD

C = W x CA + W X CB + W'X CC +‘W— x CD + . . . .

Where C is the average specific heat of the substance.
A, B, C, D, . . . are the weights of the

various substances in the mixture.

C C C C are the individual

A' B' c' 0""
specific heats of substances A, B, C, D,
. . ., respectively.

W is the total weight of the mixture.

W = A + B + C + D + . . .

Now, for meat:

C Percent Protein x C + Percent Water

(Protein)

+ Percent Fat x C

X

C(Water) (Fat)

+ Percent Ash x C(Ash)

Table 5.1 shows the calculated specific heats of

meat in specific temperature ranges and the latent heats of

5-3

fusion at the transition temperatures.

Table 5.1. Calculated specific heats of ground beef of
average composition in various temperature
ranges and the latent heats of fusion at the
transition temperatures.

 

 

 

Tinggatgre Sgiiifég Latent heat of fusion‘
32 -- 121.8 0.75 (c-form)
121.8 13.75 (a-solid to liquid)
121.8 -- 139.1 0.80 (a—form)
139.1 -4.86 (a- to B-form)

139.1 —- 156.4 0.74 (B-form)
156.4 19.37 (B-solid to liquid)

156.4 and over 0.80 (B-form)

 

5.2 Calculation of geometrical angle factors

The general geometrical angle factor equation for
determining the portion of the radiation emitted by a

differential area dAl to a finite area A2 is:

cos¢l cos¢>2 dA2

F =
(dl)2 nrz
A2

 

Where r is the distance between the areas dAl and dA2

costlll is the angle measured from the normal

to dAl to r

cos¢>2 is the angle measured from the normal

to dA2 to r

5-4

dA2 is a differential area on the surface of

A to which r is measured

2!
A2 is the total surface area receiving energy

from dAl

If A2 is parallel to dAl, cos<1>l = cos<l>2 = c050,
and if a, b and c are defined as in Fig. 5.1, and B = b/a

and C = c/a, then:

 

 

 

F = 1_. B sin—1 c + c sin—l
(d1)2 2n (1+BZ)l/2 (1+B2+C2)l/2 (1+C2)l/2
B ]
(1+£32+02)1/2
Hence, the angle factor from the total surface Al
to A2 is F12 which is defined as:
F =-$— F dA
12 A (d ) l
l l 2
A1

Jakob (33) further states that if A is an arbitrary

1

profile whose generatix is parallel in A dAl may be rep-

2!
resented by its projected surface. A similar procedure was
first called the ”unit sphere method" by Herman and again

suggested by Nusselt. If A is a horizontal cylinder its

1
projected area would then be LD, this then becomes the
radiating surface area Al' If it is then broken into
elemental areas, each elemental area is dAl. Also, if

AL is the length of each area, the projected elemental

area (dAl) is ALD. This procedure was used to calculate

geometrical angle factors.

The heat source was divided into elemental lengths,
one half of the source was studied, as the other half is
symmetrical. The angle factors to one half of the parallel
surface were determined from each of the elemental areas.
See Fig. 5.2. The sample size was 3 inches (2c) x 6 inches
(b) and the distances from the source to the sample were
3, 6, 9 and 12 inches (a).

From Fig. 5.2 it can be seen that areas dAl, dAZI
dA3 and dA4 will emit energy to the surface. The distance
for c will be constant (l-l/2") but b will vary dependent
upon the elemental area, b could be 2, 4, 6, 8 or 10 inches,

designated as areas 2, 4, 6, 8 and 10, respectively. Hence

the following angle factors for the various c distances are

calculated:
dAl to c/2 surface : F(dl)2 + F(dl)4
dA2 to c/2 surface 3 F(d2)
6
dA3 to C/2 surface‘ ‘ F(d3)8 _ F(‘31)2
dA4 to c/2 surface = F(d4)10 ‘ F(dl)4

Hence the angle factor from one half of the source

to a c/2 surface becomes:

1
- A F = (F + F + F ) dA
2 1 12 (dl)6 (d1)8 (dl)10 1

Where dAl = dA2 = 6A3 = dA4

Now, since only one half of the source was used and

Pig.

Pig.

5.

5.

l

3

Q;

 

l 8: I’/0
' C= c/a
:a
I
I
l a

At c

 

Relationship of a, b. and c for determining the
geometrical angle factor between a differential
surface and a finite rectangular surface parallel
to it.

Heat Element

«In, M, a?! 4?,

 

(a distances)

Fig. 5.2 Relationships of a, b, and c for determining
the geometrical angle factors from a heat source
to a finite surface.

Heat Elements

 

 

 

 

 

l"
I I I
II t ' l "
| l
l l l 0
I t I
| l l
' I
I
L 4 Sample Surtace
Ty; 2";

lc distances)

Relationships of c and a for determining the
geometrical angle factors from a group of three
heat sources to a finite surface (b relationships
are the same as in Pig. 5.2).

5-7

the other half is symmetrical and c/2 was used for the

surface and the other half of the surface is symmetrical, the

total angle factor becomes:

A F = 4(F F )dA

+ + F
l 12 (dl)6 (dl)8 (d1)1o l
and, if: A1 = LWD
dAl (projected surface area) = ALD
AL4
then: F =—(F +F +F ),

and for the quartz lamp, L =

16 inches and with 8

elemental lengths AL = 2 inches, so F12 =
%F(F(d) +F(d) +F(a) )°
1 6 l 8 l 10

Similar calculations were made for the quartz tube

and the calrod unit.
culations for 3, 6,

The geometrical angle

a surface of 18 square inches.

radiant heat exchange between
will be in Btu per sq ft-hr.
flux could then be calculated

the 18 square inch surface as

uses an equivalent angle factor,

multiplied by the angle factor from A

inch surface.

(a) distances are shown in Table 5.3.

angle factors are used in the

Table 5.

2 is a summary of these cal-

9 and 12 inches (a) distances.

factors in Table 5.2 are for
Using these factors the
the source and the surface
The equivalent surface heat
in Btu per sq ft-hr, using
a basis. This calculation

which is the ratio 144/18

1 to the 18 square

These equivalent angle factors for the various

If these equivalent

following equation,* the

 

u_ 1
—€ € OFlZ

*
qs 1 2

4..
A (Tl T

4)

l 2

Where qs" is the surface heat flux (Btu per sq ft—hr).

F

4
El, 62’ G, Al, T1 1 T2

defined.

12 is the equivalent geometrical angle factor.

have been previously

5-8

computation will result directly in surface heat fluxes.

Table 5.2. Geometrical angle factors between single unit
heat sources and a parallel centered 18 square

inch surface at different perpendicular distances.

 

 

Perpendicular distance Geometrical angle factor

 

 

Between surfaces Quartz Quartz
(inches) lamp tube Calrod
3 0.051439 0.051795 0.059496
0.025652 0.025733 0.027395
0.014988 0.015407 0.015521
12 0.009742 0.009912 0.009680
Table 5.3. Equivalent geometrical angle factors between

single heat sources and a parallel centered
surface with an equivalent surface area of

one square foot,

using an 18 square inch

surface as a basis at different perpendicular

distances.

 

 

Perpendicular distance

Between surfaces

Equivalent geometrical angle factor

Quartz

Quartz

 

(inches) lamp tube Calrod
0.411511 0.414360 0.475968
6 0.205219 0.205864 0.219160
9 0.119903 0.123256 0.124168
12 0.077937 0.079296 0.077440

 

The geometricalaangle factors were also calculated
for the case in which three similar heat sources were used.
For this case the sources were placed one inch on center
and were parallel to each other.

The sample surface was

placed parallel to the three heat sources and its center

5-9

was perpendicular to the center of the center heat source.
See Fig. 5.3. The angle factor from the center heat source
to the sample surface would be the same as above, with the
same (a) distances. The two remaining heat sources would
have (c) distances of 1/2 inch and 2-1/2 inches, with b's
similar to those above (2, 4, 6, 8, and 10 inches). The
procedure for determining angle factors was similar to that
above.

As each of the three sources are emitting equal amounts
of energy a combined angle factor may be used with the area
of a single heat source. The combined angle factor is the
sum of the angle factors between the three heat sources and

the sample surface, i.e., (F (source 1) + F12 (source 2) +

12
P12 (source 3)). The following equation expresses the

radiant heat exchange between the three heat sources and

the sample surface:

_ 4 4
q ‘ e1 62 0 F12 1 (T1 T2 )

Where Al is the area of one heat source.

Table 5.4 shows the combined angle factors from the

(combined) A

three heat sources to the 18 square inch surface area and
Table 5.5 shows the equivalent combined angle factors from
the three heat sources to a square foot surface area,

using the 18 square inch surface area as a basis.

5-10

Table 5.4. Combined geometrical angle factors between a
group of three similar heat sources and a
parallel centered 18 square inch surface at
different perpendicular distances.

 

 

Perpendicular distance

Between surfaces

Combined geometrical angle factors

3 Quartz

3 Quartz

 

(inches) lamps tubes 3 Calrods
0.144151 0.145554 0.167783
6 0.074638 0.075892 0.080557
0.044402 0.045648 0.046151
12 0.028849 0.031769 0.022384

 

Table 5.5. Combined equivalent geometrical angle factors
between a group of three similar heat sources
and a parallel centered 18 square inch surface

at different perpendicular distances.

 

 

Perpendicular distance

Between surfaces

Combined geometrical angle factors

3 Quartz

3 Quartz

 

(inches) lamps tubes 3 Calrods
1.153205 1.164432 1.342264

0.597107 0.607136 0.644456

9 0.355217 0.365184 0.369208

12 0.230789 0.254152 0.179072

 

5.3 Determination of the sample size for statistically
equal heat fluxes on the sample surface

Hottel (28) was the first to derive and publish

a computational equation for the geometrical angle factor

from a differential element to a parallel finite surface.

McAdams (42) represented the equation graphically, using

the same symbols as Hottel.

Jakob (33) presented a

5-11

similar graphical solution but changed the symbols and
increased the range of the graphical solution. Jakob's
equation with symbol changes checks with Hottel's original
equation and with McAdam's graphical solution, but Jakob's
graphical solution gives lower geometrical angle factors
than his equation and McAdams's graphical solution. This
discrepancy appears as an incorrect labelling of one of
the parameters (distance—width ratio). Following the
procedure given by Jakob and the graphical solution of
McAdams the maximum sample size was calculated.

The graphical solution to the geometrical angle
factor equation depends on the parameters B (b/a) and
C (c/a), where a is the distance between surfaces, b the
length of the surface and c the width of the surface,
measured from the center of the differential element.
See Fig. 5.1. The geometrical angle factor equation gives
the total angle factor to a finite surface, and as one
approaches the heat source on a horizontal plane, that is
reducing the C-parameter, the angle factor diminishes.
This results in a higher relative surface heat flux
(Btu per sq ft-hr) when the finite surface area is
used as the area basis, i.e., if from a radiant heat exchange
between two surfaces it was found that 100 Btu per hr is
transmitted to a 14.4 sq in surface, the corresponding
surface heat flux would be 1000 Btu per sq ft-hr, using the
14.4 sq in as a basis. However, not all differential surface

elements are receiving exactly the same amount of heat per

5—12

hour, the above 1000 Btu per sq ft-hr is only an average

for the entire surface. This averaging technique was used
to determine geometrical angle factors for increment surface
increases on a hypothetical sample surface.

The heat source, a single element parallel to the
sample surface, was divided into eight equal element sizes.
each two inches in length (corresponding to the 16 inch
quartz lamp filament length). A hypothetical parallel
surface was placed four inches from the heat source unit,
parallel to it and the center of the hypothetical surface
was placed perpendicular to the center of the heat source.
An arbitrary sample width of five inches and length of ten
inches was selected. The geometrical angle factors to
fifteen surface elements on one quarter of the surface were
determined, from the eight heat source elements. See Fig.
5.4.

Jakob (33) states the total geometrical angle factor
to a finite area from a series of differential areas is
the sum of the individual geometrical angle factors. There—

fore, the angle factor to surface element 1 is:

H
F = >3 (Fn)dA
n=A
Where PA = P7 - F6 ; b = 7 and 6 inches
FB = F5 - F4 7 b = 5 and 4 inches
PC = F3 — F2 : b = 3 and 2 inches
FD = Fl : b = 1 inch
F = F - F : b = 2 inches and 1 inch

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Al.
8 l
5 I0 I5
4 9 l4 2
C 'a’
3 8 )3 'ln ‘2
7 l2 ‘ s“ 6
D 2 g") f
I 6 u L?» ,
1,2. I'"
Z ' I:
E Z'lz"
(c distances)
Fl)
A,B, ...... H are heat source elements;
l,2, ..... )5 are surface elements
61)
Hx
Fig. 5.4 Relationships of c and b distances for determining
the sample surface area.
5 l0 )5
J 0.056 J 0.05I J 0.048
4 9 I4
/ 0.058 J 0.053 0.048
3 8 )3
J 0.060 J 0054 / 0.050
2 7 I2
j 0.060 J 0.055 0.050
V y

 

 

 

 

I:
0.060 0.055 J 0.052
A B C

 

Fig. 5.5 (F/dA) values for surface elements from
Fig. 5.4.

5-14

FF = F4 - F3 , b = 4 and 3 inches
FG = P6 - F5 ; b = 6 and 5 inches
FH = F8 - F7 : b = 8 and 7 inches

Hence F = F8(dA) ; b = 8 inches, and c = 1/2 inch,
a = 4 inches.
The geometrical angle factors to elements 6 and 11
would be similar, except that c would be 1—1/2 and 2*1/2
inches, respectively. This procedure was followed for all

fifteen surface elements, i.e., the geometrical angle factors

for surface elements 2, 7, 12 were ; F (F9 + F - F8)dA:

7
for surface elements 3, 8, 13 were ; F = (F10 + F8 + F6
- F9 - F7)dA: for surface elements 4, 9. 14 were.

F = + F + F + F -

(F11 9 7 5 F10
elements 5, 10, 15 were, F = (F

- F - F6)dA: and for surface

8

12 + Flo + F8 + F6 + F4 -

Fll - F9 - F7 - F5)dA. These individual geometrical angle

factor values were then taken from McAdam's graphical solution:

they appear in Table 5.6.

Table 5.6. Geometrical angle factors for various sample
widths (c) and lengths (b) at a distance of
4 inches. The values in the table are
F/dA(sq ft-l).

 

 

 

Length (b, inches) Width (c, inches)

0.5 1.5 2.5

4 0.025 0.070 0.110

5 .027 .075 .115

6 .028 .079 .120

7 .029 .082 .125

8 .030 .083 .130

9 .031 .084 .130

10 .032 .085 .130

11 .032 .086 .130

12 .032 .087 .130

 

5-15

The geometrical angle factors in Table 5.6 were
then adjusted to a unit surface element area of one square
inch for each of the elements, according to the averaging
technique. For an elemental width of one half inch, the
element has a corresponding surface area of one half square
inch, hence dividing by one half square inch would give
an angle factor or corresponding heat flux on a unit surface
basis (Btu per sq in). This technique was used for c equal
to 1.5 inches and 2.5 inches. Fig. 5.5 shows the results of
this averaging technique with the F/dA factors indicated
for each of the surface elements based on a unit surface
element area of one square inch. Statistical differences
of these results were tested by an analysis of variance
technique. The elements corresponding to the c's of 1/2
inch, l-l/2 and 2-1/2 inches are placed in columns A, B and
C, respectively, while elements corresponding to b's of
1 inch, 2, 3, 4, and 5 inches are placed in rows 1, 2, 3, 4
and 5, respectively, as in Fig. 5.3. Table 5.7 shows the
analysis of variance of the columns and rows of the sample
surface.

The F—ratios for both columns and rows in Table
5.7 are insignificant at the 95% confidence level. It can
then be concluded that the sample surface has an equal
flux distribution over its entire surface when unit surfaces
of one square inch each are compared in elemental rows and
columns. Therefore, a 5 inch width by 10 inch length or

lesser dimensioned sample may be used with a statistically

5-16

uniform surface heat flux. A three inch width and six inch

length sample was for all tests.

Table 5.7. Analysis of variance of F/dA of the various
rows and columns of one quarter of a 5 in by
10 in surface reduced to elemental finite
areas (see Fig. 5.4).

 

 

Source of variance Sum of squares dF Mean square F-ratio

 

 

Rows 0.032 4 0.008 0.064*
Columns 0.2128 2 0.1064 0.849**
Residual 1.0032 8 0.1254
Total 1.2480 14
* =
F,95(4,8) 3.84

*‘k =
F.95(2,8) 4.46

5.4 Electrical energy characteristics of the heat sources

Tables 5.8 and 5.9 show the comparison between the
manufacturers data and volt—ampere measurements of quartz
lamps and calrod heat sources. Input watts are calculated,
based on an average of three ampere readings at each of the
voltages.

The rated watt input of the quartz tube was
550 watts and the calculated heat input, based on 120
volts and three ampere measurements, was also 550 watts.

The differences indicated in Tables 5.8 and 5.9 are
probably the result of comparing a single unit to an average

number of similar units produced by the manufacturer.

5-17

Table 5.8. Comparison of manufacturers data and calculated
watt inputs. based on volts and ampere averages.
for the 1600 watt quartz lamp.

 

 

 

Volts Watts (manufacturer) Watts (calculated)
220 1425 1474.0
200 1200 1270.0
180 1040 1076.4
160 865 904.0/2
140 688 732.2/
120 560 573.6
100 416 433.0
80 288 305.6

 

Table 5.9. Comparison of manufacturers data and calculated
watt inputs, based on volt and ampere averages.
for the 1000 watt calrod unit.

 

 

 

Volts Watts (manufacturer) Watts (calculated)
220 830 847.0
200 680 693.4
180 560 554.9
160 460 434.7
140 340 333.6
120 245 246.0
100 173 175.0

 

5.5 Calculation of the radiant heat outputs of three heat
sources

5.5.1 Quartz lamp source

The calculation of the radiant heat output of the
quartz lamp at different voltages is based on the following
basic assumptions: (a) the electrical energy input to the
lamp is converted to heat: (b) heat is lost by convection

and radiation to a 80 F room with surfaces at the same

5-18

temperature as the room; (c) the room surfaces have an
emissivity of unity: (d) the lamp is a gray body with
emissivity equal to absorptivity. Other assumptions will

be indicated below.

5.5.1.1 The radiation from the tungsten lamp

filament is:

_ 4 4

Where e = 0.023 + 7.6 x 10’5

1 (t1), emissivity of the

filament. Marks Handbook (40) states
that the emissivity of tungsten is 0.032
and 0.35 at 80 F and 6000 F, respectively,
and that linear interpolation is possible
between these temperatures; with t1 the
filament temperature in F.
A is the filament surface area, the length

and diameter of the filament were 16 and

0.065 inches, respectively. If the filament

is assumed to be a rod, its surface area

is 0.0227 ft2.

0 = 0.174 x 10'8
T is the filament temperature, R
T is the room temperature. 540 R

The filament temperatures were taken from the tungsten

color temperature data supplied by the manufacturer.

5.5.1.2 The heat radiated to the room from the

filament is: q = quT, where T is the transmittance of

5-19

quartz subject to various source temperatures. The
Fostoria Pressed Steel Corporation (12) states the following

relationships between T and source temperature (t):

 

 

T t, F
0.495 1200
0.530 1300
0.633 1800
0.715 2240
0.780 2680
0.820 3140
0.845 3580
0.860 4030

Linear interpolation is permissible between the
temperature increments given above. Marks Handbook (40)
and Jakob (32) state that e of fused quartz at room temper-
ature is 200 F. Assuming that linear interpolation is
permissible between 200 and 1200 F, the following relation-
ship will be true for this range:

2

e = 0.935 - 4.3 x 10‘ (t-200)

5.5.1.3 The radiation from the quartz shell is:

4 4
qr2 = 62 A2 0 (T2 ' TR )
Where t2 is taken from above
A2 is the shell surface area, and assuming the

18 inch length of the shell is at a constant
temperature. The shell diameter is 0.375

inches. therefore A is equal to 0.147 sq ft

8

2
0 = 0.174 x 10"

T2 is the shell temperature, R

TR is the room temperature, 540 R

5—20

5.5.1.4 The convection from the quartz shell to the

room is:
qc2 = hA2 (t2 - tR)
Where h = Q4%%4 (t2 - tR)l/4 as stated by Jakob (32) and
D2
and Giedt (24), for N - N = 104 to 108

GR PR

at the average surface film temperature, the

maXimum and minimum NGR-NP
4

10 and 2.59 x 104. based on the manufacturers

R products were 2.69 x

ratings at different filament voltages.

A = 0.147 sq ft

2
t2 = shell surface temperature, F
tR = room temperature, 80 F

or by substituting the computational equation of h into qC

0.24XA2

- _ _______ _ 5/4

qc2 ‘ 1/4 (t2 tR)

5.5.1.5. The heat balance of the quartz shell is:
the heat absorbed by the quartz shell is equal
to the heat input to the filament. as calcu-
lated from the measured wattage input, minus
the heat radiated from the filament to the
room, or heat transmitted by the quartz shell.
or

q(absorbed by the quartz shell) = qr2 + qC2

0.24xA2

1/4
D2

_ 4 4
— €2A20(T2 - TR )

+ (t2 - tR)5/4

The quartz surface temperature was computed by using
an iteration technique, forcing qr2 and qC2 to equal the
heat absorbed by the quartz shell, a.i 2% limit was used
in the iteration process. Therefore, the heat absorbed by
the quartz shell was equal qr2 plus qC2 plus A, where A
was within 2% of the heat absorbed by the quartz shell.

Table 5.10 shows the results of the computations
and the last column of the table is the computed percent

radiation at different voltages based on the radiation at

240 volts.

Table 5.10. Calculated heat balances of the quartz heat

lamp at different voltages.

 

 

 

Volts q input qu qr2 qC2 A qu+qr2 Percent qr
240 5461 4620 497 348 4 5117 '100.0
220 5032 3929 676 431 4 4605 90.1
200 4336 3334 610 398 6 3944 77.2
180 3675 2659 610 398 8 3269 63.9
160 3086 2080 610 398 2 2690 52.6
140 2500 1626 517 357 0 2143 41.9
120 1958 1156 470 335 3 1626 31.8
100 1478 801 378 291 8 1179 23.1

80 1043 494 301 252 4 795 15.5

 

Table 5.11 shows the comparison between the calcu—
lated radiation based on wattage measurements and the radiation
percentages at different voltages based on 240 volts as
supplied by the manufacturer.

In all cases the calculated radiations were higher
than the radiation percentages supplied by the manufacturer.

However, the manufacturers data is an average for many

5-22

Table 5.11. Comparison of calculated percent radiations
from a 240 volt quartz lamp rated at 1600
watts at different voltages to the manu-
facturers data.

 

 

 

Volts Percent Percent Percent
qr (manufacturer) qr calculated difference*

240 100.0 100.0 0

220 87.0 90.1 3.57
200 73.0 77.2 5.75
180 61.0 63.9 4.54
160 50.0 52.6 5.20
140 40.0 41.9 4.76
120 30.5 31.8 4.26
100 21.5 23.1 4.27
80 14.0 15.5 10.70

 

*Percent difference =

(Percent 9; calculated - Percent gxmanufacturer) 100%

Percent qr manufacturer

quartz lamps, while the calculated radiation is dependent

on the measured wattage inputs to the filament. The calculated
radiation also assumes an 80 F environment temperature,

whereas the environment temperature used by the manufacturer

is unknown. Due to windings of the filament an electrical
inductance probably occurs so that the 100% electrical
conversion to heat is not an exact assumption. The

calculated radiation is used as a basis to determine surface

heat fluxes.

5.5.2 Calrod heat source

The calculation of the radiant heat output of the

calrod at different voltages is based on the following

5—23

basic assumptions: (a) all of the electrical energy input

to the unit is converted to heat: (b) heat is lost by
radiation and convection to an 80 F room with surfaces at

the same temperature; (c) the room surfaces have an emissivity
of unity; (d) the unit is a gray body. Other assumptions

will be indicated below.

5.5.2.1 The radiation from the unit is:

_ 4 4
qu ' 61 A1 0 (T1 ' TR )

Where 61 = 0.79, Marks Handbook (40) and DeWerth (19)

Al is the radiating surface area of the calrod

at T the diameter of the calrod unit

1'
was measured and found to be 0.43 inches.
the length of the surface at T1 was
determined as 13 inches, as this was the
length that appeared as a cherry red color
when the unit was operated at 220 volts,
so A = 0.122 sq ft

1
_ -8
0 - 0.174 X 10

TR is the room temperature, 540 R

T1 is the surface temperature as supplied by

the manufacturer, R

5.5.2.2 The convection heat loss from the unit is:
gel = hAl (t1 ' tR)

4 8

0.24 1/4 to 10

Where h = BI7Z (tl - tr) , for N N = 10

GR. PR

5-24

at an average surface film temperature, the

maximum and minimum N N R products were

GR. P

6.17 x 104 and 3.64 x 104 at 100 and 240
volts, respectively, based on the manu-
facturers unit surface temperatures at these
voltages.

A = 0.122 sq ft, based on a diameter of 0.43
inches and a length of 13 inches

tl is the unit surface temperature, F

tR is the room temperature, F

5.5.2.3 The end heat losses of the calrod unit

Heat may be lost by convection and radiation by the
ends of the unit.

For the convection heat loss, Jakob (32) states the
following equation may be used for a not very long rod

protruding from a heat source:

1/2 1 —pe-m2L
-m2L

 

t )

qc = (khAC) (tl — R

l + pe

Where k is the thermoconductivity of the rod, k=26
h is the convective film coefficient, for this
case it is assumed to be equal to the h
computed above for the convective heat loss
to the environment.
A is the cross—section area of the conducting
rod, it is further assumed that only the

steel shell portion of the rod will conduct

5-25

heat, the inner diameter is 0.375 inches
and the outer diameter is 0.43 inches for
the steel shell.

C is the outer surface area of the rod, the
diameter is 0.43 inches and the length is

2.25 inches.

_ £E_:_h .
p — km + h . k and h are defined above

hC 1/2
m = _A . h. C. k and A are defined above

L = length of the rod, 2.25 inches
t1 = source temperature, temperature of the 13
inch length of calrod as supplied by the
manufacturer
tR = room temperature, 80 F
The total convection heat loss is 2qC as there are

two ends. To determine the radiation end losses, the average

rod temperature was used:
t =t qc
average R hAc

 

Where tR is the room temperature, 80 F
qC is computed from above, convection heat loss
h is computed from above

C is the surface area of the rod

_ 4 4
then, qr — 61 C 0 (Taverage - TR ), where 61, C, O,

T and T are defined above and q
average R r2

the radiative heat loss of one of the ends,

so the total radiative heat loss for

U1

-26

both ends is
qr2 = qu-
Table 5.12 shows the results of the above computation.
The A column indicates the difference between qtotal heat
losses and the measured wattage inputs. The last column is
the percent heat input based on the 240 volt, wattage input,

which may be compared to the manufacturer's watt input of

the calrod and the measured wattage input in Table 5.9.

 

 

 

Table 5.12 Calculated heat balances of the calrod unit at
different voltages.

q total Percent
Volts qu qcl qr2 qC2 calculated q input A q input
240 2480 585 228 124 3417 3413 4 100.0
220 2030 538 194 115 2877 2891 14 84.3
200 1550 477 160 103 2290 2367 77 67.0
180 1230 428 132 93 1883 1894 11 55.2
160 888 362 100 80 1430 1484 54 41.9
140 622 309 80 69 1080 1139 59 31.7
120 432 258 58 58 805 840 34 23.7
100 271 199 42 46 558 597 41 16.4

 

Table 5.13 shows the comparisons between the calcu-

lated radiation and the radiation percentages at different

voltages based on 240 volts as supplied by the manufacturer.

The last column of the table shows the percent difference

based on manufacturers data.

In all cases the calculated radiations were higher

than the radiation percentages supplied by the manufacturer.

The calculated radiations assume an 80 F environment temper-

ature, whereas the environment temperature used by the

5-27

manufacturer is unknown. Also the assumptions made by the
manufacturer regarding the emissivity of the surface are
unknown. Lastly, these calculated radiations will
correspond to the measured heat fluxes with a higher cor-
relation than those supplied by the manufacturer. See
Table 5.16. These calculated radiations are used as a
basis to determine surface heat fluxes.

Table 5.13. Comparisons of calculated percent radiation

from 1000 watt, 240 volt calrod unit at dif-
ferent vcltages to the manufacturers data.

 

 

 

Percent q radiation Percent q radiation Percent

Volts (manufacturer) (calculated) difference*
240 100.0 100.0 0

220 78.0 82.1 5.26

200 59.0 63.2 7.12

180 45.0 50.3 11.20

160 31.0 36.5 17.72

140 20.5 26.0 26.85

120 13.0 18.1 39.10

100 7.3 11.6 59.0

 

*Percent

5

difference

ercent qr (calculated)

— Percent a: (manufacturer

 

Percent

(manufacturer)

))100%

Quartz tube heat source

The calculated heat balance at 120 volts for the
quartz tube is dependent upon the following basic assumptions:
(a) all the electrical energy input to the unit is converted
to heat: (b) heat is lost by convection and radiation to an
80 F room with surfaces at the same temperature: (c) the

room surfaces have anemissivity of unity: (d) the unit is

5-28

a gray body. Other assumptions will be indicated below.

5.5.3.1
qr

Where 6
1

0

5.5.3.2

Shell is:

The radiation from the filament is:

4 4
FlAlou‘l -TR)

= 0.753, the emissivity of the chromnickel

filament, DeWerth (19) and Marks Handbook
(40) state the emissivity is 0.76 and

0.64 at 1894 F and 125 F, respectively,

and that linear interpolation is permis—
sable between these temperatures. At

120 volts and 550 watts the filament has

a 1800 F rating, as stated by the manu-
facturer (12).

0.05081 sq ft, the diameter of the filament
is 0.137 inches and its length is 17
inches, it is assumed that the coiled

type filament is a rod of the same diameter
and length.

0.174 x 10‘8
2260 R, the filament temperature, the

filament is rated at 1800 F

540 R, the room temperature, 80 F

The heat transmitted by the fused quartz

qu = Tqr

Where T

0.633, the transmittance of fused quartz,

subject to a radiation at 1800 F, Foetoria

Pressed Steel Corporation (12).

5.5.3.3

qr2

Where 62

5.5.3.4
shell is:

qC2

Where h =

A2

t2

5.5.3.5
The

to the heat input

5-29

The radiation from the quartz shell is:

_ , 4 4
‘ ‘2 A2 R )

0.935 - 0.043 X 10

0 (T1 - T

'2 (t-200),

relationship
derived from above (quartz lamp)

0.1477 sq ft, where the shell diameter is
0.375 inches and the shell length is 18

inches, it is assumed the entire shell

is at a constant temperature.

0.174 x 10’8

is the shell temperature, R

540 R, room temperature

The convection heat loss from the quartz

 

= hA2 (t2 - tR)
0.24 1/4 _ 4
01/4 (t2 tR) , for NGR-NPR — 10

to 108 at the average surface film

N

the N P

temperature, R product was

GR

3.44 x 104, based on the manufacturers

rating at 120 volts, the diameter of

and t are

shell is 0.375 inches. 2 R

t

given above

0.1477 sq ft, given above

and t

R are given above

The heat balance on the quartz shell is:
heat absorbed by the quartz shell is equal

to the filament, as calculated from the

5-30

measured watt input, minus the heat radiated from the filament
to the room, or heat transmitted by the fused quartz shell.

q (absorbed by the quartz shell) = qr2 + qc2

4) 0.24A2
2 R + D 1/4 “:2 " tR)
2

5/4

The quartz surface temperature was computed by using

an iteration technique, forcing qr2 and q to equal q

c2
absorbed by the quartz shell, a .1 1% limit was used.
Therefore, the heat absorbed by the quartz shell was qr2
plus 4, where A was within : 1% of the heat absorbed by
the quartz shell. The results were: qf (filament) =
1096 Btu per hr; qr2 (shell) = 448 Btu per hr: qc2 = 327
Btu per hr; 4 = 6 Btu per hr.

These calculations, or q (radiation) = 1544 Btu per

hr, were used as a basis to determine heat fluxes at various

distances.

5.6 Heat flux measurements

5.6.1 Quartz lamp comparisons between measured and

calculated heat fluxes are shown in Tables 5.14 and 5.15
for different distances and voltages. The percent differences
are also shown. Table 5.14 is for one lamp and Table 5.15
is for three lamps.

The results in Tables 5.14 and 5.15 indicate the
influence of distance or geometrical angle factor on the
measured heat fluxes. As the pyrheliometer is moved further

from the heat source the measured heat fluxes approach the

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5-33

calculated heat fluxes. The Eppley pyroheliometer is primarily
used for measuring solar radiation fluxes, which do not
approach the higher heat fluxes above. In addition the

crystal on the pyroheliometer does not transmit beyond a

12 micron wave length, so with low lamp surface temperatures
only a fraction of this energy is received by the thermopile.
The angle factor influence is also indicated in the above
tables. As the pyroheliometer is moved a greater distance

from the heating source the angle factor is decreased,
approaching the angle factor used in solar radiation measure-

ments.

5.6.2 Calrod comparisons between measured and calculated
heat fluxes are shown in Table 5.16 for different distances

and voltages. The percent differences are also shown.

5.6.3 Quartz tube comparisons between measured and
calculated heat fluxes are shown in Table 5.17 for different
distances at a constant voltage of 120 volts. The percent
differences are also shown.

The interpretation of these and the calrod results

is similar to that given for the quartz lamp.

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5-35

Table 5.17. Comparison of calculated radiant heat fluxes
to measured radiant heat fluxes for different
distances for a 120 volt, 550 watt quartz tube.

 

 

 

Distance
6 inches 9 inches 12 inches
q measured 296.89 173.90 112.01
q calculated 317.85 190.31 122.43
Percent difference* -3.69 -9.45 -9.31

 

qgmeas.- thal.) 100%

*Percent difference = ( q cal

5.7 Fitting of third degree polynominals to heat flux
calculations for various distances between the sample
surface and heat source units

Third degree orthogonal polynominals were fitted to
the calculated surface heat fluxes. Five heat source temper—
atures were selected, namely, 4230.0, 3465.0, 2260.0,

1864.5 and 1648.7 R, to determine the effect of source
temperature on the rate of processing. By using the
previous calculated radiant heat outputs of the three heat
sources at their respective voltages to give the above
temperatures and by using the appropriate equivalent geo-
metrical angle factors at various distances, it is possible
to calculate surface heat fluxes at given distances.

The following equation could be used:

u _ l
‘ qr X F12

qs
Where qs" is the surface heat flux, Btu per sq ft-hr
qr is the total radiant heat output of the

source, Btu per hr

5-36

F12l is the equivalent angle factor for a particular
distance, sq ft-1

This technique is shown because it gives an accurate
heat flux from a source to a surface when angle factors have
been calculated for several distances and it is desired to
determine heat fluxes at increment intermediate distances,
without going through the complete geometry of the system
each time the distance between source and sample is changed.
Also, if a definite heat flux is desired, the polynominal
could be solved for the appropriate distance between surfaces,
if the rest of the geometry of the system remains the same.

A third degree polynominal was fitted to the cal-
culated heat fluxes for 3, 6, 9 and 12 inches. This polynominal
is to be used only for distances between 3 and 12 inches
from the heat source and only for a 3 inch by 6 inch sample
surface. If the range, 3 inches to 12 inches, is to be
increased, it is recommended that several more geometrical
shape factors be calculated to cover all distances in the
new range and a new polynominal be fitted. The degree of
the polynominal is only limited by the desired correlation
and the number of increment angle factors used.* The
orthogonal polynominal fitting technique is given by
Snedecor (56).

The general form of the third degree polynominal is:

qs" = A + Bd + Cd2 + Dd3

 

*The maximum polynominal degree is (n-l) where n
is number of orthogonal angle factors.

5-37

Where qs" is the surface heat flux, Btu per sq ft-hr
A, B, C and D are the polynomial constants
d is the perpendicular distance, inches.
The results of the orthogonal polynominal fitting
are given in Table 5.18. The table also includes, the
correlation coefficient and the maximum deviation of qs"
from actual calculations. It was interesting to note that
the maximum deviations always occurred at the greatest
distance from the heat source.
These orthgonal polynominals could then be used
to calculate surface heat fluxes at any distance between 3

and 12 inches.

5.8 Effect of surrounding walls and reradiation

The data showing the effect of reradiation from
surrounding enclosure walls and the data without these
walls are in Table 5.19.

The maximum enclosure surface temperature at the
end of the processing was 128 F and the minimum temperature
was 120 F. The maximum internal air temperature of the
enclosure was 97 F while the minimum was 90 F. The actual
effects of the enclosure can be shown by the following

analysis of variance tables.

5-38

 

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5-40

Analysis of variance of percent yields for
enclosed volume vs. non—enclosed volume
samples at 946 Btu per sq ft-hr and A =

 

 

 

 

 

lelg4 )J‘e
Source of Sum of Mean
variance squares df square F ratio*
Means 35.09 1 35.09 26.19
Within 5.34 4 1.34
Total 40.42 5
*F.95 (1,4) = 7.71

Table 5.21.

Analysis of variance of percent yields for
enclosed volume vs. non-enclosed volume

 

 

 

 

samples at 946 Btu per sq ft-hr and A = 1.194 u.
Source of Sum of Mean
variance squares df square F ratio*
Means 34.99 1 34.99 9.41
Within 14.88 4 3.72
Total 49.87 5

 

*F.95 (1,4)

Table 5.22.

= 7.71

Analysis of variance of percent volatile losses
for enclosed volume vs. non-enclosed volume

 

 

 

samples at 946 Btu per sq ft—hr and A = 1.194 u.
Source of Sum of Mean
variance squares df square F ratio*
Means 0.80 l 0.80 1.21
Within 2.62 4 0.66
Total 3.42 5

 

*F.95 (1,4)

= 7.71

5-41

Table 5.23. Analysis of variance of relative processing
time (60 to 170 F) for enclosed volume vs.
non-enclosed volume samples at 946 Btu per
sq ft-hr and A = 1.194 0.

 

 

 

 

1 zlji
Source of " Sum of Mean
variance squares df square F ratio*
Mean 0.61 1 0.61 0.48
Within 5.13 4 1.28
Total 5.74 5

 

*F.95 (1,4) = 7.71

From the above tables it is apparent that: (a) there
is a difference in percent yield, with the enclosed volumed
samples having a significantly higher yield; (b) there is a
difference in percent drippings, with the non-enclosed
volume samples having a significantly higher dripping
weight; (c) the enclosure has no significant effect on
volume loss; (d) the enclosure has no significant effect
on relative processing time.

The effect of the enclosure on heat transfer and
processing time is not significant at a heat flux of 946
Btu per sq ft-hr at a A of 1.194 u. The apparent factor in
this test was the volatile loss which contributes a
latent heat loss factor or an apparent h. The apparent h
was not significant while holding the other heat transfer

factors (A, qs, t ti’ area and final temperature)

RI
essentially constant. The relative processing time should

not have shown a change, unless the reradiation of the

5-42

surrounding walls would increase heat transfer. This was
not significant.

Due to the low wall surface temperature in the
enclosed volume, the volatile loss of the product increased
the water vapor pressure of the enclosed air and as the
transmission of water vapor above 5 u is insignificant.
any reradiated heat would be absorbed by the water vapor.
This would also be true for the non-enclosed volume. How-
ever, this would not be true for highly reflective surface
enclosures.

As a result, all subsequent tests were conducted
in non-enclosed volumes (except for the physical size of
the room) and all highly reflective surfaces which could
influence the radiative angle factor were shielded with a
high emissivity surface.

Higher yields have also been reported by Keating
(34) with a forced convection enclosure (oven) containing a
free liquid surface. The higher percentage yield is a result
of a lower dripping weight. It could then be hypothesized
that dripping weight is a function of at least four
factors: (a) the product: (b) produce moisture content:
(c) surface temperature or surface heat flux: (d) vapor
pressure of the environment. The latter two factors would
then be critical in this experiment. With an essentially
constant heat flux, the moisture diffusion would be at
some specified rate, also with a constant surface vapor

pressure the moisture diffusion would be at another rate.

5—43

With the enclosed volume the surface vapor pressure should
be higher than with the non-enclosed volume, which could
reduce moisture diffusion and result in a lower dripping
weight and hence higher product yield.

A second degree orthogonal polynominal was fitted
to the actual data (relative times for 60 to 170 F) for
each of the six tests* and the corresponding constants
were analyzed by the analysis of variance technique. The
polynominal constants and corresponding correlation co-
efficients are shown in Table 5.24.

Table 5.24. Polynominal constants for the fitting of time
vs. temperature at the one inch depth for
ground beef at 946 Btu per sq ft-hr and a
A of 1.194 u in an open room and i5 an
enclosed volume. (Y = A + BX + CX , Y

is the temperature in F at the one inch
sample depth and X is the time in minutes.)

 

Sample A B C Correlation coefficient(R)

 

Open room

1 56.76 2.6914 -0.0152 0.9990

2 58.19 2.3510 -0.0115 0.9995

3 56.07 2.5773 —0.0131 0.9944
Enclosed volume

4 57.00 2.4631 -0.0121 0.9935

5 57.53 2.3052 -0.0099 0.9993

6 57.61 2.3694 -0.0113 0.9996

 

*The fitting of a third degree polynominal was not
significant at the 99% level as measured by an F test ratio
on the remaining sum of squares.

Table 5.25.

5-44

Analysis of variance of (A) constants in the
fitted polynominal equation of temperature
vs. time at a one inch depth for ground

beef at 946 Btu per sq ft—hr and at a A of
1.194 u in an open room and in an enclosed
volume.

 

 

 

Source of Sum of Mean
variance squares df square F ratio*
Means 0.21 l 0.21 0.328
Within 2.56 4 0.64

Total 2.77 5

 

*F.95 (1,4) = 7.71

Table 5.26.

Analysis of variance of (B) constants in the
fitted polynominal equation of temperature
vs. time at a one inch depth for ground
beef at 946 Btu per sq ft—hr and at a A of
1.194 u in an open room and in an enclosed
volume.

 

 

 

Sources of Sum of Mean
7ariance squares df square F ratio*
Means 0.0387 1 0.0387 1.877
Within 0.0827 4 0.0206

Total 0.1114 5

 

*F.95 (1.4) = 7.71

Table 5.27.

Analysis of variance of (C) constants in the
fitted polynominal equation of temperature
vs. time at a one inch depth for ground beef
at 946 Btu per sq ft—hr and at a A of 1.194 u
in an open room and in an enclosed volume.

 

 

 

 

 

Source of Sum of Mean
variance squares df squares F ratio*
Means 704.31x10-8 1 704.31x10—8 3.01
Within 936.67x10-8 4 234.17x10-8
Total 1640.98x10—8 5
*F.95 (1,4) = 7.71

5-45

Tables 5.25, 5.26 and 5.27 show that there is not a
significant difference in the fitted polynominal constants
of the open room vs. enclosed volume environments. There-
fore, there is not a significant difference in temperatures
at the one inch depth vs. time relationship. This was also
indicated in Table 5.23 in terms of total processing time.
This indicates that there is no appreciable reradiation
from the walls of the enclosure and that the absorption of
energy by water vapor is insignificant.

5.9 Transient processing rates of ground beef with infra-
red heating.

Samples of ground beef (one inch depth, three inches
width, six inches length) were processed at different sur-
face heat fluxes generated by five different source temper-

atures. The following results were obtained:

5.9.1 Initial ground beef weights

5.9.2 Dripping losses

5.9.3 Volatile losses

5.9.4 Surface time-temperature relationships

5.9.5 Time-temperature relationships at the one
inch sample depths

5.9.6 Time volatile weight losses

5.9.7 Sample length and width changes

Table 7.1, in the appendix, shows the initial ground
beef sample weights, dripping losses, volatile losses,

sample length and width changes and total processing times

5-46

between the initial product temperature and 170 F.

Fig. 7.1, in the appendix, shows typical surface
temperature—time relationships for several tests at dif-
ferent source temperatures. The average surface temper-
ature was calculated for all tests by taking the sample
surface temperatures in five minute increments starting with
the initial surface temperature and ending with the final
surface temperature, these average product surface temperatures
were then plotted against the surface heat flux. See Fig. 5.6

The following linear equation was obtained:

ts = 139.60 + 0.04251 qs",

with: R = 0.9218 and S1 = 4.12,

Where ts is the average surface temperature, F

qs is the surface heat flux, Btu per sq ft-hr

R is the linear correlation coefficient

S1 is the standard error estimate

The above relation was obtained so the average

percent volatile loss rate could be obtained. The con-
version of water to water vapor should be a first order
chemical reaction, if it is first order the familiar empiri—
cal equation proposed by Arrhenius should follow (18).
According to the empirical equation a straight line would
be obtained when the logarithm of the rate constant, in this
case, the percent volatile loss per unit of time is

plotted against the reciprocal of the absolute temperature.

Fig. 5.7 shows the result of such a plot. The following

L”
l

47

 

2:0 1
LS: 139 60+0 04251.10

R. = O92I8
s. = 4,12

 

 

00

\\
\ \
\

 

WC

\
\
\ \\

 

af'
p’

”"
.14?

 

I60 ,7

 

I50 J

 

//
/.

 

 

 

 

 

 

 

 

 

 

Pig.

 

400

5.

500 600 700 .00 900 IOOO H00 l200
Q‘s

Relationships Of t. (average product surface temperature) and qs" for ground
beef.

 

l l 1

L06 [(M°'") f'] = 4.5084 4.2689: 10%.”

 

Mo
\ a, = -o. 8664

 

 

\\\§ 5. = 0. 0765
\.

 

.\&\\

 

-28

 

 

 

 

 

 

 

 

 

 

 

 

L50

L52 154 L56 L56 L60 L62 L64 L66

 

l -s
-1 1: IIO
Mo-M T 3
Fig. 5.7 Log M and (l/T.) x 10’ relationships for ground beef.

L68

linear equation was obtained:

0 ' M 1'1 3 -1
LOG ‘74—" = 4.5084 - 4.2689 x 10 Ts .
O

with: R = 0.8664 and S = 0.0765,

1
Where MO is the initial weight of the product
M is the final weight of the product including
dripping losses
is the total processing time, hours

T is average surface temperature, R.

It can be noted from the above expression that

M — M —1
———O M )1. is the volatile loss per hour or the reaction
0

rate of converting water to water vapor.

Fig. 7.2, in the appendix, shows several typical
time—volatile loss relationships, from these it can be
noted that a linear relationship very closely approximates
the rate of volatile loss for a particular surface heat
flux and source temperature. This apparent linear relation—
ship will be used next.

McCance and Shipp (43) have reported that water and
weight losses from lean beef processed at a constant
temperature are linear with respect to time.

Heisler (26), Carslaw and Jaeger (13) have developed
time-temperature relationships that in part depend upon the
surface heat loss when a substance is heated at the surface

by radiation. If the surface is in an environment at a

5-49

temperature different than its surface, the surface may gain

or lose heat to its environment. Equations have been developed
for surface heat losses by convection and radiation. Giedt
(24) and Jakob (32) give the following equation for the con-
vection heat transfer coefficient for a horizontal surface
being heated or cooled and facing upward:

8 9

or 10 , all N N

GR. PR
9

hC = 0.25 (tS -te)l/3, for NGR'NPR.> 10
products were greater than 109, with an average of 8.2 x 10
for the experimental data.
Where hC is the convection heat transfer coefficient,
Btu per sq ft-hr F
ts is the surface temperature, F
te is the envinpnment temperature, ta > te in
this case, the surface is losing heat to the
environment, F
L is the characteristic surface length, ft

Mark's Handbook (40) gives the following equation

to determine the equivalent radiative coefficient:

TAV 3

Where hr is the radiative heat transfer coefficient,
Btu per sq ft-hr F
e is the emissivity of the radiation surface
TAV is the average temperature of the surface
and its environment, R

Jakob (33) also states that an apparent coefficient

of heat transfer may be used for the heat of condensation.

5-50

This apparent coefficient of heat transfer is given by the
following equation:

qL=WL=hL (ts-te)l

Where qL is the total latent heat gain, Btu per hr
W is the weight of the condensed product, lbs per hr
L is the latent heat of condensation, Btu per lb
h is the apparent coefficient of heat transfer,
Btu per sq ft-hr F
t is the surface temperature, F

S

te is the environment temperature, F

The linear relationship obtained above, see Fig. 5.6.
can now be used to determine an apparent coefficient of heat

transfer, h As the volatile losses from food products

LO
consist of water vapor (3, 37) the latent heat of vapori-

zation may be taken from steam tables. The apparent coefficient

of heat transfer may be defined by the following equation:
Percent V M L
h = O
L (t —t)'r
s e

 

Where hL is the apparent coefficient of heat transfer,
in Btu per sq ft-hr F

V is the volatile loss, percent

M is the initial sample weight, lb

L is the latent heat of vaporization of water
at a temperature ts, in Btu per lb

t is the average surface temperature, F

t is the environment temperature, F

T is the processing time, from the initial product

temperature to 170 F, hours.

5-51

The combination of he, hr and hL represents the
coefficient of heat transfer from the sample surface in
Btu per sq ft-hr F, then h is the sum of the three co-
efficients. The hC and hL coefficients may be combined
because the velocity of the surface volatile loss is approxi-

mately 1.1 x 10—5

ft per sec as compared to a velocity of
approximately 1 ft per sec at a 0.5 ft distance above the
surface for free convection of air, based on average surface
conditions. This h should then satisfy the requirement
of equation developed by Heisler. These results, hc’ hr
and hL, are given in Table 5.28 as well as the average

surface temperature for each of the tests.

This sum of coefficients was then used in the K/hs
parameter, for the plotting of the data. The other two
parameters are:

CLT/s2 and

h(tl - tO)/qs",

Where a is the thermal diffusivity, a = €31 where k

is the themal conductivity, Btu ft per sq ft-hr
F; p is the density, lb per cu ft; c is the
specific heat, But per lb F.

T is the time, hours

3 is the depth at which the temperature is measured,
ft

h is the sum of the coefficients of heat transfer,
equal to hc+hr+hL, in Btu per sq ft-hr F

t is the temperature at a depth 5, F

Table 5.28.

The convective,

5-52

radiative and apparent co—

efficients of heat transfer from the surface
of the sample to the room for various room
temperatures and sample surface temperatures

for each of the tests.

 

 

 

Test No. A tS te hC hr hL hc+hr+hL
35 1.233 182 80 1.21 1.03 3.85 6.09
34 179 80 1.21 1.03 4.00 6.24
33 183 79 1.22 1.03 3.37 5.62
32 175 79 1.20 1.03 3.39 5.62

l 178 78 1.21 1.03 4.24 6.48

2 166 78 1.17 1.00 2.93 5.10

3 163 77 1.16 0.99 3.70 5.85

4 171 78 1.19 1.02 3.37 5.58

5 177 80 1.21 1.03 3.18 5.41

6 169 78 1.18 1.00 2.92 5.10

7 171 79 1.19 1.02 3.02 5.23

8 163 79 1.16 1.00 2.53 4.69

9 159 80 1.14 0.99 2.38 4.51
10 1.505 198 79 1.26 1.05 5.94 8.25
11 190 79 1.24 1.03 4.51 6.78
12 185 80 1.22 1.03 5.04 7.29
13 182 79 1.21 1.03 4.11 6.35
36 181 80 1.21 1.03 3.59 5.83
14 176 80 1.20 1.03 3.98 6.21
15 170 81 1.17 1.03 3.92 6.12
16 163 81 1.15 1.00 4.41 6.56
37 169 80 1.17 1.02 3.23 5.42
17 170 79 1.18 1.02 3.25 5.45
18 169 80 1.17 1.02 3.02 5.21
38 160 80 1.14 0.99 2.39 4.52
59 2.308 186 79 1.23 1.03 4.94 7.20
63 188 79 1.23 1.03 3.81 6.17
57 185 78 1.23 1.03 4.16 6.42
58 182 78 1.22 1.03 3.92 6.17
69 179 78 1.21 1.03 4.54 6.78
60 173 79 1.19 1.03 3.78 6.00
62 173 79 1.19 1.03 3.82 6.10
66 167 79 1.17 1.00 3.91 6.08
61 168 79 1.17 1.00 3.06 5.23
68 162 79 1.16 1.00 3.28 5.44
65 165 80 1.16 1.00 3.03 5.19
67 156 78 1.13 0.98 2.49 4.60
64 156 79 1.13 0.98 2.29 4.40

Table 5.28.--Continued.

 

 

 

 

Test No. A t t h h h h +h +h
s e c r L c r L

55 2.797 182 83 1.21 1.03 5.56 7.80
56 178 80 1.21 1.03 4.66 6.90
29 177 77 1.21 1.03 3.64 5.88
54 182 80 1.21 1.03 4.36 6.60
28 173 79 1.19 1.03 3.81 6.03
53 180 79 1.21 1.03 3.82 6.06
27 178 78 1.21 1.03 3.73 5.97
26 172 78 1.19 1.02 3.42 5.63
25 167 78 1.17 1.00 3.29 5.46
19 171 78 1.19 1.02 3.00 5.21
20 167 79 1.17 1.00 3.20 5.37
21 166 79 1.17 1.00 3.12 5.29
22 165 78 1.17 1.00 3.03 5.20
23 159 78 1.14 0.99 2.99 5.12
24 161 78 1.16 0.99 2.19 4.34
31 157 78 1.14 0.98 2.15 4.28
30 156 78 1.13 0.98 2.12 4.23
39 3.164 205 79 1.28 1.07 5.64 7.99
52 186 79 1.23 1.03 6.40 8.66
47 186 78 1.23 1.03 4.77 7.03
46 184 78 1.23 1.03 4.59 6.85
45 183 79 1.22 1.03 4.36 6.61
42 183 79 1.22 1.03 4.03 6.28
44 174 78 1.20 1.03 3.90 6.13
40 173 79 1.19 1.03 3.80 6.02
41 170 79 1.18 1.02 3.60 5.80
43 171 79 1.19 1.02 3.16 5.37
49 161 78 1.16 0.99 3.21 5.36
51 163 79 1.16 1.00 3.24 5.40
50 158 79 1.14 0.99 2.47 4.60
48 156 80 1.12 0.98 2.42 4.52

 

to is the initial product temperature,

F

qs is the surface heat flux, in Btu per sq ft-hr

The thermal diffusivity was assumed to be constant
within a given temperature range. The values of specific
heat were given in Table 5.1. As latent heats are involved

in the changing of fat from solid to liquid in both the G-

5-54

and B- forms and from the a— to B—state, at specific temper—
atures, one graphical presentation of the data covering the
entire processing range could not be used. Four plots are
used for each of the five source temperatures at different
heat fluxes. The first plot covers the range from the initial
product temperature to 122 F, the temperature at which
a-solid fat changes to a-liquid fat (actually 121.8 F).
The second plot covers the range from 122 to 140 F, the
latter temperature is the temperature at which a-liquid
fat changes to B-solid fat (actually 139.1 F). The third
plot includes the spread from 140 to 157 F, the latter
temperature is the temperature at which B-solid fat changes
to B-liquid fat (actually 156.4 F). The final graph pre-
sents the temperatures above 157 F, where the B-fat remains
in the liquid state for normal processing product tempera—
tures. Several of these plots for different source temper-
atures and heat fluxes are shown in Fig. 7.3 in the appendix.
The above initial temperatures for the four plots
change for each graph, dependent on the latent heat temper-
ature of the fat in the product. The following parameters

are then used for each of the changes of state of the fat:

5.9.8 First plot: h(tl - tO)/qs", the terms are defined
above

5.9.9 Second plot: h(tl - 122)/qs", the 122 F temperature
is the temperature at which a—solid fat changes

to a-liquid fat

5-55

5.9.10 Third plot: h(tl - 140)/qs", the 140 F
temperature is the temperature at which a—liquid
fat changes to B-solid fat

5.9.11 Fourth plot: h(tl - 157)/qs", the 157 F temper—
ature is the temperature at which B-solid fat
changes to fi-liquid fat

Heisler (26) has also shown his graphical solutions
for CLT/s2 values less than 0.2 on linear Cartensian co-
ordinates. Within certain limits of OLT/s2 the plotting
of Heisler graphical solutions are very nearly linear, with
a high linear correlation. Therefore, straight lines were
drawn through the various plots of h(tl - tO)/qs" vs
GT/s2 for each of the k/hs parameters for the various source
temperatures. See again Fig. 7.3 in the appendix. Fig. 7.4,
in the appendix, shows an example of the plotted experimental
data for various k/hs values, with a radiation source temper-
ature of 3465.0 R.

These data were then correlated by holding the
h(tl - tO)/qs" parameter constant at three different values
and finding a linear regression line for the remaining two
parameters, k/hs and aT/sz. This represents a transformation
of axis. The linear regression transformation was carried
out for each of the five source temperatures, at each of the
four temperature ranges and at each of three constant
h(ti - tO)/qs" values. These correlations are shown in

Tables 5.29, 5.30, 5.31, 5.32 and 5.33.

5-56

Table 5.29. Correlation of temperature vs time distribution
patterns for various surface heat fluxes from
a source temperature of 4230. 0 R, A of 1. 233 u.
Y = A + BX represents the linear regression
equation of Orr/s2 (Y) vs. k/hs(X) at a constant
h(tl - tO)/qs". R is the correlation of Y on
X and the standard error is 81.

 

 

 

 

h(tl-to)[qs" t,F A B R* 51
0.30 < 122 0.1988 0.2479 0.5560 0.0281
0.40 0.2281 0.3769 0.6082 0.0334
0.50 0.2527 0.5119 0.6736 0.0383

122 £_to < 140
0.08 -0.0798 0.3242 0.9796 0.0246
0.10 -0.1044 0.4154 0.9046 0.0133
0.12 -0.1302 0.5101 0.8919 0.0176
140 £_to < 157
0.06 -0.3552 0.8528 0.8483 0.0362
0.09 —0.6l30 1.4311 0.8301 0.0654
0.12 -0.8792 2.0232 0.8263 0.0933
157 £_to
0.06 —0.2909 0.7507 0.9103 0.0232
0.08 -0.3804 0.9875 0.9161 0.0294
0.10 -0.4752 1.2315 0.9109 0.0379
*R.95 0.476, if R e 0

5-57

Table 5.30. Correlation of temperature vs time distribution
patterns for various surface heat fluxes from

a source temperature of 3465.0 R, A of 1.505 u.
Y = A + BX represents the linear regression
equation of GT/82(Y) vs k/hs(X) at a constant
h(t - t )/qs". R is the correlation of Y on

X and the standard error is 81.

 

 

 

 

h(tl-to)/qs" t,F . A .8' R* 81
< 122
0.30 0.1439 0.2620 0.5806 0.0321
0.40 0.1463 0.4222 0.7351 0.0362
0.50 0.1400 0.5830 0.8245 0.0372
122 S_to < 140
0.08 -0.0551 0.2692 0.8360 0.0164
0.10 -0.0811 0.3485 0.8635 0.0189
0.12 -0.0984 0.4159 0.9634 0.0115
140 £_to < 157
0.06 -0.1975 0.5460 0.8647 0.0295
0.09 -0.3241 0.8901 0.9233 0.0344
0.12 —0.4492 1.2314 0.9302 0.0452
157 S-to
0.06 —0.2499 0.6658 0.9424 0.0219
0.08 -0.2977 0.8333 0.9418 0.0276
0.10 -0.3461 1.0055 0.9344 0.0356
*R.95 (N=12) = 0.497, if R ¢ 0

5-58

Table 5.31. Correlation of temperature vs time distribution
patterns for various surface heat fluxes from

a source temperature of 2260.0 R, A of 2.308 u.
Y = A + BX represents the linear regression
equation of OLT/s2 (Y) vs k/hs(X) at a constant
h(tl - to)/qs". R is the correlation of Y on

X and the standard error is 81.

 

 

 

 

h(tl-to)/qs" t,F A B R* 81
< 122
0.30 0.1153 0.2737 0.8253 0.0170
0.40 0.0887 0.4695 0.9024 0.0201
0.50 0.0574 0.6718 0.8763 0.0331
122 < to < 140
0.08 -0.0568 0.2358 0.9601 0.0061
0.10 -0.0891 0.3313 0.6424 0.0326
0.12 -0.1308 0.4411 0.9822 0.0075
140 < to < 157
0.06 -0.2330 0.5724 0.9319 0.0199
0.09 -0.3872 0.9382 0.9623 0.0230
0.12 -0.5024 1.2318 0.9753 0.0250
157 S_to
0.06 -0.259 0.6351 0.9496 0.0159
0.08 -0.2964 0.7558 0.9791 0.0140
0.10 -0.3837 0.9684 0.9728 0.0225
*R.95 (N=13) = 0.476, if R # 0

5-59

Table 5.32. Correlation of temperature vs time distribution
patterns for various surface heat fluxes from a
source temperature of 1864.5 R, A of 2.797 u.
Y = A + BX represents the linear regression
equation of'OL'r/s2 (Y) vs k/hs (X) at a constant
h(tl - to)/qs". R is the correlation of Y on
X and the standard error is $1.

 

 

 

h(tl-tO)/qs" t,F A B R* 81
< 122
0.30 0.1911 0.1588 0.5178 0.0275
0.40 0.2260 0.2476 0.5885 0.0356
0.50 0.2305 0.3893 0.7503 0.0359

122 < tO < 140

0.08 -0.0287 0.1978 0.9173 0.0088
0.10 -0.0464 0.2712 0.9976 0.0019
0.12 -0.0676 0.3501 0.9880 0.0057

140 < to < 157

0.06 -0.2508 0.6209 0.8821 0.0348

0.09 -0.4528 1.0948 0.9057 0.0537

0.12 —0.6304 1.5203 0.9378 0.0590
157 S to

0.06 -0.2486 0.6386 0.9101 0.0304

0.08 -0.3364 0.8663 0.9171 0.0394

0.10 —0.4290 1.1000 0.9186 0.0496

 

*R.95 (N=l7) = 0.412, if R # 0

5-60

Table 5.33. Correlation of temperature vs time distribution
patterns for various surface heat fluxes from a
source temperature of 1648.7 R, A = 3164 u.
Y = A + BX represents the linear regression
equation of aT/82(Y) vs k/hs (X) at a constant
h(t - t )/qs". R is the correlation of Y on
X and the standard error is s1.

 

 

h(tl-to)/qs" t,F A B R* s

 

1
< 122
0.30 0.1379 0.2426 0.7264 0.0247
0.40 0.1515 0.3780 0.8271 0.0276
0.50 0.1677 0.4960 0.8108 0.0385

122 < to < 140

0.08 -0.0289 0.1937 0.9386 0.0076
0.10 -0.0461 0.2622 0.9686 0.0072
0.12 —0.0644 0.3328 0.9696 0.0090

140 < to < 157

0.06 -0.1248 0.3946 0.8954 0.0220

0.09 -0.2099 0.6515 0.9156 0.0307

0.12 —0.2919 0.9047 0.9288 0.0388
157 £.to

0.06 —0.1261 0.4041 0.9569 0.0131

0.08 —0.l630 0.5314 0.9608 0.0164

0.10 —0.2121 0.6824 0.9507 0.0240

 

*R.95 (N=l4) = 0.458, if R # 0

5-61

The results of the previous five tables, Tables
5.29, 5.30, 5.31, 5.32 and 5.33 are plotted in Fig. 5.8 through
5.27.

At this point it may be desirable to summarize the
steps involved in computing the time (T) required to reach
a temperature at a depth (5) or given a time (T) the steps
involved to determine the temperature at some depth (s).

The steps are:

5.9.12 Given a heat flux, Btu per sq ft-hr, the
average surface temperature of the product can be found from

Fig. 5.6, F.

5.9.13 Knowing the average surface temperature, the
volatile rate loss can be found in Fig. 5.7 in percent of the

initial product weight per hour, hence pounds per hour.

5.9.14 Knowing the average surface temperature and
the volatile loss in pounds per hour, the convective, radia—
tive and apparent coefficients of heat transfer can be

computed and the combined h can be found.

5.9.15 Having selected a product with known thermal
properties and latent heat changes, and having selected a
source temperature, either one or several of the Figs. 5.8
through 5.27 could be used to determine the time or times
to reach a specific temperature or specific temperatures can

be determined.

5-62

 

 

 

 

 

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radiant heat source at 4230.0 ll.

5-63

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5-67

5.9.16 The final step, if two or more of the Figs.

 

5.8 through 5.27 add together the determined times from
each of the figures.

The solution for a product temperature at a specific
depth would follow a similar pattern, but the final step
would be eliminated, as the time would already be known.

Examples of the use of the above figures and steps
are included in the appendix.

These results are similar to Heisler's, in that with
increased surface heat fluxes the time to reach a particular
temperature at a depth (5) is less, for a constant k/hs
parameter. Also, as the surface heat flux increases the
surface temperature increases which in turn affects the
Arrhenius empirical equation, that is volatile losses
increase, which generates a higher coefficient of heat
transfer on the surface. But, a high surface temperature
also causes an increased heat flow into the product and
hence reduces the time to reach a specific temperature.

This phenomenon is also indicated on the Heisler charts (26).
Also if the surface heat flux could be held constant and
different coefficients of heat transfer, say h2 > hl, both
at the same heat flux, the time required to reach a specific
temperature would be greater for the higher coefficient of
heat transfer (greater surface heat loss) than for the

lower coefficient, this is also shown by Heisler (26).

The major difference between Fig. 5.8 through 5.27 and

Heisler's plots is the linear relationships at specific k/hs

5—68

parameters. However, Heisler has even broken his graphical
solutions in two parts, one solution for OLT/s2 values equal
to or greater than 0.2 and another solution for those values
less than 0.2. The latter graphical solution has a linear
region of h(tl - tO)/qs" vs aT/sz, and a high linear cor—
relation exists in the other region for low values of QT/Sz.
The thermal diffusivity is the major factor that keeps the
d7/SZ values low and in a highly correlated linear region.
With moist food products the thermal conductivity is low,
lower than water (36). The density is low, when compared
to metals, and the specific heat is rather high, less than
that of water. These factors contribute to a low thermal
diffusivity and hence a low OL'r/s2 parameter. The product
thickness is important, but generally it again tends to
keep OLT/s2 factor low, first by appearing as sz, so when
the depth is increased at a fixed time, the OL'r/s2 parameter
is reduced. It also appears in another parameter, k/hs,

and as s is increased k/hs is reduced for fixed k/hs values
and this again tends to reduce OLT/s2 values.

The results of Lukianchuk's (38) dry heat and deep
fat processing of beef also indicate four possible tempera—
ture ranges in processing. Within temperature regions she
gave heat penetration data, minutes per degree centigrade
rise. These results were checked with the latent heat of
fusion temperature of the a- and B-forms of fat and the
heat penetration data indicated a linear temperature rise

within the various temperature ranges for both types of

5-69

processing. Similar results were also found in other

data, unpublished, on heat penetration at the Department of
Foods and Nutrition, Michigan State University, East Lansing,
Michigan.

Lowe (2, 37) presents graphs of temperature vs time
data for the processing of lean beef. Linear relationships
exist for the above temperature ranges except for a temper—
ature lag period at the beginning of heating and at temper-
atures above 80 C it is apparent that a logarithmic temper-
ature-time relationship exists, because the product
temperature is approaching the source temperature.

A consideration of the above factors, plus the
rather low final product temperatures reached in processing
support the linear relationships obtained in Figs. 5.8 through
5.27.

Utilizing known information about the product, the
thermal properties, density and rate of moisture loss and
comparing the results of the procedure given above to the
Heisler graphical solution for a specific heat flux and a
final product temperature, the Heisler charts always indi-
cate a greater processing time than was actually required
or as determined from above. Jakob (33) indicates that for
transpiration cooling, that is when a liquid is moving through
the void spaces in a product, an apparent conductivity of
the mixture should be used. This apparent conductivity is
lower than the conductivity of the liquid moving through

and higher than the conductivity of the porous substance.

5-70

Again, at a fixed heat flux and fixed final temperature,
this would result in lower processing times, hence reducing
the differences between Heisler's charts and the above
results. Another factor could influence the above difference,
Jakob's apparent conductivity is based on the fact that the
fluid was primarily moving in one direction, toward the
transpirating surface. However, if this was not the case,
the fluid could move with freedom to other parts of the
product, convection could then take place within the product
itself. This could then further increase the rate of heat
transfer at a depth 5, and again reduce the above differences
between the results and Heisler's graphical solution.

It is apparent that the above or similar such con—
siderations are included in the graphical presentation of
the results. Until such a time when these effects are
measured and correlated for moist food products, a dif-
ference will probably exist between Heisler charts and
actual processing time—temperature distributions within a
product.

Finally, Heisler assumed a boundary condition of
qs"/h as the final temperature of the body above its initial
temperature, which did not hold true in these experiments,
for the entire processing range. This boundary condition
would increase the time to reach a particular temperature at
a particular heat flux, if the final product temperature
or equilibrium temperature was greater than qs"/h, plus

the initial product temperature.

5-71

Fig. 7.28 shows a comparison of the effect of heat
source temperature, or X's, on a constant k/hs parameter for
various values of h(tl - tO)/qs" and 01/52. This figure
indicates that the higher X's or lower source temperatures,
that is A > 1.505 u or a source temperature < 3465.0 R, are
approximately equivalent in time—temperature relationships
at the same heat fluxes. For shorter wave lengths or higher
source temperatures greater times are required to reach a
specific product temperature at a given heat flux. DeWerth
(l9) and Sayles (48) state that the absorption of electro-
magnetic energy by water is the critical factor and the
critical wave length is about 1.5 u. Water has a high
reflectivity for wave lengths below 1.5 u and a high absorp-
tivity above 1.5 u. This is also indicated in Fig. 5.28.

The percent volatile and dripping losses and the
decrease of product volume are shown in Table 5.34. The
decrease of volume, assumes a constant depth, which was not
measureable, however Lowe (37) points out that the depth of
the product increases, while there is a decrease in both
length and width. Daniels and Alberty (18) state that
coefficient of volumetric expansion or contraction is at a
constant rate in the three dimensions. But the American
Meat Institute Foundation (3) indicates the depth does
increase because of the relative change in protein linkages,
which appear to unfold. Lowe also indicates that the change
in volume is always less than the sum of the volatile and

dripping losses, as indicated in Table 5.34.

 

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Fig. 5.28 h(t1—157)/qs" and err/s2 relationships at

k/hs - 0.6 for ground beef (c = 0.80) at
different radiant heat source temperatures. R.

 

5-73

Table 5.34. Percent volatile and dripping losses and
volume change in length and width for ground
beef processed to 170 F at various radiant heat
source temperatures and at different heat

 

 

 

 

fluxes.
Losses, percent
Volume

Test Heat reduction
no. flux Volatile Dripping Total percent
(Source temperature, 4230.0 R)

35 1124.01 7.51 18.27 25.78 22.8
34 1077.69 8.34 17.79 26.13 20.0
33 1024.06 8.20 17.28 25.48 22.8
32 967.05 8.04 17.86 25.90 21.9
1 903.57 10.41 16.52 26.93 17.8
2 843.72 7.22 17.94 25.16 19.0

3 777.33 10.33 14.94 25.27 20.0
4 729.93 10.32 15.45 25.87 20.0

5 692.37 11.40 14.26 25.66 20.0
6 643.27 10.33 15.86 26.19 19.0
7 580.94 12.16 11.42 23.58 19.0
8 545.35 10.15 14.91 25.06 21.9
9 472.90 12.15 14.25 26.40 20.0
(Source temperature, 3465.0 R)
10 1163.87 11.05 13.66 24.71 21.0
11 1077.48 9.37 14.84 24.21 21.9
12 1009.85 9.37 15.12 24.59 21.9
13 934.40 8.83 16.64 25.47 19.0
36 899.23 7.17 18.30 25.47 22.0
14 868.11 9.35 16.68 26.03 21.9
15 797.34 8.92 17.18 26.10 20.0
16 716.54 9.33 15.15 24.48 21.0
37 671.65 9.09 16.15 25.25 21.0
17 637.57 9.69 16.28 25.97 21.9
18 562.60 9.89 15.08 24.97 17.0
38 507.88 10.04 17.47 25.51 20.0
(Source temperature, 2260.0 R)
59 1151.82 7.32 20.42 27.74 25.5
63 1081.34 6.26 22.20 28.46 22.8
57 1016.45 7.61 18.83 26.44 22.0
58 947.25 7.19 19.92 27.11 25.5
69 893.41 8.19 19.13 27.32 20.0
60 836.52 7.18 21.81 28.99 24.7
62 778.42 7.43 20.15 27.58 22.8
66 721.09 7.90 20.99 28.89 23.8
61 666.42 8.02 20.07 28.09 20.0

-—v - .._-.-....-.-:~ ~— .1 . _ - 4 _

Table 5.34.--Continued.

 

 

 

 

 

Losses, percent Volume
Test Heat reduction
no. flux Volatile Dripping Total percent
68 624.24 7.80 20.36 28.16 22.8
65 576.10 8.46 20.10 28.56 21.0
67 528.96 8.41 21.81 30.22 22.0
64 484.86 8.92 21.57 30.49 23.8
(Source temperature, 1864.5 R)
55 1029.76 8.71 17.17 25.88 23.8
56 955.46 8.44 16.97 25.41 22.8
29 916.62 7.43 20.67 28.10 25.3
54 913.90 8.00 17.57 25.57 22.8
28 862.77 8.14 18.53 26.67 22.8
53 860.29 7.93 18.32 26.25 23.0
27 813.66 8.76 15.24 24.00 20.0
26 761.61 8.79 17.20 25.99 22.0
25 712.07 8.29 18.95 27.24 21.0
19 650.08 8.93 17.70 26.63 20.0
20 601.10 10.86 17.03 27.89 22.8
21 561.91 10.85 16.22 27.07 20.0
22 510.22 11.31 14.31 25.62 20.0
23 489.10 10.31 15.75 26.06 19.0
24 426.28 9.57 20.69 30.26 21.9
31 387.42 12.12 16.00 28.12 20.0
30 348.24 12.45 14.86 27.31 20.0
(Source temperature, 1648.7 R)
39 1281.52 9.69 14.85 24.54 26.3
52 1203.40 9.73 15.87 25.60 22.8
47 1144.89 8.37 17.45 25.82 25.5
46 1063.17 7.77 17.65 25.42 24.7
45 988.37 8.07 18.02 26.09 25.5
42 931.20 7.65 18.90 26.55 23.8
44 857.93 7.48 18.83 26.31 24.7
40 792.69 8.83 16.58 25.41 21.9
41 718.77 8.23 17.82 26.05 22.8
43 655.43 9.77 18.67 28.44 23.8
49 595.28 8.01 19.16 27.17 21.9
51 544.16 8.58 19.24 27.82 22.8
50 487.96 8.37 18.62 26.99 20.0
48 436.25 9.84 18.56 28.40 21.0

 

5-75

Table 5.35. Analysis of variance of total processing losses
for the different heat source temperatures.

 

 

 

Variance Sum of squares df Mean square F ratio*
Means 72.21 4 18.0525 14.75
Within 78.33 64 1.2239

Total 150.54 68

 

*F.95 (4, 64) = 2.52

The total processing losses are not equal, as shown
in Table 5.35. Therefore, the heat source temperature
affects the total processing losses. This could be expected
as the heat source temperatures covered the critical range
of the water absorption spectrum. From the water absorption
spectrum, it appears that the energy from lower heat source
temperatures would be more readily absorbed and lead to
higher product temperatures and hence, higher product losses,
if the product losses are dependent on temperature. In
order to isolate the source temperature or temperatures
which lead to higher processing losses the means and
deviations of total losses must be investigated. Table 5.36
is a table of contrasts, comparing the average losses and
their variances for each of the heat source temperatures.
The results in the table are "t" test results.

It is apparent from Table 5.36 that a heat source
temperature of 2260.0 R leads to significantly higher total
losses. This particular source temperature corresponds to

a black body energy emission curve that has a maximum energy

5-76

Table 5.36. Summary of "t" tests for comparing the percent
total losses for each of the heat source
temperatures. (Column means are subtracted
from row means.)

 

 

Heat source temperature, R

 

Heat source
temperature, R 4230.0 3465.0 2260.0 1864.5 1648.7

 

4230.0 -- 0.43 —1.97* -0.67 —0.58
3465.0 -- —2.42* -0.99 -0.97
2260.0 —- 0.90 1.16
1864.5 —— 0.14
1648.7 --

 

*These t's are significant at a 95% level of
confidence.

level at 2.308 microns. This energy emission curve also
exists in the critical water absorption area. See Fig. 2.2.
The heat source temperatures lower than 2260.0 R have higher
average total product losses than those temperatures above
2260.0 R, but the differences are not statistically dif-
ferent. It is also interesting to note that while a heat
source temperature of 2260.0 R results in statistically dif—
ferent total losses with both the higher temperatures, it is
not statistically different from the lower heat source
temperatures. This might indicate that a maximum total

loss heat source temperature exists between 3465.0 and 1864.5
R. Also, as the water absorption curve is rapidly changing
in the area of two microns, this could suggest a transition
region, similar to the transition region between laminar

and turbulent boundary layers in convection heat transfer.

5-77

If this were the case, one specific heat source temperature
could not be defined for maximum total product losses only
a region. In the case of food processing this region would
then be avoided, because it is desirable to have maximum
product yields.

According to Lowe (37) the volume change in a product
is a function of final product temperature. If this hypo—
thesis is accepted, an analysis of the volume changes for
products subjected to different heat source temperatures
would not have any significant effect, because all products
were processed to a final temperature of 170 F. However,
the hypothesis of Lowe must be rejected as an analysis
of variance of volume changes indicates that the percent
volume change is a function of heat source temperature.

See Table 5.37.

Table 5.37. Analysis of variance of percent volume change
for the different heat source temperatures.

 

 

 

Variance Sum of squares df Mean squares F ratio*
Means 92.26 4 23.065 7.859
Within 187.85 64 2.935

Total 280.11 68

*F.95 (4,64) = 2.52

Lukianchuk (38) processed meat in an oven and in
deep fat, the fat temperature was lower than the oven temper—
ature, and she reported significantly higher percentage

volume changes with the lower temperature of processing. She

5-78

did not explain the phenomenon. It should be possible to
isolate the heat source temperature or temperatures causing
the differences in Table 5.37. Table 5.38 is a table of
contrasts, comparing the average volume changes and their
variances for each of the heat source temperatures. The
results in the table are "t" test results.
Table 5.38. Summary of "t" tests for comparing the percent
volume change for each of the heat source

temperatures. (Column means are subtracted
from row means.)

 

 

Heat source temperature, R
Heat source
temperature, R 4230.0 3465.0 2260.0 1864.5 1648.7

 

4230.0 —— —0.19 -1.17 -O.56 -1.74*
3465.0 —- -1.02 -0.39 -1.17
2260.0 -- +0.60 -0.14
1864.5 —- -0.70
1648.7 --

 

*This "t" is significant at the 95% level of

confidence.

Table 5.38 reveals only one significant difference,
at the 95% level of confidence. This value is not significant
at the 99% level of confidence. It could be stated that
this is a chance difference and a hypothesis could not be
formulated without further investigation. However, Table 5.37
indicates that there is a very significant effect of source
temperature on percent volume change. As the source temper—

ature is reduced, the wave length of the maximum energy

5-79

is increased. Planck (46) states this energy is not absorbed
on the geometrical surface, but is destroyed in a depth

below the surface. Hall (25) has stated that the absorptivity
of non-conductor or insulators increase as the wave length

of electromagnetic radiation in the infrared region is
increased and most hygroscopic materials have high absorption
beyond 3 microns. As the point of maximum energy emission

is 3.164 microns for a 1648.7 R source, which according to
Hall has a higher absorption than for higher source temper—
atures, the rate of heat absorption would be higher. This
higher rate of heat absorption could then cause faster chemical
reactions within the product, especially the contraction of
the meat fibers and would then lead to greater volume changes.

This effect is indicated in Tables 5.37 and 5.38.

6.0 SUMMARY AND CONCLUSIONS

The processing of ground beef by a radiant heat
source is dependent on two major factors: (a) the tempera-
ture of the radiant source, and (b) the product surface heat
flux as generated by the heat source. The latter factor
also affects the volatile weight loss of ground beef.

Three different electric heat source units were used
to investigate the effects of heat source temperature on
processing times within similar product temperature ranges.
Varying the electrical voltage on the heat source resulted
in different heat source temperatures. Changing the dis-
tance between the heat source and the surface of the product
resulted in different surface heat fluxes. The radiant
heat sources were: fused quartz lamps; metal sheathed
resistance elements, commonly known as calrods; and fused
quartz tubes. The quartz lamp filament was operated at two
tenperatures, 4230.0 and 3465.0 R. The calrod was operated
at metal sheathed temperatures of 1864.5 and 1648.7 R.

The fused quartz tube was operated at a filament temperature
of 2260.0 R. These temperatures correspond to a black body
radiator, with a maximum energy emission of 1.233, 1.505,
2.797, 3.164 and 2.308 microns, respectively. The heat flux
range varied from about 350 to 1290 Btu per sq ft—hr. All
samples were of ground beef and were processed from about

45 F to a final temperature of 170 F.

6-1

 

 

6-2

6.1 Calculated and measured heat fluxes

The radiation and convection heat losses were cal-
culated for three heat sources. The calculated radiation
losses were then compared to the manufacturer's radiation
rating of the units. In all cases the calculated radiant
heat output was higher. The maximum percent difference at
the actual operating voltage was 11.20%; this occurred with
the calrod unit operated at 180 volts.

An accurate comparison could not be made between
calculated and measured heat fluxes. The measured heat
flux, as measured by an Eppley pyroheliometer, was a function
of the distance between the heat source and instrument. The
measured heat fluxes approached the calculated heat fluxes
at greater distances between the source and the instrument.

6.2 The effect of environment wall reradiation on processing
time.

Six samples of ground beef were processed at 946
Btu per sq ft-hr, which was generated by a source temper-
ature of 4365 R. Three of the samples were processed in an
open room. The remaining three samples were processed in
an enclosed volume, which was interiorly painted black-
board black. All samples were processed from about the
same initial temperature to 170 F. The following is a

summary of the results:

6.2.1 A higher product yield was observed with the

enclosed volume.

6-3

6.2.2 A high dripping loss occurred in the non-
enclosed volume.

6.2.3 There was no significant difference in volatile
loss.

6.2.4 There was no significant difference in total
processing time.

6.2.5 There was no significant difference in the time-
temperature relationships at a one inch sample
depth.

6.3 The effects of heat source temperatures and surface

heat fluxes on processing times and weight losses
of ground beef

Five different heat source temperatures were
selected, 4230.0, 3465.0, 2260.0, 1864.5 and 1648.7 R.
A range of heat fluxes was selected for each of the heat
source temperatures. The following data were obtained:
(a) product weight losses, volatile and dripping: (b) rate
of volatile loss; (c) time-temperature relationship on the
surface of the product; (d) time-temperature relationship,
one inch below the surface of the product, this corresponded
to the maximum depth of the product; (e) volume change of

the product. The following is a summary of the results:

6.3.1 A linear relationship exists between surface
heat flux and the average surface temperature of
the product.

6.3.2 A linear relationship exists between volatile

loss and time at a given surface heat flux, or

6.3.4

6—4

at an average product surface temperature.

The volatile loss rate follows the empirical
Arrhenius equation, for first order chemical
reactions.

A linear relationship exists for values of

h(t — tl)/qs" vs Ctr/s2 for various parameter
values of k/hs, within the following product
temperature ranges: (a) above freezing to

122 F; (b) 122 to 140 F; 140 to 157 F: 157 F and
above, to at least 170 F.

The linear relationships in 6.3.4 above, also
depend on another parameter, heat source
temperature.

A procedure is given to determine the total
processing time to reach a specific product

temperature. The procedure is summarized below.

6.3.6.1 Given a surface heat flux, the average

surface temperature can be found from

Fig. 5.6.

6.3.6.2 The percent volatile weight loss per

hour can be found, if the surface tempera-

ture is known, Fig. 5.7.

6.3.6.3 If the surface temperature and volatile

weight loss per hour are known the radia-
tive, convective and apparent coefficients

of heat transfer on the sample surface can

6.3.6.4

6.3.6.5

6.3.6.6

6—5

be calculated, the sum of these three
coefficients is then called the combined
coefficient of heat transfer.

If the thermal properties of the product
are known, the time to reach specific
temperatures at a specific depth can be
determined from Fig. 5.8 to 5.27, for
various radiant heat source temperatures.
The final step consists of summing the
increment times determined from step
6.3.6.4.

If a temperature is desired at a specific
time, an iteration technique can be used

by reversing the above five steps.

.7 Some general remarks concerning the time-

temperature relationships at various k/hs

parameters are given below.

6.3.7.1

6.3.7.2

6.3.7.3

The higher the heat flux, the shorter the
time required to reach a specific temper-
ature at a specific depth.

The higher the heat flux, the higher the
surface temperature, which results in
higher surface coefficients of heat
transfer.

If two equal heat fluxes could be compared
with different surface coefficients of heat

transfer, a shorter processing time would be

6-6

required for the lower surface coefficient.
A high coefficient indicates a greater loss

of heat from the surface to the environment.

6.3.7.4 The greater the product depth, the longer

6.3.10

the required processing time to reach a
specific temperature at the depth.
Decreasing the radiant heat source temperatures
from 4230.0 to 2260.0 R results in decreased
processing times at the same heat flux. Any
further reduction of heat source temperatures
to 1648.7 R does not essentially affect the
processing time required at 2260.0 R.
The maximum total product losses occurred with a
source temperature of 2260.0 R. The total losses
at 4230.0, 3465.0, 1864.5 and 1648.7 R were not
significantly different.
The percent volume changes were not significantly
different except for a radiant heat source tem—
perature reduction from 4230.0 to 1648.7 R.
For the latter case, the volume reduction was
significantly greater with a 1648.7 R heat source

temperature.

In general the following recommendations could be made,

concerning radiant heat processing. It appears that

the 1864.5 R heat source temperature has the most

desirable processing effects on ground beef. A higher

6-7

total product loss occurred with a heat source tem-
perature of 2260.0 R and a larger volume reduction
occurred with a heat source temperature of 1648.7 R.
Also, processing times were longer at 4230.0 and
3465.0 R. And finally, a higher surface heat flux
results in shorter processing times, at the heat

source temperatures investigated.

 

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31.

729.93 4230.0
1163.87 3465.0
562.60 3465.0
510.22 1864.5
1077.69 4230.0
1281.52 1648.7
718.77 1648.7
955.46 1864.5
1151.82 2260.0

 

Time, min.
Fig. 7.1 Product (t.-t°) and time, min.. relationships at different surface heat fluxes.
Btu per sq. ft.-hr.. and heat source temperatures. R. t.. product surface temper-
ature. P. to. initial product temperature. I.

Volaiile Less. Pence)

 

)0 20 30 40 50 00 TO 00 90 I00 "0
Tune, min.
P19. 7.2 Volatile loss. percent of initial product weight. and time. min.. relation-

Ohiva at different surface heat fluxes. Btu r . f .-h .,
temperatures. R. 9‘ sq t t and heat source

Source tempsrature,R.

 

Time min.
Fig. 7.3 Product (t1- to) and time. min.. relationships at different surface heat fluxes,
Btu per sq. ft. ohr an hea source temper ratures, R. t1, pr roduct temperature.

one inch depth. P. to, initial product temperature.

'1 “I. 'd

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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91
s I

rig. 7.4 h(t 1— to)/qs' and 01/32 relationships at four experimental k/hs values for
ground beef (c - 0.75) and a radiant source at 3465.0 R. t1 (maximum) 3 122 F.

8.0 EXAMPLE CALCULATIONS

Example Problem: Determine the processing times at surface
heat fluxes of 1100 and 600 Btu per sq ft-hr at heat
source temperatures of 4230.0 and 2260.0 R. Product
is ground beef: K = 0.276 Btu ft per sq ft-hr F:

S (depth) = 1/12 ft; initial temperature 50 F and final

 

temperature at S is 170 F.
1. Surface temperature for ground beef (Fig. 5.6)

for qs" = 1100 , t 186 F

s
for qs" = 600 , t8 = 165 F

2. Volatile product loss (Fig. 5.7)
for t8 = 186 F , loss a 7.74% per hr
for t8 = 165 F , loss = 4.77% per hr

3. Compute the coefficients of heat transfer:

 

qs" 1100 600 1
h 1.23 1.17
c
h 1.03 1.00
r
hL 5.60 3.50 i
h 7.86 5.67
therefore: k/hs 0.421 0.584

4. Processing times to attain specific temperatures

(Fig. 5.8 to 5.28).

8-2

Product Temperature Processing times, minutes
qs"=1100 qs"=600
4230.0 R 2260.0 R 4230.0 R 2260.0 R

 

122 37 27 57 46
140 7 5 20 15
157 2 3 32 22
170 4 3 26 18

5. Total processing times: minutes.

 

qs
1100 600
Heat source temperature, R
4230.0 50 135
2260.0 38 101

 

10.

11.

9.0 REFERENCES

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1!
d

 

fit”
‘5'. .

12.

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Barber, I. J. (1957)
Volts vs. temperature and radiant heat output of
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Carslaw, H. S. and J. C. Jaeger (1959)
Conduction of Heat in Solids. Oxford University
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Chase, D. R. (1961)
Some aspects of heat transfer in oven design.
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Equipment manufacturers and food processors.
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Proximate composition of American food and materials.
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Study of the thermal properties of foodstuffs
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Physical Chemistry. John Wiley and Sons, Inc.
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Literature review of infra—red energy produced with
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Temperature charts for induction and constant temper-
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"fZfiEfl

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(191% EN 1” l” LEE

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