COMPARISON OF THERMAL PROCESS EVALUATION METHODS
< CONDUCTION
HEATING FOODS I N C Y L I N D R I C A L CONTAIN
by
TRUDI SMITH
.Sc.(Agr.) Honours, U n i v e r s i t y
o f B r i t i s h C o l u m b i a , 197
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS
FOR THE DEGREE OF
MASTER OF SCIENCE
in
THE FACULTY OF GRADUATE STUDIES
(Department of Food
Science)
We a c c e p t t h i s t h e s i s a s c o n f o r m i n g
to the required
standard
THE UNIVERSITY OF B R I T I S H
COLUMBIA
S e p t e m b e r , 1981
© Trudi
S m i t h , 1981
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is
thesis
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i i
ABSTRACT
Five
methods
formula
methods
f o r determining
compared w i t h
a
applicability
to
to
three
thermal
reference
numerical
process
method
conduction
containers. Hypothetical
curves
and
to
heating
lethality
demonstrate
their
temperature
t o diameter
history
(H/D) r a t i o s o f 0.1
3.0 were g e n e r a t e d f o r a r a n g e o f p r o c e s s i n g
conditions
u s i n g computer s i m u l a t i o n . A f i n i t e - d i f f e r e n c e model
on
Teixeira
simulation
The
by
et
based
a l . ( 1 9 6 9 b ) was u s e d a s t h e b a s i s o f t h e
program.
delivered lethality
Z=10C°
was
evaluated
compared t o t h e l e t h a l i t y
t o an
using
organism
each
calculated
characterized
o f t h e methods and
using
the
reference
method.
F o r each of t h e t e s t methods, s i m u l a t i o n data
provided
f o r one m i n u t e i n t e r v a l s , b u t
method, d a t a
Each
were p r o v i d e d
of
the
f o r the
intervention.
s e l e c t e d formula
are
reference
m e t h o d s was a d a p t e d t o
The most s i g n i f i c a n t p a r t o f t h i s
was t h e d e v e l o p m e n t o f a s y s t e m t h a t e n a b l e d
the
operator
adaptation
computer
s e l e c t the l i n e a r p o r t i o n of the heat p e n e t r a t i o n
to f a c i l i t a t e
required
handling
calculation
by
of the parameters f
a l l of the formula
and j
methods.
curve
which
m e t h o d s . A method f o r
l a r g e t a b l e s was a l s o d e v e l o p e d f o r u s e w i t h
of t h e f o r m u l a
were
f o r i n t e r v a l s o f 0.05 m i n .
a l l o w c a l c u l a t i o n s t o be done by c o m p u t e r w i t h o u t
to
were
foods i n c y l i n d r i c a l
centerpoint
f o r cans with height
general
some
For
the general
methods, the d e v i a t i o n s
method w e r e g r e a t e s t
when t h e h e a t i n g
H/D
and
were
small
the
from t h e
reference
r a t e index
unaccomplished
( f ) and
h
temperature
difference
( g ) was l a r g e . Whereas t h e t h e v a l u e
of
the
significant
a c c u r a c y of
most
factor
c a l c u l a t i o n s done u s i n g
the
affecting
general
the
method,
f
h
was
i t d i d not
greatly
a f f e c t t h e p e r f o r m a n c e o f t h e f o r m u l a m e t h o d s . The
factors
that
between
the
most
significantly
f o r m u l a methods and t h e r e f e r e n c e
H/D a n d g. The l a r g e s t d e v i a t i o n s
when
g
were
mostly
in
deviations
method were
a l l cases
occurred
was l a r g e a n d H/D was c l o s e t o u n i t y . T h e s e e r r o r s
implications
retort
influenced
on
the
could
temperature
be
"safe"
side,
significant,
processes.
but
the
energy
especially
use
f o r high
iv
TABLE OF
CONTENTS
ABSTRACT
i i
L I S T OF TABLES
vi
L I S T OF FIGURES
v i i
ACKNOWLEDGEMENTS
viii
INTRODUCTION
1
LITERATURE REVIEW
3
A. F i n i t e - d i f f e r e n c e S i m u l a t i o n
3
B. G e n e r a l M e t h o d s
6
C. F o r m u l a M e t h o d s
7
1 . Background
7
2. Computer
Applications
3. U n c e r t a i n F a c t o r s
10
i n Thermal Process C a l c u l a t i o n s
10
4. P r e v i o u s C o m p a r i s o n s a n d R e v i e w s
EXPERIMENTAL
A. G e n e r a t i o n o f H e a t P e n e t r a t i o n D a t a
13
15
15
1. I n t r o d u c t i o n
15
2. T h e o r y
16
3. Time a n d S p a c e I n c r e m e n t S t u d y
17
4. H e a t T r a n s f e r C o n s i d e r a t i o n s
22
5. P r o c e s s i n g C o n d i t i o n s U s e d
23
6. S i m u l a t i o n P r o g r a m
24
B. P r o c e s s C a l c u l a t i o n M e t h o d s
1 . G e n e r a l Methods
27
27
a. Average t e m p e r a t u r e method
27
b. P a t a s h n i k ' s method
27
V
c . C u b i c p o l y n o m i a l method
2. F o r m u l a
28
Methods
29
a. B a l l ' s t a b l e method
29
b. B a l l ' s e q u a t i o n method
30
c . Stumbo's m e t h o d
30
d. S t e e l e a n d B o a r d ' s method
30
e. Hayakawa's m e t h o d
31
C. A d a p t a t i o n f o r C o m p u t e r S o l u t i o n
32
1 . Table Access
32
2. D e t e r m i n a t i o n o f f a n d j V a l u e s
32
3. R e f e r e n c e M e t h o d a n d C a l c u l a t i o n
of D e v i a t i o n s
34
RESULTS AND DISCUSSION
35
A. G e n e r a l M e t h o d s
35
B. F o r m u l a
39
Methods
1. I n i t i a l
Studies
39
2. E f f e c t s o f Can Shape a n d g V a l u e
43
3. C o m p a r i s o n o f M e t h o d s
52
4. C a l c u l a t i o n E r r o r s i n Terms o f P r o c e s s i n g Time
54
5. P o s i t i o n o f C o l d S p o t
56
i n Container
6. C o n v e c t i o n H e a t i n g P r o d u c t s
C. G e n e r a l C o n s i d e r a t i o n s a n d F u t u r e R e s e a r c h
57
Needs
57
CONCLUSIONS
60
REFERENCES
61
LIST
Table
I
formula
Errors
in
methods
for
OF
TABLES
calculated
various
can
lethalities
sizes
using
5
and
values
of
lethalities
using
5
g
Table
II
Errors
formula
and
Table
f
in
methods
calculated
for
various
thermal
diffusivities
n
III
formula
retort
Errors
methods
in
calculated
for
temperatures
various
lethalities
values
of
using
g
and
5
two
vii
' L I S T OF FIGURES
Figure
1.
Space increment
Figure
2.
Time i n c r e m e n t
Figure
3.
Flow c h a r t
Figure
4.
Effect
study
study
5.
of h e a t i n g
Effect
21
f o r s i m u l a t i o n program
using average temperature
Figure
20
of
26
r a t e on e v a l u a t i o n e r r o r s
method
height
to
36
diameter
ratio
e v a l u a t i o n e r r o r s using average temperature
Figure
6.
Effect
of
average temperature
Figure
7.
g
on
evaluation
on
method
errors
using
method
Errors i n process
38
lethality
determinations
using Ball's tables
Figure
8.
Errors
45
i n process
lethality
determinations
using B a l l ' s equation
Figure
9.
46
Errors i n process
lethality
determinations
u s i n g S t e e l e a n d B o a r d ' s method
Figure
10.
Errors i n process
47
lethality
determinations
u s i n g Hayakawa's m e t h o d
Figure
11.
Errors i n process
48
lethality
determinations
u s i n g Stumbo's m e t h o d
Figure
12.
49
Errors i n process
lethality
determinations
as r e l a t e d t o t h e c o o l i n g l a g f a c t o r
Figure
13.
using
Figure
Errors i n process
five
14.
processing
lethality
51
determinations
f o r m u l a methods
Calculated
time
37
lethal
53
effect
relative
to
55
vi i i
ACKNOWLEDGEMENTS
The
to
Dr.
author wishes
Marvin
encouragement
A.
t o express her sincere
Tung
throughout
appreciation
for h i s interest,
the course
of
advice
this
and
research
project.
She
W.D.
i s t h a n k f u l t o t h e members o f h e r c o m m i t t e e : D r s .
Powrie
Science,
and J . Vanderstoep
and
Engineering,
Dr.
K.V.
for their
Lo,
of t h e Department
Department
interest
i n and
of
of
Food
Bio-resource
review
of
this
thesis.
She
Smith,
i salso extremely g r a t e f u l
t o her husband, R i c h a r d
f o r h i s encouragement, understanding and support,
without which
t h i s s t u d y w o u l d n o t h a v e been
possible.
1
INTRODUCTION
The p r e s e r v a t i o n o f f o o d t o e n s u r e
supply
throughout
earliest
t h e year has always
preservation
curing,
used
Fermentation
centuries
cheese,
methods
mostly
to
processes
to
drying,
also
dairy
adequate
salting
meats
been
products,
and
developed
until
considered
a
preservation
the
late
relatively
as
new
technique.
At
time,
was an a r t , s i n c e l i t t l e
of p r o d u c t i o n of t h e r m a l l y s t a b i l i z e d
eat
was n o t
that
or f a i l u r e
to
and
1 8 t h c e n t u r y , a n d c a n t h u s be
by c a n n i n g t r u l y
safe
for
The a r t
sterilization
about t h e p r i n c i p l e s which
were
fish.
yoghurt
understood
that
and
employed
a n d some v e g e t a b l e s , a s p i c k l e d p r o d u c t s .
o f f o o d p r e s e r v a t i o n by means o f h e a t
food
been i m p o r t a n t . The
preserve
have
preserve
were
an
after
governed
the
considerable
was
success
foodstuffs
periods
of
storage.
Since that time, preservation
has
developed
and
is
no
to
govern
and
thermal
an
art,
kinetic
and
but
a
science.
engineering principles
the e f f e c t i v e n e s s of the process a r e w e l l
research
processing
in
the
refinements
field
in
is
now
terms
of
directed
research
is
processes
the
evaluation
i n terms of t h e i r
which
must
of
lethal
be i n a c t i v a t e d
The
that
understood
towards
p r o d u c t q u a l i t y and
p r o d u c t i o n e f f i c i e n c y . One o f t h e i m p o r t a n t
spores
processing
a stage of c o n s i d e r a b l e s o p h i s t i c a t i o n ,
longer
microbiological,
by
f a c e t s of
thermal
sterilization
e f f e c t on t h e
t o render
this
bacterial
the processed
2
food s h e l f
s t a b l e and
safe to eat.
S i n c e t h e p u b l i c a t i o n o f t h e f i r s t g e n e r a l method
thermal
much
process
has
been
processes
and
e v a l u a t i o n by B i g e l o w
written
about
for thermally s t e r i l i z e d
c o m p a r i s o n s of p r o c e s s
(Hayakawa,
Longley,
the
1977,1978;
coworkers
(1920),
d e t e r m i n a t i o n of
foods.
Several
safe
reviews
e v a l u a t i o n methods have a p p e a r e d
Merson
1966), a l t h o u g h
and
for
et
none
al.,
offers
1978;
Stumbo
extensive
and
numerical
evaluat ions.
In
the
the
l a s t d e c a d e , more a t t e n t i o n has
effects
quality.
of
The
processing
desire
to
on
nutritional
improve
types,
such
overprocessing. Packaging
sizes
and
shapes,
as e l e v a t e d r e t o r t
temperatures,
are
computer technology
these
developments, there
and
process
evaluation
evaluation
reliability
to
applications.
i s an
is
higher
filling
i n t r o d u c t i o n of
making
possible
increasing interest
of t h e c u r r e n t l y a v a i l a b l e
methods.
prepare
methods
would i n c l u d e
reduce
c o n t r o l of p r o c e s s i n g c o n d i t i o n s . B e c a u s e o f
accuracy
was
to
c o n d i t i o n changes,
and
for retort control
precise
t h e need
changes, i n c o n t a i n e r
process
temperatures
to
sensory
i n a move t o
b e c o m i n g i m p o r t a n t . The
more
study
and
and
q u a l i t y and
c o n t r o l p r o c e s s i n g c o s t s have r e s u l t e d
unnecessary
been g i v e n
an
using
traditional
Thus,
in
thermal
t h e o b j e c t i v e of
evaluation
of
the
the
this
selected
a w i d e r a n g e of c o n d i t i o n s t h a t
and
novel
thermal
processing
3
LITERATURE REVIEW
A. F i n i t e - d i f f e r e n c e S i m u l a t i o n
The
finite-difference
Teixeira
et a l .
several
researchers
processing
behind
(1969b)
of f o o d s .
the numerical
s i m u l a t i o n m o d e l i n t r o d u c e d by
has
to
been
study
adapted
and
various aspects
used
of
by
thermal
The o r i g i n a l p a p e r o u t l i n e d t h e t h e o r y
modelling
technique
and i n d i c a t e d t h a t
temperature h i s t o r i e s obtained
u s i n g t h e s i m u l a t i o n program
agreed w e l l with corresponding
temperatures
Heisler
of
compared
integrated
lethality
favourably w i t h other
and
then
of the e f f e c t s of various processing
nutrient
r e t e n t i o n . Optimal
to
nutrient
processing
range of c o n v e n t i o n a l
results
used
processing.
a container
v
was
not
in a
processing
variety
k i n e t i c s of t h e
temperatures.
of
can
of
sizes
survival
after
thermal
indicated that the l o c a t i o n within
where s p o i l a g e w o u l d most
center
were
b u t were g e n e r a l l y f o u n d t o be i n t h e
The r e s u l t s
the
a
t e m p e r a t u r e s on
T h i s same p r o g r a m was u s e d t o d e t e r m i n e s p o r e
distributions
in
temperatures
be a f u n c t i o n o f t h e d e g r a d a t i o n
i n question,
the
methods a v a i l a b l e f o r t h e s e
c a l c u l a t i o n s . The s i m u l a t i o n p r o g r a m was
shown
from
c h a r t s . The s i m u l a t i o n p r o g r a m was u s e d a s a means
calculating
study
obtained
likely
first
occur
t h e c a n , b u t some o t h e r l o c a t i o n
d e t e r m i n e d by t h e c a n g e o m e t r y
and
processing
conditions
( T e i x e i r a e t a l . , 1 9 6 9 a ) . H o w e v e r , f o r most c a n s h a p e s , t h e
greatest
s p o r e c o n c e n t r a t i o n p e r u n i t v o l u m e w o u l d be n e a r
4
the c e n t e r p o i n t ; the e x c e p t i o n being a short can,
tuna
can,
not
fall
for
which the g r e a t e s t spore
t h e h e a t i n g and
c o o l i n g phases of a thermal
Teixeira
the
temperature
during
feasibilty
the
reported
that
that
little
in
could
container
be
geometry
of t h e
process,
midway
through
to
was
to
was
temperature
with
a
the
the
processed
gained
was
thiamine
thermal
b e g i n . I n t h i s way,
al.,
processes
1970)
and
for
nutrient
thermal
limiting
r e t e n t i o n . The
best
puree
From
peak
this
heat
transfer
approximately
point,
was
rectangular
retort
final
cooling
i n t o the
package
i n terms of t h i a m i n e
concept
part
outer
layer,
retention.
extended to modelling
containers
(Manson
of
et
t o p e a r s h a p e d c o n t a i n e r s (Manson e t a l . ,
1974). In both c a s e s ,
evaluate
this
r a t i o s close to
allowed to drop slowly u n t i l
simulation
from
the
a
foods.
p r o f i l e s d u r i n g the e a r l y
process.
o p t i m i z e the p r o c e s s
as
r e t e n t i o n i n pea
temperature
to
retort
process
t r a d e d o f f a g a i n s t o v e r p r o c e s s i n g of t h e
The
during
process.
height to diameter
i n the poorest
increasing
was
can
of a t h e r m a l
r e t o r t c o n t r o l programs f o r t h i a m i n e
temperature
a
varying
retention
f a c t o r , w i t h cans having
resulting
of
course
means t o i m p r o v e t h i a m i n e
a p p r o a c h , but
within
of
e t a l . (1975) u s e d t h e s i m u l a t i o n p r o g r a m
investigate
had
may
on t h e c e n t e r p l a n e . T h e s e e f f e c t s a r e a r e s u l t
gradients that exist
unity
a
concentration
the temperature
They
like
the
simulation
processes
model
i n terms of s p o r e
r e t e n t i o n . Whereas b o t h
was
used
to
survival
and
of these models
considered
5
three d i m e n s i o n a l heat t r a n s f e r , Ohlsson
(1980b)
simplified
the s i m u l a t i o n model f o r r e c t a n g u l a r c o n t a i n e r s t o c o n s i d e r
only
one
dimensional
dimension.
cannot
significantly
the
be
pouches
approach
was
on k i n e t i c
if
other
tests
two.
and
semi-rigid
thin
infinite
is
Ohlsson
with
trays.
effect
on q u a l i t y
not
reported
optimization
flat
The
well
cans,
simulation
processes
in
f a c t o r d e g r a d a t i o n , based
f a c t o r s o u t l i n e d by O h l s s o n
in
an
dimension
conducted
showed t h a t p a c k a g e t h i c k n e s s was
factor
one
to
used t o e v a l u a t e v a r i o u s r e t o r t
of t h e i r
smallest
p r e d i c t e d by t h e m o d e l a g r e e d
penetration
retort
the
i s acceptable for very
used
l e s s than the
temperatures
w i t h heat
terms
through
w h i c h b e h a v e i n a manner s i m i l a r
but
that
flow
This s i m p l i f i c a t i o n
packages,
slab,
heat
(1980a).
The
study
t h e s i n g l e most i m p o r t a n t
since,
at
high
processing
t e m p e r a t u r e s , o v e r c o o k i n g a t t h e s u r f a c e became
a
if
up t o
15mm
140°C
did
t h e p a c k a g e was
not v e r y t h i n . With packages
i n t h i c k n e s s , p r o c e s s i n g t e m p e r a t u r e s o f up
not
result
package
in
thickness
conditions
the
was
tended
t e m p e r a t u r e s of
The
significant
damage.
However, as
optimal
processing
conventional
processing
increased,
towards
120 t o 125°C.
f i n i t e - d i f f e r e n c e m o d e l has a l s o been a d o p t e d
development
of
tables
e s t i m a t i o n . J e n e t a l . (1971)
develop
surface
to
problem
tables
for
for
process
first
calculation
used
evaluation
this
o f mass a v e r a g e
method
for
and
to
lethality
a n d n u t r i e n t d e s t r u c t i o n . T h e s e t a b l e s were t h e n r e f i n e d
by
6
Purohit
and
Stumbo
calculating
formula
(Stumbo,
single
point
1973)
and
lethality
presented
a c c o r d i n g t o Stumbo's
method.
B. G e n e r a l
Methods
The
general
standard
thermal
center
method
method
determination.
This
introduction
long
history
(Bigelow
of
cycles
a
e t a l . , 1920)
lethality
w i t h the
container
a
an
hypothetical
and
t h e use
The
thermal
of l e t h a l
r a t e paper
Since
its
improvements
and
history
container
its
and
This
history
temperature
is
the
if
i s used, but,
data are obtained
(Ball,
Olson,
temperature
a
lethality
methods
time
are
degraded
from
plotting
the
very
the
within
a
such as s l o p e
r e c o r d of
i n most p r a c t i c a l
at
finite
data
and
values.
consuming
optimum
by
1940).
on
point
continuous
f u n c t i o n and
give very accurate
1928)
i s based
time
and
can
measuring
estimate
areas,
to
graphical
their precision
physical
the
intervals.
be e x p e c t e d
However,
and
situations,
Even s o , t h e g r a p h i c a l forms of t h e g e n e r a l method
continuous
concept
s h o u l d n o t be a f f e c t e d by
p e n e t r a t i o n curve
true
the
determination
coldest
performance
a t t r i b u t e s of the heat
curvature.
of
time curve
( S c h u l t z and
g e n e r a l method l e t h a l i t y
the temperature
thermal
death
measured
the
process.
many
about
during
s i m p l i f i c a t i o n s h a v e been i n t r o d u c e d , i n c l u d i n g
of
the
information
spores
of
considered
process
combines
of b a c t e r i a l
cooling
been
thermal
method
temperature
and
has
for
destruction
heating
the
for
is
limitations
on
as w e l l as
the
7
inevitability
the
o f human e r r o r . T h e s e f a c t o r s
popularity
of numerical
contribute
to
g e n e r a l methods w h i c h a r e n o t
subject to "operator" d i f f e r e n c e s .
Patashnik
process
(1953) i n t r o d u c e d t h e concept
lethality
lethality
integration,
accuracy
or
in
variability
conclusion
is
4
to
errors
from
lost
the
5
min
time
were
t o can.
more
commonly
used,
of
the
due
to
the
the trapezoidal
1953).
between
Patashnik s
1
t o be a d e q u a t e ,
the
T h i s was a v e r y
accurate
of
i s not required.
within
i n 1953, b u t a t p r e s e n t ,
possible
forms
interval
intervals
a d d i t i o n a l e f f o r t . C u r r e n t l y , time
are
using
(Patashnik,
that
can
improved
of t h e data
on
measurements
suggested
resulting
make
the o r i g i n a l
depending
temperature
integration
r a t e ( L ) v s . t i m e . T h i s method i s
method s i n c e g r a p h i n g
Some d e g r e e o f
study
trapezoidal
p l o t as l e t h a l
much f a s t e r t h a n
general
using
of c a l c u l a t i n g
appropriate
technological
analysis,
inherent
advances
with
little
i n t e r v a l s o f one
minute
improvements i n data
logging
equipment.
C. F o r m u l a M e t h o d s
1 . Background
Although
sufficient
process,
g e n e r a l methods f o r p r o c e s s
f o r determining
they a r e
processing
time
not
very
required
the
lethal
useful
to
evaluation
e f f e c t of a given
f o r determining
deliver
are
a
given
the
target
8
lethality.
I f a g e n e r a l m e t h o d were t o
purpose,
of
experimental
conditions
lethality.
these
A
which
evaluated
using
"trial
in
interpolation.
and e r r o r "
to
give
an
p r o c e s s e v a l u a t i o n and
order
t o reduce
which
include
heating
temperature
is
extended
of the required
l e t h a l i t y . This
determination
is
approach
tedious
and
product
semilogarithmic
enter
The
initial
bacterial
temperature,
and
time
for this
first
when
final
plotted
as the temperature
on
difference
(Bigelow
et
a l . ,
l i n e was c o m b i n e d w i t h t h e
order thermal death
kinetics
s p o r e s , and i n t e g r a t e d over t h e d u r a t i o n o f
the l i n e a r p o r t i o n s of the process curve.
heat
factors
r e l a t i o n s h i p t h a t was f o u n d t o e x i s t
coordinates
relationship describing
various
t e m p e r a t u r e . The b a s i s o f t h e method
temperature
equation
the
i n t o t h e c a l c u l a t i o n " . These
behavior,
linear
for coordinating
between t h e p r o d u c t and i t s environment
1920).
(1923)
the time necessary t o obtain r e s u l t s ,
and r e t o r t
the almost
between
many
a
t e c h n i q u e c o u l d be a p p l i e d i n
f o r m u l a m e t h o d was i n t r o d u c e d by B a l l
factors
for
delivered
Alternatively,
approximation
as w e l l as t o o b t a i n a b a s i s
was
range
consuming.
The f i r s t
"in
this
over a
of
the e x p e r i m e n t a l heat p e n e t r a t i o n curve
shortened
time
terms
for
p r o c e s s t i m e c o u l d be d e r i v e d f r o m
process time f o r a s e l e c t e d t a r g e t
for
used
r u n s must be c o m p l e t e d
required
results
graphical
or
and
be
After
study
of
p e n e t r a t i o n c u r v e s , B a l l d e v e l o p e d an e m p i r i c a l
formula t o d e s c r i b e the n o n - l i n e a r p o r t i o n of
the
cooling
9
curve,
which
hyperbolic
method,
al.
was
found
to
relationship.
the
review
be
For
well
further
estimated
details
of i t s t h e o r e t i c a l
by
on
an
this
b a s i s by M e r s o n e t
( 1 9 7 8 ) i s recommended.
All
anyone
of these
details,
employing
Ball's
however,
are
transparent
f o r m u l a method, s i n c e t h e r e s u l t s
of t h e i n t e g r a t i o n s a r e p r o v i d e d i n t a b u l a r
some
of
the u n d e r l y i n g assumptions
form.
t h a t were
However,
important i n
t h e d e v e l o p m e n t o f t h e method a r e o f t e n n o t v a l i d ,
importance
of
meeting
to
these
assumptions
is
and
not
the
well
understood.
One o f t h e most
s i g n i f i c a n t , a n d most
often
invalid,
assumptions
i s t h a t t h e c h a r a c t e r o f t h e c o o l i n g c u r v e does
not
Board
vary.
retort
e t a l . (1960) d i s c u s s e d f a c t o r s ,
pressure,
conduction
which
affect
cooling
such as
behavior
of
h e a t i n g f o o d s , and n o t e d t h a t B a l l ' s method f o r
process
lethality
calculation
process
lethality,
but t o a v a r i a b l e e x t e n t , depending
several
factors
processing
including
usually
been
conditions.
many
modifications
f o r m u l a method
suggested
a l . , 1969,1971;
Hicks,
and
1958; P f l u g ,
Longley,
Hayakawa,
Stumbo,
1951;
Griffin
1970; H e r n d o n e t a l . ,
1968; S t e e l e a n d
1966;
there
( B a l l and Olson,
1957; F l a m b e r t a n d D e l t o u r , 1972b; G i l l e s p y ,
et
on
t h e n a t u r e of t h e p r o d u c t and t h e
Since the i n t r o d u c t i o n of B a l l ' s
have
underestimated
Board,
1979;
1968;
Stumbo
1973). These m o d i f i c a t i o n s o f
t h e f o r m u l a method d e a l i n v a r i o u s ways
with
the
cooling
10
portion
of
a
thermal
process,
using
e m p i r i c a l r e l a t i o n s h i p s between t h e
line
portions
of
the temperature
more a c c u r a t e l y e s t i m a t e
p o r t i o n of t h e r m a l
theoretical
curved
and
straight-
h i s t o r y curve
the l e t h a l e f f e c t of
and
to t r y to
the
cooling
processes.
2. C o m p u t e r A p p l i c a t i o n s
One
was
to
of t h e aims of the development of f o r m u l a
simplify
process
computer t e c h n o l o g y
in
t h e use
Tung and
procedures
the
suggested
to f a c i l i t a t e
of
the
approaches f o r computer
calculations
a
have
series
manipulation
techniques
H a y a k a w a , 1967)
(Manson e t
T e i x e i r a et a l . ,
al.,
1969a,
of
computer
statistical
using
treatment
A number o f
of
thermal
other
process
either adaptations
f o r m u l a m e t h o d s ( H a y a k a w a , l 9 7 7 ; M a n s o n and
T i m b e r s and
interest
evaluation i s high.
calculations.
appeared,
years
r a p i d h a n d l i n g of l a r g e
p e n e t r a t i o n d a t a and
results
recent
become more a c c e s s i b l e and
(1978)
volumes of heat
of
In
of the computer f o r p r o c e s s
Garland
oriented
has
calculations.
methods
Zahradnik,
of
1967;
or f i n i t e - d i f f e r e n c e s i m u l a t i o n
1970;
Manson
et
al.,
1974;
1969b).
3. U n c e r t a i n F a c t o r s i n T h e r m a l P r o c e s s C a l c u l a t i o n s
Since
process
into
perspective
subject
work d e a l s w i t h t h e
c a l c u l a t i o n methods, i t i s of
uncertainty
years,
this
various
into thermal
"accuracy"
some
value
f a c t o r s which tend
process
of
to
thermal
to
put
introduce
determinations. This i s
that
has
r e c e i v e d c o n s i d e r a b l e a t t e n t i o n over
since
i t
is
only
on
the
basis
of
a
a
the
sound
11
understanding
of
the
role
t h e r m a l p r o c e s s e s c a n be
Uncertainties
determination
is
with
(Herndon,
since
reduced
by
from
container
the
This
into
to
greatly
thermal
container
Secondly,
process
magnitude of s a f e t y
dealt
be
significantly
the
practices.
control
non-homogeneity
still
be
can
of
an
most
important
1954).
control
factors
temperature
problems
required.
or
or process time
factors w i l l
there
due t o t h e
manufacturing
thermally processed products w i l l
temperature
process
being
formulation or f i l l
but
(Evans and Board,
are
cannot
in
by p o o r
reduced,
safe
i s one o f t h e most i m p o r t a n t
variability
improvement
processing
that
developed.
introduced
1971).
V a r i a b i l i t y caused
factor
factors
nature of the m a t e r i a l s which
factors
be
these
i n a number o f d i f f e r e n t w a y s . F i r s t l y ,
variability
biological
are
of
is
can
Where
a f f e c t the
control
pressure,
cooling
water
not
greater
safety
good,
be r e q u i r e d .
Thirdly,
the
applicability
of
bacteriological
k n o w l e d g e i s somewhat u n c e r t a i n , s i n c e v a r i o u s f a c t o r s
as t h e t h e r m a l h i s t o r y and s u s p e n s i o n
spores
are
organisms
effects
lethality
minor
known
to affect
i n question (Hicks,
Hicks
(1952) p r o v i d e d a
of
of
some
of
these
media
bacterial
the thermal r e s i s t a n c e of the
1961).
brief
table
variables
of a t h e r m a l p r o c e s s . I n terms
variation
of
such
on
of
approximate
the
of spore
delivered
survival,
i n p r o c e s s c o n t r o l was shown t o be o f
less
12
significance
than e r r o r s i n the
estimates
of t h e r m a l
p a r a m e t e r s . Ross e t a l . (1979) a l s o p r e s e n t e d
on
t h e e f f e c t s of v a r i a b i l i t y
Lund
of
(1978) p r e s e n t e d
various
f a c t o r s on
the
safety
"
appropriate
a study
d e a l i n g w i t h the e f f e c t s
c a l c u l a t e d process
of t h i s
f a c t o r s . Tung and
statistical
appropriate
only
use
the
approach
of
using
(1978)
container
the
in
confidence
o f how
of
it
is
not
safety
unnecessarily
through
Hence, i t
important
is
reliability
of
these
to
given
determination
the
methods i n o r d e r
and
information
a p p l i c a t i o n of
d e a l t w i t h as a s e p a r a t e
issue.
penetration
having
that
a
those
without
variabilty
of
process
introduce
error
calculation
determine
i s more
than
the c a l c u l a t i o n
inappropriate
a
tests.
the
is
methods.
accuracy
t o have
t h a t the c a l c u l a t e d "answers" are as a c c u r a t e
be,
that
approach,
to
as
considering
chooses to deal with
reasonable
a
determining
regimes
conventional
one
of
i n a heat
heating
in p h y s i c a l f a c t o r s which a f f e c t
lethality,
in
made
suggest
approach
r e q u i r i n g more numerous h e a t p e n e t r a t i o n
Regardless
using
to deal with t h i s v a r i a b l i t y
slowest-heating
calculated
information
than the c o n v e n t i o n a l
degree
lethality
c o n c l u s i o n was
Garland
t e s t . This approach r e s u l t s
greater
studies
i n measured q u a n t i t i e s .
M o n t e C a r l o p r o c e d u r e ; h o w e v e r , no
to
some
death
as
on
and
confidence
they
can
hand.
The
s a f e t y f a c t o r s can
then
be
13
4.
P r e v i o u s C o m p a r i s o n s and
Although
review
Hayakawa
Reviews
(1978)
produced
a
comprehensive
of the development of a v a i l a b l e p r o c e s s
methods,
dealing
limitations,
no
with
some
numerical
of
their
calculation
assumptions
and
d a t a were p r o v i d e d by w h i c h
compare t h e m e t h o d s . M e r s o n e t a l . (1978) b r i e f l y
to
discussed
v a r i o u s c a l c u l a t i o n m e t h o d s , r e c o m m e n d i n g H a y a k a w a ' s method
(1970)
as
comparisons
the
most
were
not
versatile;
however,
p r o v i d e d . Stumbo and
Longley
(1966)
methods
which
calculated using
Ball's
p r o v i d e d a summary o f c o m p a r i s o n s o f a
indicated
original
calculated
conditions
that
lethality
method
(1923)
using
values
were
their
new
i n v e s t i g a t e d was
numerical
5-15%
few
lower
than
those
t a b l e s ; however, the range of
not c l e a r . Board et a l .
(1960)
p r o v i d e d a c o m p a r i s o n o f t h e g e n e r a l method ( B i g e l o w e t a l .
1920),
Ball's
indicating
method,
t h a t i n most c a s e s
process
lethality
process
lethality.
In
food
and
and
v i e w of t h e
industry,
it
determining
r e a s o n i n g has
with
B a l l ' s method
importance
of t h e r m a l
i s s u r p r i s i n g how
required
and
thermal
canning
w o u l d be u n n e c e s s a r y .
activity
terms
of
p r o c e s s i n g i n the
a t t e n t i o n has
of methods
so
Perhaps
few
safety i n recent years
investigation
in
overestimated
processes.
been
development
However,
of
(1951)
underestimated
little
reliability
been t h a t t h e r e h a v e
commercial
method
G i l l e s p y ' s method o f t e n
been g i v e n t o t h e a c c u r a c y
for
Gillespy's
new
the
and
used
the
problems
that
this
research
modified
14
c a l c u l a t i o n methods would
In
any
which
case, l i t t l e
t o judge t h e
calculation
start
to f i l l
this
It
and
chosen,
t h e most
various
including
was
methods. Computer
in
into
been
of
previously
process
cited,
b o t h t h e most w i d e l y u s e d
the
evolution
histories
as
five
methods
also allowed the
the
calculation
the
means
to
t o be e v a l u a t e d u s i n g t h e s e
not
introduce
t h e s t u d y a n d was w e l l a c c e p t e d
processing
possible.
of process
s i m u l a t i o n was c h o s e n
temperature
T h i s approach
range
thermal
the goal of t h i s p r o j e c t to
methods
methods, s i n c e s i m u l a t i o n would
errors
available
r e c e n t l y developed, as r e p r e s e n t a t i v e s of
stages
generate
of
i n f o r m a t i o n gap.
Of t h e many f o r m u l a
were
conclusion.
n u m e r i c a l i n f o r m a t i o n i s a v a i l a b l e by
merits
methods.
tend to dispute t h i s
investigation
c o n d i t i o n s than would
extraneous
i n the f i e l d .
of
a
wider
o t h e r w i s e have
15
EXPERIMENTAL
A. G e n e r a t i o n
of Heat P e n e t r a t i o n Data
1. I n t r o d u c t i o n
Thermal h i s t o r y curves
cylindrical
f o rconduction
c a n s o f v a r i o u s s h a p e s a n d s i z e s were
u s i n g a FORTRAN l a n g u a g e s i m u l a t i o n
Teixeira
h e a t i n g foods i n
e t a l . (1969b).
program
o f a g r e a t many p r o c e s s i n g
short
and a t a r e a s o n a b l e
time,
w o u l d be v e r y
adapted
Simulation techniques
investigation
generated
from
allowed the
situations
in a
cost. Pilot plant studies
t i m e c o n s u m i n g a n d w o u l d be l i m i t e d
in
scope
by t h e a v a i l a b i l i t y o f s u p p l i e s ( c o m m e r c i a l l y a v a i l a b l e c a n
sizes)
and t h e p h y s i c a l l i m i t a t i o n s of a v a i l a b l e
(retorts
in particular).
hindered
and
Physical experimentation
by measurement a c c u r a c y
by o t h e r e x p e r i m e n t a l
pilot
plant
Simulation,
and
equipment
i s also
only
c o n t r o l of
to
achieve.
however, a l l o w s v e r y p r e c i s e "process
good
interacts with i t s
complication
control"
by u n c o n t r o l l a b l e
errors.
however,
of
the
i n d e f i n i n g t h e s y s t e m a n d how
environment,
to
avoid
model o r u n w a r r a n t e d
unnecessary
simplification.
f i n i t e - d i f f e r e n c e model used i n t h i s s t u d y has a
basis
in
are
a s t h e model used t o d e s c r i b e t h e system i n
q u e s t i o n . C a r e must be t a k e n
The
difficult
r e s u l t s of a s i m u l a t i o n experiment,
as
i s also
o f a t b e s t ± 0.5C°
e r r o r s . S t r i c t process
factors leading to experimental
it
limits
therefore the r e s u l t s are not clouded
The
equipment
engineering
p r i n c i p l e s of heat
sound
t r a n s f e r and has
16
been shown t o be an a p p r o p r i a t e s y s t e m
thermal p r o c e s s i n g of canned
2.
for
simulation
of
foods.
Theory
The
finite-difference
simplification
for a f i n i t e
is
dT
1 oT
d T
1 dT
or
r or
dy
o ot
2
was
r
2
is
2
radial
distance
a x i s , y i s v e r t i c a l d i s t a n c e from
thermal
solution
diffusivity
and
is
the c e n t e r
time.
the
plane,
u s i n g the f i n i t e - d i f f e r e n c e form of t h i s
equation
program.
demonstration
(adapted
of the f i n i t e - d i f f e r e n c e method f o r
heat
flow i s h e l p f u l
dimensional
in understanding
model
for
cylinder.
The
calculating
the temperature
the time
from
numerical
following
t
1964)
two
equation
A
the b a s i s of the s i m u l a t i o n
The
Fourier
cylinder:
where T i s t e m p e r a t u r e ,
a
b a s e d on t h e
of t h e d i f f e r e n t i a l heat c o n d u c t i o n
2
central
m o d e l was
derivation
i n t e r v a l At
Equation
for
d i m e n s i o n , x:
from
heat
one
Kreith,
dimensional
t h e more c o m p l i c a t e d
transfer
results
from
in
an
in
a
finite
equation
for
change i n volume element n
over
t=t t o t=t+1.
unsteady
state
heat
conduction
in
o T
2
1
oT
a ot
For
f i n i t e A t and
Ax:
1
a
A T
t
At
ox
A
—
(2)
2
2
X
Ax
T
2
(3)
one
17
The
subscripts
t
and
x
indicate
whether
t h e change of
t e m p e r a t u r e w i t h t i m e , t , o r l o c a t i o n , x, i s b e i n g
referred
to.
Rewrite left-hand side
as:
A T
^ t
1
1
a
=
^
T
Recombining
T
n
+
1
T
this
T
T
=
n 1
~
+
2 T
n
was
the
transfer
the
(5)
T
n-1
(6)
2
was
applied
equations
for
finite-difference
to
the
heat
the
finite
transfer
study.
adapted
developed
applications.
+
technique
FORTRAN l a n g u a g e
temperature
t
n-1
Ax
Ax
heat
in this
study
although
- n
to develop
The
T
Ax
finite-difference
model used
T
Ax
At
differential
cylinder
(4)
gives:
a
The
1
At
Ax
2
T"
_n
as:
t
t
t
n+1 ' n _ n ~
Ax
I
-
t + 1
o
At
Rewrite right-hand side
Ax
1 T
_ _n
1
I t can
program
s i m u l a t i o n program d e v e l o p e d f o r
from
Teixeira
program
simulate
and
is
et
a l .
(1969b),
i s more v e r s a t i l e
processes
with
any
in i t s
time-
easily modified for specific
purposes.
3. Time and S p a c e I n c r e m e n t
To
apply
cylindrical
the
Study
finite-difference
container,
the
container
approach
was
divided
to
a
into
18
l a y e r s of equal thickness v e r t i c a l l y ,
thickness
and
rings
of
equal
horizontally.
The s i z e o f t h e s e d i v i s i o n s h a s a
b e a r i n g on t h e s t a b i l i t y
o f t h e model and t h e a c c u r a c y w i t h
which
i t s i m u l a t e s a heat t r a n s f e r p r o c e s s .
A s t u d y was u n d e r t a k e n
to
sizes
of t i m e and space
Jaeger
(1959) i n d i c a t e d t h a t
stability
of the f i n i t e
determine
i n c r e m e n t s t o be u s e d . C a r s l a w a n d
a
sufficient
aAt
Ax
either
radial
solution
values
1
< -
cost.
as
or
Ax
axial
and
2
2
Ax
direction.
and
A t mean
At
The
spacing i n
accuracy of the
decrease,
but
increased computation
smaller
time and
I t i s t h e r e f o r e d e s i r a b l e t o s e l e c t Ax a n d A t
large
as
for
(7)
t h e m o d u l u s a n d Ax i s t h e g r i d
i n c r e a s e s as
of
condition
difference solution i s :
M =
where M i s c a l l e d
the appropriate
i s permissible
for
t h e degree
to
be
of accuracy
required.
Most of t h e t e s t
runs f o r the increment study used can
d i m e n s i o n s o f 4 cm r a d i u s a n d 8 cm
diffusivity
initial
to
66°C
height
and
a
thermal
o f 0.100 c m / m i n . R e t o r t t e m p e r a t u r e was
2
temperature
after
121°C,
71°C, a n d w a t e r a t 21°C c o o l e d t h e c a n s
a 40 m i n p r o c e s s t i m e . O t h e r p r o c e s s
and c a n s i z e s t e s t e d c o n f i r m e d t h a t d i f f e r e n c e s
for
times
other
c o n d i t i o n s were n o t s i g n i f i c a n t .
Teixeira
e t a l . (1969b) r e p o r t e d t h a t time
of 0.125 m i n a n d a v o l u m e e l e m e n t
10 v e r t i c a l
d i v i s i o n s were used
matrix with
for
their
increments
10 r a d i a l a n d
work.
Although
19
f i g u r e s were p r o v i d e d t o v e r i f y
t h e i r c h o i c e , no d e t a i l s o f
t h e s t u d y were p r o v i d e d . The r e s u l t s o f t h e i n c r e m e n t
done
here
were
showed, f o r t h e
calculated
less
optimistic
main
process
integrated
15x15 m a t r i x was u s e d
than
used
lethality
Teixeira s.
They
the
that
1
in
tests,
d i d not s t a b i l i z e
may
until a
( F i g u r e 1) w h e r e a s T e i x e i r a ' s r e s u l t s
i n d i c a t e d a l e v e l i n g o f f f o r a 10x10 m a t r i x . T h i s
disagreement
be
due
to
differences
apparent
in
the
c o n d i t i o n s b e t w e e n t h e two s t u d i e s . S i n c e t h e c o s t
simulation
increases
as
h o r i z o n t a l and v e r t i c a l
cost
the
product
increments, a
of
matrix.
Whereas
at 8 increments
15x15
increment
Teixeira's figures
per min, t h i s
o f f d i d n o t occur a t fewer
study
than
study
cylinder
temperature
strongly
were
was
was
as
of
not
the
major
affected
the
number o f
matrix
would
indicated that
20 i n c r e m e n t s
10x10
the
The
grid
leveling
per min.
at the
interest.
by
for a
center
of
centerpoint
spacings
as
i n t e g r a t e d l e t h a l i t y v a l u e s were. At t h e
o f a 40 m i n p r o c e s s , t h e p r e d i c t e d c e n t e r
temperatures
108.21°C a n d 108.23°C f o r a 10x10 a n d a 2 5 x 2 5 e l e m e n t
matrix, respectively.
temperature
time
of
indicated leveling o f f
For t h i s work, o n l y t h e temperature
end
the
test
2.25 t i m e s a s much t o u s e a s a 10x10 m a t r i x . F i g u r e 2
shows t h e r e s u l t s o f t h e t i m e
the
study
predictions, a grid
intervals
study, time
In order t o
of
reliable
center
s p a c i n g o f a b o u t 0.5 cm a n d
0.05 m i n s h o u l d be s u f f i c i e n t .
increments
t o 0.4 cm were u s e d ,
obtain
In t h i s
o f 0.05 m i n a n d g r i d s p a c i n g s o f 0.3
corresponding
t o M values of
0.02
to
Integrated
OZ
lethality
(z«10C°).
min
8
Time
Figure
2.
Time increment
12
increments
study
20
16
per
f o r 10x10
m in
matrix.
24
2 8
22
0.07 f o r t h e c o n d i t i o n s t e s t e d , w e l l b e l o w
for
stability
radial
the requirements
o f t h e s o l u t i o n . The number o f v e r t i c a l a n d
elements
used ranged
f r o m 6 t o 25 a n d was d e t e r m i n e d
f o r e a c h s i m u l a t i o n by t h e c o n t a i n e r shape a n d s i z e .
4. H e a t T r a n s f e r C o n s i d e r a t i o n s
The
r a t e of temperature change a t t h e c e n t e r of a
can
d u r i n g a t h e r m a l p r o c e s s i s d e p e n d e n t upon t h e s u r f a c e h e a t
transfer
coefficient,
the
thermal
p r o d u c t and t h e temperature
heat
transfer.
The
diffusivity
gradients
temperature
which
bring
between
the
believe
that
product
and
i t s environment i s
temperature. Although there
the
thermal
change w i t h temperature
the thermal d i f f u s i v i t y
constant
throughout
heating
curve,
facilitate
was
the
work. T h i s a s s u m p t i o n
diffusivity
(Evans,
comparison
previously
coefficient
simplification
phase,
was
is
However,
cooling
in
was
cited,
to
a product
may
considered
the
desired
certainly
steam
of
the
considered
is
reason
1958), d a t a a r e l i m i t e d and
of the l e t h a l i t y
when s a t u r a t e d
approaches
to
process f o r the purposes
In a l l of t h e a p p l i c a t i o n s
model
is
of
therefore
results
which
about
temperature
l a r g e , and d e c r e a s i n g as t h e p r o d u c t t e m p e r a t u r e
the environment
to
simplest
in
this
study
to
appropriate
methods.
finite-difference
surface
be
of t h i s
of
calculation
the
be
type
heat
transfer
infinite.
This
f o r the heating
i s used as the h e a t i n g
usually
the
g r a d i e n t s change over t h e
c o u r s e o f t h e p r o c e s s , b e i n g g r e a t e s t when t h e
difference
of
medium.
a c c o m p l i s h e d by f i l l i n g t h e
23
r e t o r t w i t h c o l d w a t e r , and
situation
low
thermal
transfer within
number
transfer
is
at
conductivity,
the product i s
a
the
the
transfer
to
ratio
the
factor.
of
the
infinite
in
to
heat
s u r f a c e . F o r B i o t numbers o f 40 o r more,
f o r B i o t numbers
introduced
The
internal
resistance
s u r f a c e h e a t t r a n s f e r c a n be c o n s i d e r e d t o be
may
this
i n most c a s e s h e a t
limiting
dimensionless
r e s i s t a n c e t o heat
even
in
i s not as good. However, s i n c e f o o d p r o d u c t s have
relatively
Biot
s u r f a c e heat t r a n s f e r
as
small
by t h i s a s s u m p t i o n
as
10
infinite,
little
error
o v e r e s t i m a t e the r a t e of heat
some c a s e s . T h i s w o u l d
indicating
a
process
is
(Heldman, 1975). Assuming
heat t r a n s f e r c o e f f i c i e n t d u r i n g the c o o l i n g
tend to s l i g h t l y
and
result
in
more
t o have s l i g h t l y
rapid
cycle
transfer
cooling,
less lethal
t h a n i t w o u l d h a v e i f c o o l i n g were s l i g h t l y
an
effect
slower.
5. P r o c e s s i n g C o n d i t i o n s U s e d
For
most
temperature
performed
lethality
Cooling
of
was
the
120
processes
°C,
t o t e s t whether
calculation
water
temperature,
but
be
was
consistent
h
temperature
collapse to cooling
would
be
the
case
tests
errors
and
for
a
p r o c e s s i n g s i t u a t i o n . Thermal
Instant
continuous
were
retort
°C
were
process
temperature.
retort
assumptions
environment
temperature
in
below
the
tables.
instant
water
100 C°
with
the
a t 140
were a f f e c t e d by r e t o r t
B a l l ' s a n d Stumbo's f / U t o g
retort
some
the r e l a t i v e
temperature
to
simulated,
comeup
of
to
temperature
assumed,
as
r a t h e r than batch
p r o p e r t i e s were h e l d c o n s t a n t
24
within
each
simulation,
distribution
the
was
and
uniform.
the
initial
temperature
R e s i s t a n c e t o heat t r a n s f e r a t
s u r f a c e was c o n s i d e r e d t o be n e g l i g i b l e , a n d t h e e f f e c t
of
headspace
on h e a t t r a n s f e r was n o t c o n s i d e r e d .
Thermal
diffusivity
v a l u e s r a n g i n g f r o m 0.075 t o 0.125
c m / m i n were u s e d , c o v e r i n g t h e r a n g e o f t h e r m a l
properties
2
e n c o u n t e r e d c o m m e r c i a l l y f o r c o n d u c t i o n h e a t i n g foods (Rha,
1975).
Various
temperature
initial
- product
temperature
center temperature)
and g v a l u e s ( t e m p e r a t u r e d i f f e r e n c e
0.05
to
ratios
can
differences
at
(retort
from
15 t o 95 C°
steam
o f f ) from
15 C° were i n v e s t i g a t e d . H e i g h t t o d i a m e t e r
f r o m 0.1 t o 3 were s t u d i e d . F o r most
of
(H/D)
the
study
d i a m e t e r s o f 8 cm were u s e d , e x c e p t f o r c a n s w i t h v e r y
s m a l l H/D
ratios
(0.1 a n d 0.25) f o r w h i c h l a r g e r
diameters
w e r e u s e d , t o a l l o w a minimum h e i g h t o f 2 cm t o be u s e d .
6. S i m u l a t i o n
The
and
a
Program
simulation
number
calculations
of
to
subroutines
that
performed
program
iterative
f o l l o w the temperature changes,
process l e t h a l i t y ,
to
program c o n s i s t e d of a d r i v e r
calculate
and c o n t r o l t h e program's o u t p u t .
Input
t h e p r o g r a m i n c l u d e d c o n t a i n e r d i m e n s i o n s , t h e number o f
space
increments
i n each d i r e c t i o n , t h e time increment t o
be u s e d a n d t h e t h e r m a l d i f f u s i v i t y
temperature
and
other
process
p r o v i d e d . Any u n i t s c o u l d be u s e d
of the p r o d u c t .
specifications
Program
outputs
were
also
f o r these v a l u e s , as long
a s t h e u n i t s f o r a l l q u a n t i t i e s were c o n s i s t e n t
other.
Retort
included centerpoint
with
each
temperatures
25
logged
at
lethality
10C°.
one
minute
intervals,
and
of the p r o c e s s a t the can c e n t e r
Figure
3
is
a flowchart
the
equivalent
f o r a z value
of
t h a t o u t l i n e s t h e f l o w of
c o n t r o l b e t w e e n t h e m a i n p r o g r a m and t h e
subroutines.
26
Figure
3.
Flowchart
for simulation
program.
27
B. P r o c e s s
C a l c u l a t i o n Methods
1. G e n e r a l
Methods
Three
"general"
determination
relative
examined
for
to
process
determine
lethality
their
accuracy
t o t h e r e f e r e n c e method t h a t was c o n s i d e r e d t o
equivalent
history
were
methods
to
a
continuous
be
i n t e g r a t i o n of the l e t h a l i t y
curve.
a. A v e r a g e t e m p e r a t u r e
method
The a v e r a g e t e m p e r a t u r e
method s t u d i e d was i d e n t i c a l
r e f e r e n c e m e t h o d ( d e s c r i b e d i n s e c t i o n C3) e x c e p t
interval
between
that
the
d a t a p o i n t s was i n c r e a s e d t o one m i n u t e .
T h i s m e t h o d was a v a r i a t i o n o f P a t a s h n i k ' s
extrapolation
of
lethality
the
for
to the
the
technique
simulation
used
model
method
for
and
an
accumulating
(Teixeira
et a l . ,
1969b).
b. P a t a s h n i k ' s
method
Patashnik's
method
integration
(Patashnik,
average
temperature
employed
1953).
method
p o i n t s were n o t a v e r a g e d t o
but,
rather,
constant
T h i s time
before or a f t e r
could
be
It
obtain
value
that
a
was
of t r a p e z o i d a l
similar
to
the
successive
data
temperature
considered
for
one
value,
t o remain
complete
i n t e r v a l c o u l d be c o n s i d e r e d
time
t o be t h a t
t h e i n s t a n t t h a t t h e measurement a p p l i e s t o
considered
t o s p a n midway i n t o e a c h o f
two i n t e r v a l s . As l o n g a s t h e p r o c e s s
sub-lethal
was
except
temperature
at the given data
interval.
or
the
the technique
temperatures,
however,
these
s t a r t e d and ended
at
the r a t i o n a l i z a t i o n of
28
t h i s p o i n t was
not
significant,
c. C u b i c p o l y n o m i a l method
The
c u b i c p o l y n o m i a l method was
similar
to
methods
since
t
four
i+l'
it
1+2
1+z
that
was
smoothed
out
the
curve
more
rather
i t as a s t e p f u n c t i o n . For each t i m e
a
c
u
b i
points:
(t..,_,L.
method
a g r a p h i c a l g e n e r a l method t h a n most n u m e r i c a l
considering
t o
a
(
), was
interval,
i n t e r p o l a t i o n p o l y n o m i a l based
c
t
i - i ' i - i ^ '
L
( f c
±' l '
L
}
( t
i n t e g r a t e d . These p o i n t s
than
on
the
i+l' i+l*'
L
were
a n d
'
calculated
lethality
v a l u e s c o r r e s p o n d i n g t o temperatures measured a t
one
time i n t e r v a l s .
minute
function
subprogram
For
could
facility,
or
calculator.
be
system,
adapted
possibly
Fitting
for
even
of
was
use
a
the
used;
with
any
programmable
four
t h e i n t e g r a t i o n was
the
the o p e r a t o r would
i f temperatures
system
v a l u e s would
could
unknowns
program
only enter time-temperature
were measured a t e q u a l t i m e
be
simplified
so t h a t o n l y
h a v e t o be e n t e r e d , w i t h t h e t i m e
g e n e r a t e d by t h e p r o g r a m .
the
was
e a s i l y a c c o m p l i s h e d . A l l of
t h e o p e r a t i o n s c o u l d be c o m b i n e d i n t o a s i n g l e
and
computing
the c u b i c p o l y n o m i a l r e q u i r e d
in
on
the
p r i c i p l e s o f m a t r i x a l g e b r a . Once t h e p o l y n o m i a l
determined,
that
FORTRAN
however,
hand-held
s o l u t i o n of f o u r s i m u l t a n e o u s e q u a t i o n s
using
study,
QINT4P (Madderom, 1 9 7 8 ) , a v a i l a b l e
the u n i v e r s i t y ' s computing
method
this
so
pairs,
intervals,
temperature
base
being
29
2. F o r m u l a M e t h o d s
Five
formula
determination
methods
were
representative
f o r center
examined.
These
point
were
lethality
chosen
to
be
o f c u r r e n t l y a p p l i e d methods as w e l l as t h e
most r e c e n t d e v e l o p m e n t s i n p r o c e s s
evaluation,
a. B a l l ' s t a b l e m e t h o d
This
formula
processing
first
was
a
great
milestone
value
(Ball,
1923).
Ball
(U) w i t h r e s p e c t
the
retort
at
curves
integrals.
The
start
determined e m p i r i c a l l y
data,
and
heating
e q u a l . The h e a t i n g
product
portions
cold
spot
the
time-
mathematically
The c o o l i n g l a g
factor (Jcc)
of
was a p p r o x i m a t e d by an
straight-line
through
and
of
were e v a l u a t e d
was a s s u m e d t o be 1.41 a n d t h e c u r v e
hyperbola.
of
t h e e n d o f t h e h e a t i n g c y c l e ( g ) . The
history
using exponential
tables
t o h e a t i n g r a t e index ( f ^ )
s t r a i g h t - l i n e h e a t i n g and c o o l i n g
temperature
thermal
s i n c e i t was
developed
t e m p e r a t u r e d i f f e r e n c e between t h e
and
in
a n d h a s been t h e i n d u s t r y s t a n d a r d
introduced
process
and
method
o b s e r v a t i o n of
cooling
cooling
was
experimental
r a t e s w e r e assumed t o be
l a g f a c t o r was u s e d f o r t h e
calculation
of g b u t i t s l e t h a l
e f f e c t was n o t a c c o u n t e d f o r . M e r s o n e t
al.
a good d e s c r i p t i o n of t h e p r i n c i p l e s of
this
(1978) p r o v i d e d
method.
The
detailed
American
Can
Company
has
since developed
more
t a b l e s , i n t e r p o l a t i n g and e x t r a p o l a t i n g the t a b l e s
t h a t were p u b l i s h e d by B a l l .
e v a l u a t i o n of t h i s
method.
These t a b l e s were used f o r t h e
30
b. B a l l ' s e q u a t i o n method
While t r y i n g
formula
t o d e v e l o p a method
for
implementing
method w i t h o u t u s i n g t h e t a b l e s ,
that the values i n
equations
that
his
tables
did
Ball's
i t was d i s c o v e r e d
not
agree
were u s e d t o d e v e l o p them
with
the
( S m i t h and Tung,
1 9 7 9 ) . T h i s was c o n f i r m e d by t h e f i n d i n g s o f S t e e l e e t a l .
(1979).
Ball's
The
second
method
method
using
the
p r o d u c t i o n of t h e t a b l e s
investigated,
equations
therefore,
developed
( B a l l and O l s o n ,
for
was
the
1957).
c. Stumbo's method
Stumbo
and
Longley
evaluation taking
values.
The
(1966)
into
values
published
account
the
tables
f o r process
variability
of
graphs.
r a t e p a p e r , and subsequent
Revised
tables
finite
generated
difference
particulars,
c
from
histories
interpolation
( u s e d i n t h i s e v a l u a t i o n ) were
d e v e l o p e d through use of computer
histories
c
i n t h e s e t a b l e s were o b t a i n e d t h r o u g h
p l a n i m e t e r m e a s u r e m e n t s o f hand-drawn t e m p e r a t u r e
p l o t t e d on l e t h a l
of j
integration
heat
simulations
transfer
of
thermal
equations using
(Stumbo, 1 9 7 3 ) . I n a l l o t h e r
t h e m e t h o d was s i m i l a r
to B a l l ' s .
d. S t e e l e a n d B o a r d ' s method
Ball
and
processes
heating
Olson
(1957) d e v e l o p e d t a b l e s
exhibiting
and
cooling
broken
heating
and
cooling
curves
or
unequal
r a t e s . T h e s e t a b l e s were b a s e d on t h e
same c o n c e p t s a s B a l l ' s o r i g i n a l
heating
f o r e v a l u a t i o n of
portions
s e p a r a t e . T h i s method was
tables
of
improved
the
except
that
the
p r o c e s s were
kept
upon by G r i f f i n
et a l .
31
(1971) t h r o u g h
and
t h e use of a r e l a t i o n s h i p between t h e c u r v e d
s t r a i g h t - l i n e p o r t i o n s o f t h e c o o l i n g c u r v e . S t e e l e and
Board
(1979)
sterilizing
adapted
ratios,
this
method
for calculation
to simplify calculations.
was e v a l u a t e d u s i n g t h e e q u a t i o n s d e v e l o p e d
This
using
method
r a t h e r than the
tables provided,
e. Hayakawa's method
Hayakawa
similar
(1970) d e v e l o p e d
a method of l e t h a l i t y e v a l u a t i o n
t o those p r e v i o u s l y d e s c r i b e d except
functions
sections
for
was
divided
into
e v a l u a t i o n : curved heating, s t r a i g h t -
l i n e heating, curved c o o l i n g ,
The
circular
were u s e d t o e s t i m a t e t h e c u r v e d p o r t i o n s o f t h e
h e a t i n g a n d c o o l i n g c u r v e s . The p r o c e s s
four
that
and
straight-line
cooling.
l e n g t h s o f t h e c u r v e d p o r t i o n s were e s t i m a t e d u s i n g an
empirical
r e l a t i o n s h i p between f and j .
During
computer
testing
solution,
found. A c o r r e c t i o n
(Downes
and
of
the
errors
to
Hayakawa,
the
procedures
in
tables
1977).
using the equations developed
the
This
developed
for
p u b l i s h e d t a b l e s were
was
found
elsewhere
m e t h o d was e v a l u a t e d
r a t h e r than the t a b l e s .
32
C. A d a p t a t i o n
f o r Computer S o l u t i o n
A d a p t a t i o n of t h e v a r i o u s f o r m u l a methods f o r s o l u t i o n
solely
by c o m p u t e r r e q u i r e d two m a j o r s y s t e m s .
table
accessing
determining
system
and
the
other
' One
a
was
system
f and j v a l u e s from t h e t i m e - t e m p e r a t u r e
a
for
input
data.
1. T a b l e
Access
Table
access
was
accomplished
by
s e t t i n g up
o r g a n i z e d s o t h a t t h e l i n e number c o r r e s p o n d e d
value
for
file-line
each
varied
generally
slightly
the
from
g
one method t o
lines
interpolation
necessary,
file
necessary,
where
lines
were
next
sequentially.
For
read
line
j
the
c
v a l u e s from
cases
where
lethality
to
of
the
line
table
facilitate
were
read and, i f
could
read
system
and
c
took
for
c
j =2.00.
c c
In
i n the course of a
d e t e r m i n a t i o n , g v a l u e s were c o n v e r t e d
f r o m C° t o
tables.
o f f and j V a l u e s
Determination
iterative
be
values f o r intermediate
c c
with available
to
needed.
r e l a t i o n s h i p between g and j
t a b l e s were t o be a c c e s s e d
2. D e t e r m i n a t i o n
but
i t is difficult
u s i n g an i n d e x e d
the values f o r j =0.40
F° t o be c o m p a t i b l e
an
table
since
g i v e n v a l u e of f ^ / U , c a l c u l a t i n g
c
another,
Stumbo's t a b l e s , t h e a c c e s s
advantage of t h e l i n e a r
a
of
backwards, i f the p r e v i o u s
the
g-
v a l u e s and f ^ / U v a l u e s f o r t h e
c u r r e n t and p r e v i o u s
The
the
p a r t o f t h e t a b l e . The i n f o r m a t i o n on t h e
included
read a f i l e
to
files
o f f a n d j v a l u e s was a c c o m p l i s h e d
regression technique
to locate
the
using
start
of
33
the s t r a i g h t - l i n e p o r t i o n of t h e h e a t i n g and c o o l i n g c u r v e s
(log
g
v s . t and l o g m ( d i f f e r e n c e i n temperature
c o o l i n g water
and
can
centerpoint
during
cool)
r e s p e c t i v e l y ) . L i n e a r r e g r e s s i o n was p e r f o r m e d
deleting
f o r the curve
line.
The
In the f i r s t
was u s e d
regression
to
line
vs. t ,
iteratively,
p o i n t s up t o t h e c r o s s o v e r o f t h e f i t t e d
l i n e and t h e d a t a c u r v e .
data
between
straight
i t e r a t i o n , a l l of the
determine
the
regression
was t h e n c o m p a r e d t o t h e d a t a
c u r v e , a n d a l l o f t h e d a t a p o i n t s up t o t h e c r o s s o v e r
were o m i t t e d
f o r the next
continued u n t i l
curve
close
iteration
for
the f i t t e d
to
the
technique
of
the
point
rapidly
included
eliminated
in
was
the l a s t
the
non-linear
t h e d a t a c u r v e , and s e l e c t e d t h e l i n e a r
of
the
parameters
f
and
f was t h e n c a l c u l a t e d a s t h e n e g a t i v e
s l o p e of t h e r e g r e s s i o n
line,
described
(1973).
by
discriminating
Stumbo
up
t o the f i r s t
as
in
the
falling
and
j
The
was
heating or c o o l i n g curve.
reciprocal
was
as
more
often
40 o r more m i n u t e s o f t h e d a t a
curvilinear
theoretically
j . The
techniques,
portion.
t h e r e f o r e more c l o s e l y e s t i m a t e d
is
region
calculated
technique
than manual l i n e - f i t t i n g
discarding
which
procedure
regression l i n e crossed the data
first
calculation
parameter
obtained
This
(maximum r e l a t i v e d i f f e r e n c e 0.1 % ) .
This
portion
iteration.
point
defined
as
The
f
the true f
values
value
the asymptote of the
34
3. R e f e r e n c e M e t h o d a n d C a l c u l a t i o n o f D e v i a t i o n s
The r e f e r e n c e method t o w h i c h
t h e o t h e r s were c o m p a r e d
was a n u m e r i c a l g e n e r a l m e t h o d w i t h d a t a p o i n t s t a k e n
0.05 m i n . The a r i t h m e t i c mean t e m p e r a t u r e
interval
( A t ) was
t h i s temperature
of
the
and t h e l e t h a l
each
rate
time
(L) f o r
was c o n s i d e r e d t o a p p l y f o r t h e d u r a t i o n
interval
10 C° ( 1 8 F°)
determined
over
every
and
(250 F°) were u s e d
(Teixeira
a
et
reference
forlethal
a l . , 1969b).
A z v a l u e of
temperature
of
rate calculations.
121.1 C°
Thus,
T - 121.1
f
1
° ,
L = 10
Lethalities
.
were c a l c u l a t e d a s L A t a n d summed t o d e t e r m i n e
the t o t a l process l e t h a l i t y
intervals
(8)
( F ) . Because of t h e s m a l l time
0
( 0 . 0 5 m i n ) , t h i s m e t h o d was assumed
to
estimate
the c o n t i n u o u s p r o c e s s c u r v e and hence t h e o r i g i n a l
method, and i t s l e t h a l i t y
was u s e d
the a l t e r n a t e c a l c u l a t i o n
methods.
Each
temperature
process l e t h a l i t y
of t h e f o r m u l a
of
the
history
t o judge the a c c u r a c y of
curve
was
evaluated for
( F ) u s i n g t h e r e f e r e n c e method a n d
0
( t e s t ) methods. D e v i a t i o n s between F
reference
general
and
test
methods
percentages of t h e r e f e r e n c e F
F
Deviation =
0
(ref)
F
values
c a l c u l a t e d as
using:
" F
0
were
0
each
0
(test)
x 100%.
(9)
0
(ref)
A p o s i t i v e percentage
d i f f e r e n c e would
indicate
t e s t method u n d e r e s t i m a t e d t h e a c t u a l p r o c e s s
that
the
lethality.
35
RESULTS & DISCUSSION
A.
General
Methods
This
study
showed
that
temperature
method r e s u l t e d
calculated
lethality
method's a c c u r a c y
slope
time
and
c u r v a t u r e of t h e heat
end
o f t h e cook
t o diameter
When
than
£
diameter
g
ratio
lethality
h
held
the
were
f o r the
heating
products,
(H/D) a n d
temperature
( F i g u r e 4 ) . F o r an f
varied,
a
less
g r e a t e s t e r r o r (0.99%
f o rf
of
was t e n t i m e s
and
the height t o
dramatic
was n o t e d
but
still
( F i g u r e 5 ) . The
= 30 m i n ) was f o r s m a l l
and t h e l e a s t
h
compared t o 0.063%).
constant,
i n accuracy
to
(small values
o f 90 m i n ( 0 . 6 7 %
were
ratios,
both
deviations
underestimation
appreciable variation
to diameter
larger
ratio
( g ) were c o n s t a n t
f o r an f
and
by
t h e r e t o r t and t h e c e n t e r p o i n t a t t h e
30 m i n , t h e p r o c e s s
larger
average
p e n e t r a t i o n c u r v e . When a
f o rslower
h
between
the
deviations i n
affected
rapidly
f ) than
when t h e c a n h e i g h t
difference
used,
t h a t heat
rate index,
of
significant
was s i g n i f i c a n t l y
for products
heating
in
use
c o m p a r e d t o t h e r e f e r e n c e m e t h o d . The
i n t e r v a l o f 1 m i n was
noted
the
height
(0.66%) f o r a r a t i o c l o s e
unity.
Holding
the e f f e c t
greatest
f ^ and t h e height t o diameter
o f g was
assessed.
underestimation
Figure
of process
The
height
t o diameter
shows
lethality
l a r g e g, w i t h t h e e f f e c t more p r o n o u n c e d
ratios.
6
ratio
constant,
that
the
occurred f o r
f o r smaller
H/D
r a t i o and v a l u e of g w i l l
Figure
5.
Effect
of
height
errors
using
to
average
diameter
temperature
ratio
on
method.
evaluation
(g=5
C°)
U)
Deviation
se
from
reference
l e t h a l i t y . /,
39
affect
t h e c u r v a t u r e of t h e l e t h a l i t y p l o t , and
accuracy
with
estimates
which
the
average
temperature
be
a
(usually
used.
more
less
than
0.05%) when 1 m i n
when
by P a t a s h n i k
overestimation
method
5
min
time
time
attempt
of
lethality,
cubic
process
intervals
i n some c a s e s
polynomial
u s i n g t h e g e n e r a l method
showed
that
small
were
were u s e d , a s
lethality.
this
from use
of
underestimated
by a s much a s 2 7 % .
method
was
developed
of l e t h a l i t y
approach.
no
min
in
an
determinations
However,
i t provided
P a t a s h n i k ' s m e t h o d , e v e n when 5
as
However,
method, which a l w a y s
t o improve the a c c u r a c y
results
found
( 1 9 5 3 ) , d e v i a t i o n s were a s g r e a t
the average temperature
The
was
intervals
d e v i a t i o n was s m a l l c o m p a r e d t o t h a t r e s u l t i n g
process
method
a p p r o p r i a t e m e t h o d . E r r o r s were v e r y
However,
suggested
4%
the
the l e t h a l value of the process.
Patashnik's trapezoidal integration
to
thus,
experimental
improvement
over
intervals
were
determine
which
data
used.
B. F o r m u l a M e t h o d s
1. Initial
Studies
Initial
factors
various
studies
were
conducted
had t h e g r e a t e s t e f f e c t
methods
f o r process
r e d u c e t h e number o f e x p e r i m e n t s
performance.
history
curves
Even
after
on
to
the
accuracy
of
the
e v a l u a t i o n i n an a t t e m p t
r e q u i r e d t o compare
t h i s r e d u c t i o n , over
were e v a l u a t e d . The i n i t i a l
to
their
200 t h e r m a l
studies
showed
40
that
and
t h e t e m p e r a t u r e d i f f e r e n c e a t t h e e n d o f t h e c o o k (g)
the height
significant
to
diameter
with
consistent
thermal d i f f u s i v i t y
nature
error
compared
to
i n g and c o n t a i n e r
of
these
simulation
to
include
or
exclude
of
simulation
covering
a wide range of c o n d i t i o n s .
whereas
after
c a l c u l a t i o n varied widely
is
the
thermal
within
covering
any
one
variability
a
further
inspection
of the
The d a t a
error
a s g was v a r i e d ,
in
in
the
Table
The
effect
error
lethality
effect
table
i s small
g
for
indicated
compared t o
indicated
i n the
i n T a b l e I . The f a c t o r s o f c a n s i z e ,
were t h e r e f o r e
considered
i n s i g n i f i c a n t and were n o t i n c l u d e d
resulted
of
small. Table I I
variability
due t o v a r i a t i o n s i n
further experiments.
difference
I
range of f ^ v a l u e s and a range of
column of t h i s
column
the
f o r a sample of runs
percentage
, and thermal d i f f u s i v i t y
relatively
in
statistical
from
s i z e was r e l a t i v e l y
diffusivities.
corresponding
f
visual
of the
a summary, f o r one c a n s i z e a n d v a l u e o f g, o f d a t a
experiments
the
container
on
therefore
factors
experiments
the
size,
effects
Because
appropriate,
results
that
made
Can
experiments,
were
varying
most
t h e e f f e c t s r e s u l t i n g from
experiments
show
the
large
dimensions.
t r e a t m e n t o f t h e d a t a was n o t
decisions
were
patterns.
and f ^ d i d n o t have
magnitudes
variations
(H/D)
f a c t o r s , r e s u l t i n g i n a wide v a r i a t i o n of e r r o r
magnitude,
error
ratio
Varying
i n small
on t h e e v a l u a t i o n
the
initial
t o be
as v a r i a b l e s
temperature
d i f f e r e n c e s , m o s t l y due t o t h e
of f
h
a n d Jcht*
A
range of i n i t i a l
41
Table I-Errors
in calculated lethalities
using
5
methods f o r v a r i o u s c a n s i z e s and v a l u e s
formula
o f g-
(H/D=1. 35)
Percent
error
Hayakawa
Stumbo
56.6
46.8
17.1
68.6
57.3
•47.5
15.9
60.7
69.0
57.7
47.5
13.8
3
31.3
40.4
29.2
20.9
10.1
5
4
32. 1
41.2
30.0
21.8
10.7
5
5
32.4
41 .4
30.0
21 .4
9.2
1.5
3
18.0
22.7
15.1
9.5
4.9
1.5
4
18.4
23.0
15.6
10.2
5.9
1.5
5
18.5
23.1
15.7
10.2
5.5
0.5
3
12.1
14.5
9.4
5.7
2.1
0.5
4
12.3
14.7
9.6
5.8
2.1
0.5
5
12.3
14.7
9.7
6.0
2.2
0.15
3
9.1
9.8
6.3
3.8
1 .9
0.15
4
9.2
9.8
6.4
3.8
1 .6
0.15
5
9.2
9.7
6.4
3.8
1.5
Steele
radius
Ball's
Ball's
(cm)
Tables
Equation
& Board
15
3
59.4
67.8
15
4
60.3
15
5
5
g
(c°)
42
Table I I - E r r o r s
in calculated
lethalities
using 5 formula
methods f o r v a r i o u s t h e r m a l d i f f u s i v i t i e s
and f .
h
(H/D=1.0; g=5 C°)
Percent
£.
n
c
Ball's
Ball's
(min)
(cmVmin)
Tables
Equation
30
0.075
35.2
43.8
30
0. 100
35.6
30
0.1 25
50
error
Steele
Hayakawa
Stumbo
32.6
24.2
11.4
44.2
32.9
24.4
1 1 .4
35.9
44.5
33.2
24.7
11.6
0.075
35.7
44.3
33.1
24.7
11.8
50
0.1 00
36.2
44.7
33.7
25.5
12.8
50
0.125
36.4
44.9
33.9
25.7
13.1
70
0.075
36. 1
44.7
33.3
24.7
11.0
70
0. 1 00
36.4
44.9
33.6
25. 1
11.1
70
0. 125
36.7
45.2
33.9
25.4
1 1 .7
90
0.075
36.4
44.9
33.7
25.2
11.7
90
0. 100
36.6
45.1
33.9
25.4
1 1.9
90
0. 125
36.8
45.2
34. 1
25.6
12.2
& Board
43
temperature d i f f e r e n c e s
the
f r o m 20 t o 95 C°
s t u d y ; but data from i n i t i a l
20 C°
were
later
excluded
p o o r , e s p e c i a l l y when
g
included
in
temperature d i f f e r e n c e s of
because
was
was
e s t i m a t e s of f
large,
since
n
were
straight-line
h e a t i n g b e h a v i o r was n o t w e l l e s t a b l i s h e d b e f o r e t h e end o f
the
heating
c y c l e . The e f f e c t s were s m a l l c o m p a r e d t o t h e
e f f e c t s of other f a c t o r s being
Parallel
temperatures
product
of
120
studied.
thermal
and
histories
140 °C
were
III). A l l
subsequent
generated using a r e t o r t
percentage
to
be
thermal
temperature
of
comparable
histories
120 °C
were
but
the
e r r o r s p r e s e n t e d c a n be c o n s i d e r e d t o a p p l y f o r
higher retort
t e m p e r a t u r e s as w e l l . T h i s i s
significance
when
are
retort
e v a l u a t e d and t h e
c a l c u l a t e d p e r c e n t a g e e r r o r s were f o u n d
(Table
for
considering
of g r e a t e r importance
for
of
particular
large g values since
higher
p r o c e s s e s t h a n f o r p r o c e s s e s a t 120
retort
these
temperature
°C.
2. E f f e c t s o f Can Shape a n d g V a l u e
Figures
7 through
r e f e r e n c e method, t h a t
lethality
resulted
an
differences
of
average
35,65,
from c a l c u l a t i o n
error
and
for
95 C ° .
initial
The
of process
Each
point
temperature
deviations
are
o f b o t h c a n s h a p e (H/D) a n d g. The s h a p e s o f t h e
error curves are s i m i l a r
equation
r e l a t i v e t o the
u s i n g each of t h e f i v e t e s t methods.
represents
functions
11 show t h e e r r o r s ,
method,
for Ball's
S t e e l e and Board's
table
method,
method a n d
Ball's
Hayakawa's
44
Table I l l - E r r o r s
in calculated
lethalities
using 5 formula
m e t h o d s f o r v a r i o u s v a l u e s o f g and two
temperatures.
retort
(H/D=1.35)
Percent
error
Hayakawa
Stumbo
57.3
47.5
15.9
68.7
57.5
47.6
16. 1
32. 1
41.2
30.0
21 .8
10.7
140
32.1
41 .2
30.0
21.8
10.7
1 .5
120
18.4
23.0
15.6
10.2
5.9
1 .5
140
18.5
23.2
15.8
10.5
6.4
0.5
120
12.3
14.7
9.6
5.8
2. 1
0.5
140
12.5
14.9
9.8
6.1
2.5
0.15
120
9.2
9.8
6.4
3.8
1 .6
0.15
140
9.4
10.0
6.6
4.0
1.9
0.05
120
5.8
7.0
4.7
2.9
0.9
0.05
140
6. 1
7.4
4.8
2.9
0.8
Steele
g
retort
Ball's
Ball's
(C°)
(°C)
Tables
Equation
& Board
15
120
60.3
68.6
15
140
60.3
5
120
5
H/D
Figure
7.
Errors
Ball's
in
process
tables.
ratio
lethality
determinati
Figure
8.
Errors
Ball's
in
process
equation.
lethality
determinations
using
I
0.5
I
0
Figure
9.
I
1.0
Errors
in
Steele
and
I
1.5
H/D
ratio
process
Board's
lethality
method.
I
2.0
1
2 5
determinations
I
3.0
using
8fr
6fr
50
method, a l t h o u g h the m a g n i t u d e s of
error
curves
for
characteristics,
of
H/D,
cases
lethality,
that
increased
I t m i g h t be
would
s i n c e a p l o t of
plot
12
greater
were
of
"safe"
H/D
the
be
of
a function
a function
error
c
c
f u n c t i o n . T h e r e f o r e , some o t h e r
a l s o be
i n f l u e n c i n g the
expected
t o be
e r r o r m a g n i t u d e as
a
continuous
in
believed
shape
can
t o be
at the
The
be
end
function
most
a r e s u l t of
resulting
Errors
be
curve
from the
of
the
has
trend
H/D
cases.
The
differences
of
g,
a r e s u l t of the
factor,
similar
not
1957).
to
a
be
smooth
factors,
must
these would
since
a
shape
in
by
the
plot
smooth
of
and
effect
cooling
be
is
curve
through
the
found
to
cycle.
i n c r e a s i n g as
e f f e c t o f g v a l u e on
lag
temperature gradient
heating
became
Olson,
was
is
in l e t h a l i t y determination
a function
then
tended
or
ratio,
of
unity,
a shape
errors
factor
H/D
H/D,
cooling
e r r o r m a g n i t u d e , and
r e l a t e d t o the
small
influenced
( B a l l and
the
process
v a l u e as H/D
the
the
values,
of
near
o f H/D
although
larger j
In almost a l l
for
errors
magnitude
functions
side.
was
intermediate
The
similar
simple
smallest
when
an
shows t h a t
for
the
expected that
j as
have
underestimations
were
to
method
differ.
l a r g e v a l u e s o f g.
maximum
slowly
shape
Figure
for
errors
a p p e a r t o be
i s , e r r o r s on
to a
the
not
deviations
decreased
to
do
errors
These
can
Stumbo's
especially
these
large.
but
the
lethality
the
were a l s o
v a l u e of g
determination
temperature gradient
from the
increased.
errors
may
surface
to
• Ball
A Stumbo
A
A
A
L_
18
16
1.4
1.2
ice
Figure
12.
Errors
in
to
cooling
the
process
lag
lethality
factor.
determinations
(g=5 C°)
as
related
52
the
center
of
c y c l e . During
surface
the
container
the heating c y c l e ,
temperature
continued
t h e end o f t h e h e a t i n g
the temperature
of the can i s h i g h e r than
the h e a t i n g c y c l e i s
process
at
t h a t near the c e n t e r . I f
until
g
i s stopped
is
small,
this
at
when g i s l a r g e , t h e g r a d i e n t c a u s e s t h e
the
c e n t e r of the can t o c o n t i n u e
f o r a p e r i o d of time a f t e r
the s t a r t
and
o f t h e c a n may
any
the
g r a d i e n t becomes i n s i g n i f i c a n t . H o w e v e r , i f t h e
temperature
for
near
the center temperature
several
minutes.
This effect
of t h e
to rise
cooling
not begin
cycle
t o drop
i s not accounted
for in
of t h e f o r m u l a methods t e s t e d .
3. C o m p a r i s o n o f M e t h o d s
Figure
with
the
13 shows a c o m p a r i s o n o f t h e e r r o r s
five
associated
f o r m u l a m e t h o d s t e s t e d . E r r o r s f o r o n l y one
v a l u e o f g a r e shown, b u t t h e t r e n d s were s i m i l a r
v a l u e s o f g, a l t h o u g h
the e r r o r magnitudes d i f f e r
7 - 1 1 ) . The v a l u e o f g=5C° u s e d i n F i g u r e
of
the
largest
conventional
g
f o r other
values
that
would
13 i s i n t h e r a n g e
be e n c o u n t e r e d
method r e s u l t e d
of p r o c e s s
lethality
in relatively
using
large errors,
Ball's
f o r m u l a method a p p r o a c h h a s b e e n s i g n i f i c a n t l y
by
more
recent
that
improved
m o d i f i c a t i o n s . S t e e l e and B o a r d ' s method,
h a v i n g e l i m i n a t e d t h e a s s u m p t i o n s o f o n l y one v a l u e
e q u a l h e a t i n g and
than
table
indicating
the
better
in
processing.
Calculation
and
(Figures
Ball's
cooling
table
rates,
method
performed
f o rj c c
slightly
u n d e r most c o n d i t i o n s .
54
Hayakawa's method, w h i c h e s t i m a t e d t h e
circular
functions,
resulted
l a g using
i n s m a l l e r e r r o r s than
o f t h e s e m e t h o d s . The l a r g e s t e r r o r
f o r a g value
25%
Ball's
t a b l e s and 33% u s i n g S t e e l e and B o a r d ' s method.
(up t o 4 4 %
equation
method
method
small, this
slightly,
method r e s u l t e d
i n the largest
of
method
in
appears
to
be
the
overestimated
the
most
process
errors
accurate
lethality
some c a s e s . Stumbo's method a l s o r e s u l t e d i n
(Figure 11).
C a l c u l a t i o n E r r o r s i n Terms o f P r o c e s s i n g Time
S i n c e a l l o f t h e methods u n d e r e s t i m a t e d
of
thermal
processes
process times
longer
f o r conduction
calculated
using
these
the
heating foods, the
methods
o r more. A l t h o u g h
s i z e and i n i t i a l
other
would
be
F i g u r e 1 4 shows t h a t B a l l ' s m e t h o d o v e r e s t i m a t e d
r e q u i r e d p r o c e s s t i m e s by 6 t o 7 m i n f o r a p r o c e s s
hour
lethality
than r e q u i r e d t o achieve a s p e c i f i e d t a r g e t process
lethality.
can
Use
t h o s e t e s t e d . H o w e v e r , when g was v e r y
h i g h l y v a r i a b l e a c c u r a c y when g was l a r g e
4.
t o 36% u s i n g
f o r g=5 C ° ) .
Stumbo's
formula
compared
5 C°
of
Hayakawa's
Ball's
was
either
using
of
method
cooling
conditions.
this
figure
temperature,
Stumbo's
of
one
shows d a t a f o r o n l y one
e r r o r s were
similar
for
method o v e r e s t i m a t e d r e q u i r e d
p r o c e s s t i m e s by o n l y a b o u t 2 m i n , w h i c h i s a p p r o a c h i n g t h e
accuracy of process c o n t r o l
f o r manually
operated
retorts.
A l t h o u g h t h e s e e r r o r s c o u l d be c o n s i d e r e d t o be
safety
factors,
they
are
influenced
by
can
extra
shape a n d
H e a t ing
Figure
14.
Calculated
t i me,
lethal effect
(H/D=1.0, I h = 9 5
C°)
m i n
relative
to processing
time.
56
processing
constant
margin
necessary,
product
but
for
and
therefore
error.
should
safety.
suggested
this
conditions
be
well
( 1 9 7 8 ) may
not
provide
Safety margins are
Statistical
by L u n d
do
defined,
analysis
be a
to
certainly
help
assure
of v a r i a b i l i t y ,
reasonable
a
approach
as
to
problem.
5. P o s i t i o n o f C o l d S p o t i n C o n t a i n e r
For
conduction
of a t h e r m a l
process
heating products,
can account
the
delivered lethality
The
cooling
processes
portion
most
(Board et a l . ,
significant
for
in
l a r g e r g v a l u e s . For
reasons,
i t i s important
to
take
cooling
portion
thermal
processes.
be
into
account
when
necessary
to determine
of
the
critical
r e c e i v e s the l e a s t
various factors
cooling
and
Deltour,
considerably
of
point
lethal effect
and
the
at the c e n t e r
required
it
"critical
container.
The
from a p r o c e s s , depends
of
the
of
the
d i f f e r e n c e between t h e l e t h a l i t y d e l i v e r e d
and
for a
t h i s p o i n t may
center
the
taken,
heating
the shape of the c o n t a i n e r
1972a). A l t h o u g h
from
the
of
i n the c o n t a i n e r , which
i n c l u d i n g the nature
program
determining
the process
1960).
economic
lethality
However, i f t h i s a p p r o a c h i s
p o i n t " which i s not at the c e n t e r
position
the
of
shorter
result
may
which
for a significant part
of a p r o c e s s
is
the c o o l i n g p o r t i o n
be
and
(Flambert
displaced
container,
at
on
this
i s u s u a l l y s m a l l ( H i c k s , 1951).
the
point
57
6.
Convection
It
to
Heating
Products
must be n o t e d
foods
that the r e s u l t s reported here
t h a t h e a t a n d c o o l by c o n d u c t i o n
p r o c e s s i n g methods f o r w h i c h n a t u r a l o r
are
significant
shortened
lag
methods
can
factors
before
be
for
conduction
heating
may
convection
i n process
convection
cooling
expected
accurately
accuracy
i n heat
heating
to
forced
Thus
estimate
heating
products.
o n l y . Products or
transfer w i l l
begins.
convection
experience a
the
lethality
products
for
both
more
than
for
similar
conduction
and
p r o d u c t s , d i f f e r e n t e v a l u a t i o n methods
be r e q u i r e d .
C. G e n e r a l
Some
C o n s i d e r a t i o n s and F u t u r e Research
of
calculation
the
most
significant
u s i n g f o r m u l a m e t h o d s may
the parameter g and t h e c a l c u l a t i o n
unaccomplished
temperature
as the d i f f e r e n c e
highest
i n temperature
temperature
temperature
Needs
factors
in
reached
of f ^ , f , and j
• The
defined
between t h e r e t o r t and t h e
a t t h e c e n t e r of t h e c o n t a i n e r
often
d i f f e r e n c e a t the time
described
as
the
steam i s t u r n e d o f f . I n
some s i t u a t i o n s , n o t a b l y w i t h c o n v e c t i o n h e a t i n g
these
process
be t h e d e f i n i t i o n o f
d i f f e r e n c e , g, i s o f t e n
i n q u e s t i o n . However, i t i s a l s o
products,
two d e f i n i t i o n s may c o i n c i d e , b u t i n most c a s e s , t h e
temperature
rise
formula
In order t o achieve
estimation
apply
at the center of a c o n t a i n e r w i l l
f o r some t i m e a f t e r
temperature
continue
to
t h e s t e a m i s t u r n e d o f f due t o t h e
g r a d i e n t from t h e s u r f a c e t o t h e c e n t e r of t h e
58
container.
also
a
In batch-type
time
the c o n t a i n e r
results
is
immersed
from t h e time
is
often
container
temperature
at
to f i l l
of
cooling
continuation
many
start
water.
definition
of
f
time
of
cases,
can
the
(i960)
be
where t h e r e
have
considered
process
without
at
retort
introduction
is a
of
significant
o f c o o l i n g , e i t h e r due t o a t e m p e r a t u r e
delay
i n the
cooling conditions, i ti s clear
that the
h
, and
the
the
definitions
cooling
of
rate
a
inverse
the
index,
unambiguously d e f i n e d . T h e o r e t i c a l l l y ,
negative
time,
of g i s ambiguous.
Furthermore,
index,
delay
this
Board e t a l .
g r a d i e n t w i t h i n t h e c o n t a i n e r , o r due t o
establishment
The
w i t h water. During
this
e r r o r . In cases
the
is
s i g n i f i c a n t heat t r a n s f e r i n t o the
much
in
significant
there
r e q u i r e d t o b l o w down t h e r e t o r t a n d
still
that
equivalent to a
lag
in
from i t s s u r r o u n d i n g s .
suggested
situations,
l a g b e t w e e n when t h e s t e a m i s t u r n e d o f f a n d
to allow the retort
there
processing
heating
f
c
rate
, are not
f i s d e f i n e d as
the
slope of the asymptote t o t h e h e a t i n g or
c o o l i n g c u r v e . However, i n p r a c t i c e ,
f i s c a l c u l a t e d as t h e
negative
i n v e r s e slope of a l i n e
fitted
portion
of
t h e d i f f e r e n c e may n o t be
the
curve. Although
l a r g e when l o n g p r o c e s s e s
considered,
since
the
a p p r o a c h e s more c l o s e l y
on,
i n most p r a c t i c a l
enough t o r e s u l t
in
and
long
"linear"
to
cooling
portion
the asymptote as t h e
the
"linear"
periods
of
are
the
curve
process
goes
s i t u a t i o n s heating periods are short
considerable
discrepancies.
Cooling
59
records
are
rarely
e s t i m a t e of
f
is
c
f
and
c
long
any
enough
to
discrepancy
give
a
reasonable
i n the d e t e r m i n a t i o n
of
t r a n s l a t e d a l s o i n t o an e r r o r i n t h e c a l c u l a t i o n
of
cc*
D
The
errors
parameter, j c r
w e l l as b e i n g v e r y
a s
C
i n other c a l c u l a t e d parameters,
appropriate
cooling
descriptor
of
curve. Although
"linear"
portion
adequately
of
describe
the
j
c
c
be
drawn,
heating
the
cooling
effect
the nature
i s not
the
particularly
most
number
effort
is
clear
should
appropriate
parameters
introduction
curvilinear
research
thermal
of
c
another
portion
of
is satisfactorily
process
f
part
of
parts
towards
the
j
c
c
r
and
c
of
the
lethal
the
process.
a
process,
end
of the c o o l i n g c y c l e ,
for
and
curves
since l i t t l e
h e a t i n g foods, are the
the s t a r t
f ,
the
same i s t r u e f o r
important
important
procedures
h
the
not
unique
t h e same v a l u e s f o r g,
directed
f ,
of
does
of
since
rate i s highest.
from the above d i s c u s s i o n t h a t
be
g,
it
of
i s d u r i n g t h i s p e r i o d t h a t the l e t h a l
It
very
of the c u r v i l i n e a r p o r t i o n
initial
for conduction
t h e h e a t i n g c y c l e and
it
so
i s d e l i v e r e d i n the
However,
portion
curve,
l e t h a l e f f e c t s . The
c u r v e , but
not a
to
i t does l o c a t e the p o s i t i o n of
a l l having
but d i f f e r e n t
is itself
initial
of t h e c o o l i n g c u r v e , s i n c e any
could
sensitive
the
development
determination
and
research
perhaps
of
of
the
to
the
parameter as a d e s c r i p t o r of
the
cooling
completed,
curve.
Until
the
this
f u r t h e r comparison
c a l c u l a t i o n methods i s not
warranted.
of
60
CONCLUSIONS
The
numerical
general
method
using
i n t e g r a t i o n of l e t h a l h i s t o r y data developed
(1953)
was
found
t o agree
when one m i n u t e t i m e
l a r g e r time
The
five
lethality
i n t e r v a l s were u s e d .
heat
and c o o l
formula
methods
h e a t i n g foods
Patashnik
However,
i n greater error,
showed d e v i a t i o n s f r o m
conduction
by
w e l l w i t h t h e r e f e r e n c e method
intervals resulted
for products which
trapezoidal
use
especially
rapidly.
f o r determining
the reference
process
method
were
temperature
for
i n c y l i n d r i c a l c o n t a i n e r s under a
w i d e r a n g e o f c o n d i t i o n s . D e v i a t i o n s were g r e a t e s t
values
of
l a r g e , a s m i g h t be e n c o u n t e r e d
when
i n high
g
retort
processing. E r r o r s a l s o v a r i e d according t o the
shape of t h e c a n , w i t h t h e g r e a t e s t e r r o r s c o r r e s p o n d i n g t o
H/D c l o s e t o u n i t y . Can s i z e , t h e r m a l d i f f u s i v i t y ,
rate,
initial
did
not
temperature
greatly
d i f f e r e n c e and r e t o r t
affect
error
best
estimates
of
process
temperature
magnitudes.
c o n d i t i o n s e x a m i n e d , Stumbo's m e t h o d was f o u n d
lethality,
more s e n s i t i v e t o s l i g h t v a r i a t i o n s
in f
heating
Under a l l
to give
the
b u t t h e m e t h o d was
and j
h
c
c
than
were
the o t h e r methods.
Use o f t h e s e
times
would
processing
formula
result
time
in
methods
slight
f o r conduction
to
calculate
overestimates of required
heating
products.
o v e r p r o c e s s i n g r e p r e s e n t s an e x t r a s a f e t y m a r g i n ,
also
be
reduced
significant
plant
process
but c o u l d
i n terms of a d d i t i o n a l energy
throughput.
This
use and
61
REFERENCES
Ball,
CO.
Bull.
1923. T h e r m a l
process
time
f o r canned
7-1 ( 3 7 ) N a t ' l . R e s . C o u n c i l , W a s h i n g t o n ,
food.
DC.
Ball,
CO.
1928.
Mathematical
Solution
of
P r o b l e m s on
Thermal P r o c e s s i n g of Canned Foods. U n i v . C a l i f . P u b l .
P u b l i c H e a l t h 1, 230pp.
Ball,
CO.,
and O l s o n , F.C.W. 1957. " S t e r i l i z a t i o n
i n Food
Technology",
M c G r a w - H i l l Book Company, I n c . New Y o r k ,
NY.
B i g e l o w , W.D.,
B o h a r t , G.S., R i c h a r d s o n , A . C ,
and
Ball,
CO.
1920.
Heat
p e n e t r a t i o n i n p r o c e s s i n g canned
f o o d s . B u l l e t i n No. 16-L.
Res.
Lab.
Nat'l.
Canners
A s s ' n . , W a s h i n g t o n , DC.
B o a r d , P.W.,
C o w e l l , N.D.,
and H i c k s , E.W.
1960. S t u d i e s i n
canning
p r o c e s s e s I I I . The c o o l i n g p h a s e o f p r o c e s s e s
f o r p r o d u c t s h e a t i n g by c o n d u c t i o n . F o o d R e s . 25:449.
C a r s l a w , H.S., and J a e g e r , J . C
1959. " C o n d u c t i o n
of
Heat
i n S o l i d s " , 2nd e d . , O x f o r d U n i v e r s i t y P r e s s , U.K.
Downes, T.W.,
and
Hayakawa, K . - I . 1977. A p r o c e d u r e f o r
e s t i m a t i n g the r e t e n t i o n of
components of t h e r m a l l y
conductive
processed
f o o d s . Lebensm.
- W i s s . u.
T e c h n o l . 10:256.
E v a n s , H.L. 1958. S t u d i e s i n c a n n i n g
processes
I I . The
effects
of
the
variation
with temperature
of the
t h e r m a l p r o p e r t i e s of f o o d s . Food T e c h n o l . 12(6):276.
E v a n s , H.L., and
Board,
P.W.
1954.
Studies
in
canning
processes.
I . E f f e c t o f h e a d s p a c e on h e a t p e n e t r a t i o n
in
products
h e a t i n g by
c o n d u c t i o n . Food
Technol.
8(5):258.
Flambert,
F.,
and
D e l t o u r , J . 1972a. L o c a l i z a t i o n o f t h e
c r i t i c a l area i n thermally-processed conduction heated
c a n n e d f o o d . L e b e n s m . - W i s s . u. T e c h n o l . 5 ( 1 ) : 7 .
62
Flambert,
F.,
and D e l t o u r , J . 1972b.
Exact
lethality
calculation
f o r s t e r i l i z i n g p r o c e s s I . P r i n c i p l e s of
t h e m e t h o d . L e b e n s m . - W i s s . u. T e c h n o l . 5 ( 2 ) : 7 2 .
G i l l e s p y , T.G. 1951. E s t i m a t i o n o f s t e r i l i z i n g
v a l u e s of
p r o c e s s e s as a p p l i e d t o canned foods. I . Packs h e a t i n g
by c o n d u c t i o n . J . S c i . F o o d A g r i c . 2:107.
Griffin,
R.C.,
H e r n d o n , D.H., a n d B a l l , C O .
1969. Use o f
computer
derived tables
to calculate
sterilizing
processes
f o r packaged
foods.
2.
Application
to
b r o k e n - l i n e h e a t i n g c u r v e s . F o o d T e c h n o l . 2 3 ( 4 ) : 121.
G r i f f i n , R . C , H e r n d o n , D.H. , a n d B a l l , C O .
1971. Use
of
computer
derived tables
to calculate
sterilizing
processes
f o r packaged
foods.
3. A p p l i c a t i o n
to
c o o l i n g c u r v e s . Food T e c h n o l . 25(2):134.
Hayakawa,
K . - I . 1970.
Experimental formulas f o r accurate
e s t i m a t i o n of t r a n s i e n t t e m p e r a t u r e of f o o d and
their
application
to
thermal
process
evaluation.
Food
Technol. 24(12):1407.
Hayakawa, K . - I . 1977. M a t h e m a t i c a l methods
for estimating
proper
thermal
processes
and
their
computer
i m p l e m e n t a t i o n . Adv. Food Res. 23:75.
H a y a k a w a , K . - I . 1978. A c r i t i c a l
review
of
procedures
f o r d e t e r m i n i n g proper heat
p r o c e s s e s . Food T e c h n o l . 3 2 ( 3 ) : 5 9 .
mathematical
sterilization
Heldman,
D.R.
1975.
"Food
Process
Engineering",
P u b l i s h i n g Company, I n c . , W e s t p o r t , CT.
Avi
Herndon,
D.H.
1971.
P o p u l a t i o n d i s t r i b u t i o n of heat r i s e
c u r v e s as a s i g n i f i c a n t v a r i a b l e i n heat
sterilization
p r o c e s s c a l c u l a t i o n s . J . Food S c i . 36:299.
H e r n d o n , D.H., G r i f f i n , R . C , a n d B a l l , C O .
1968. Use
of
computer
derived tables
to calculate
sterilizing
p r o c e s s e s f o r packaged f o o d s . Food T e c h n o l . 22(4):129.
H i c k s , E.W.
1951. On t h e e v a l u a t i o n o f
Food T e c h n o l . 5 ( 4 ) : 1 3 4 .
canning
processes.
63
Hicks,
E.W.
1952. Some i m p l i c a t i o n s o f r e c e n t t h e o r e t i c a l
work on c a n n i n g p r o c e s s e s . F o o d T e c h n o l . 6 ( 5 ) : 1 7 6 .
H i c k s , E.W. 1958. A r e v i s e d t a b l e o f t h e
B a l l and O l s o n . Food Res. 23:396.
Ph
Hicks,
E.W.
1961.
Uncertainties
c a l c u l a t i o n s . Food Res. 26:218.
canning
in
function
of
process
J e n , Y., M a n s o n , J . E . , Stumbo, C.R.,
and Z a h r a d n i k ,
J.W.
1971. A p r o c e d u r e f o r e s t i m a t i n g s t e r i l i z a t i o n o f a n d
quality
factor
degradation
i n thermally
processed
f o o d s . J . F o o d S c i . 36:692.
Kreith,
F.
1964.
"Principles
of
Heat
Transfer".
I n t e r n a t i o n a l T e x t b o o k Company, S c r a n t o n , PA.
L u n d , D.B. 1978. S t a t i s t i c a l a n a l y s i s
of thermal
c a l c u l a t i o n s . Food T e c h n o l . 32(3):76.
Madderom,
P.
1978. "U.B.C. I n t e g r a t i o n
:
(quadrature) R o u t i n e s " , Computing
Centre,
of B r i t i s h C o l u m b i a , V a n c o u v e r , C a n a d a .
process
Integration
University
M a n s o n , J . E . , a n d Z a h r a d n i k , J.W. 1967. Computer
process
determination f o r conduction-heated
Food T e c h n o l . 21(9):1206.
thermal
foods.
Manson, J . E . , Z a h r a d n i k ,
J.W.,
a n d Stumbo, C R . 1970.
E v a l u a t i o n of l e t h a l i t y
and n u t r i e n t
r e t e n t i o n s of
conduction-heating
foods
i n rectangular containers.
F o o d T e c h n o l . 24( 1 1 ) : 1297.
M a n s o n , J . E . , Stumbo, C.R.,
and Zahradnik,
J.W. 1974.
E v a l u a t i o n of thermal p r o c e s s e s f o r c o n d u c t i o n h e a t i n g
f o o d s i n p e a r - s h a p e d c o n t a i n e r s . J . F o o d S c i . 39:276.
Merson,
R.L., S i n g h ,
R.P., a n d C a r r o a d ,
P.A. 1978. An
e v a l u a t i o n o f B a l l ' s f o r m u l a method o f t h e r m a l p r o c e s s
c a l c u l a t i o n s . Food T e c h n o l . 32(3):66.
64
Ohlsson,
T.
1980a.
Temperature dependence
of
sensory
quality
changes
d u r i n g t h e r m a l p r o c e s s i n g . J . Food
S c i . 45:836.
O h l s s o n , T. 1980b. O p t i m a l s t e r i l i z a t i o n
temperatures
f l a t c o n t a i n e r s . J . F o o d S c i . 45:847.
Patashnik,
M.
1953. A s i m p l i f i e d
procedure
p r o c e s s e v a l u a t i o n . F o o d T e c h n o l . 7:1.
for
f o r thermal
P f l u g , I . J . 1968. E v a l u a t i n g t h e l e t h a l i t y o f h e a t
using
a method e m p l o y i n g H i c k s ' t a b l e . F o o d
22(9):1153. .
process
Technol.
Rha, C. 1975. T h e r m a l p r o p e r t i e s
of food m a t e r i a l s .
In
"Theory,
Determination
and
Control
of
Physical
P r o p e r t i e s o f F o o d M a t e r i a l s " , E d . C. R h a . D.
Reidel
P u b l i s h i n g Company, B o s t o n , MA.
R o s s , I . J . , B r i d g e s , T.C., a n d P a y n e , F.A. 1979. A c o m p u t e r
technique f o r c a l c u l a t i n g thermal i n a c t i v a t i o n . Trans.
ASAE 22:194.
S c h u l t z , O.T., a n d Olson,F.C.W. 1940. T h e r m a l p r o c e s s i n g o f
canned
foods
in
t i n containers.
I I I . Recent
i m p r o v e m e n t s i n t h e g e n e r a l method o f t h e r m a l
process
calculations.
A s p e c i a l c o - o r d i n a t e p a p e r a n d methods
of c o n v e r t i n g i n i t i a l a n d r e t o r t
temperatures.
Food
R e s . 5:399.
S m i t h , T., a n d T u n g , M.A.
1979. U n p u b l i s h e d
data.
Steele,
R . J . , and Board,
P.W.
1979. T h e r m a l
process
calculations
using s t e r i l i z i n g
ratios.
J.
Food
T e c h n o l . 14:227.
Steele,
R.J., Board,
P.W., B e s t , D . J . , a n d W i l l c o x ,
1979.
R e v i s i o n o f t h e f o r m u l a method
tables
t h e r m a l p r o c e s s e v a l u a t i o n . J . Food S c i . 44:954.
M.E.
for
Stumbo, C R . 1973. " T h e r m o b a c t e r i o l o g y i n F o o d P r o c e s s i n g " ,
2nd e d . , A c a d e m i c P r e s s , I n c . , New Y o r k , NY.
65
Stumbo, C.R.,
and
L o n g l e y , R.E. 1966. New p a r a m e t e r s
p r o c e s s c a l c u l a t i o n . Food T e c h n o l . 20(3):341 .
for
Teixeira,
A.A.,
Dixon,
J.R.,
Zahradnik,
J.W.,
and
Zinmeister,
G.E.
1969a. Computer
determination
of
spore s u r v i v a l
distributions
in thermally-processed
c o n d u c t i o n - h e a t e d foods. Food T e c h n o l . 23(3):352.
Teixeira,
A.A.,
Dixon,
J.R.,
Zahradnik,
J.W.,
and
Zinmeister,
G.E.
1969b. Computer
optimization
of
nutrient
retention
i n the
thermal
p r o c e s s i n g of
c o n d u c t i o n h e a t i n g f o o d s . Food T e c h n o l . 23(6):848.
T e i x e i r a , A.A.,
Z i n m e i s t e r , G.E., and Z a h r a d n i k , J.W.
1975.
Computer s i m u l a t i o n of
variable
retort
control
and
container
geometry
as
a p o s s i b l e means of i m p r o v i n g
thiamine retention i n thermally processed
foods.
J.
Food S c i . 40:656.
Timbers,
G.E.
, and H a y a k a w a , K . - I . 1967. C a l c u l a t i o n by
d i g i t a l c o m p u t e r : Mass a v e r a g e s t e r i l i z i n g
value
for
t h e r m a l p r o c e s s . Food T e c h n o l . 21(8):1069.
T u n g , M.A.,
and G a r l a n d , T.D.
1978. C o m p u t e r c a l c u l a t i o n
t h e r m a l p r o c e s s e s . J . Food S c i . 43:365.
of