appendix: useful figures and tables - springer
TRANSCRIPT
APPENDIX: Useful Figures and Tables
385
F
Fro
m C
lary
et
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(19
71
)
FIG
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FIG
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FIG
. A
.4.
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390 FOOD PROCESS ENGINEERING
TABLE A.1. DIFFUSIVITY DATA FOR GASES THROUGH PACKAGING MATERIALS
Diffusivity at 25' C
Materia] Gas D Do Ed (c m2/s) (c m2/s) (J/mole)
Polystyrene He 10.4 X 10-6 0.0019 3.1 H2 4.36 0.0036 4.0 O2 0.11 0.125 8.3
CO2 0.058 0.128 8.7
Polyvinyl He 9.52 0.011 4.2 acetate H2 2.10 0.013 5.2 (glassy) O2 0.051 6.31 11.1
CH4 0.0019 2.3 X 105 19.3
Polyethylene He 3.07 0.037 5.6 (Density O2 0.17 0.43 8.8 0.964) CO2 0.124 0.19 8.5
CO 0.096 0.251 8.8 N2 0.093 0.33 9.0
CH4 0.057 2.19 10.4
Source: J. Crank and G. Park, Diffusion in Pollmers, New York: Academic Press, 1968. Note: D = Do exp (-Ed/RT). D is in cm2/sec. d = activation energy.
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Ad
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: R
aznj
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. 19
78.
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Hem
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Co
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, W
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. 19
78.
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k o
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Hem
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ub
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Co
rpo
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on
, W
ashi
ngto
n.
APPENDIX 395
TABLE A.S. PROPERTIES OF ICE AS A FUNCTION OF TEMPERATURE
Temperature (C)
-101 - 73 - 45.5 - 23 - 18 - 12 - 7
o
Thermal Conductivity (W/mK)
3.50 3.08 2.72 2.41 2.37 2.32 2.27 2.22
Specific Heat (kJ/kg K)
1.382 1.587 1.783 1.922 1.955 1.989 2.022 2.050
Density (kg/m3)
925.8 924.2 922.6 919.4 919.4 919.4 917.8 916.2
Adapted from Dickerson (1969)
TA
BL
E A
.6.
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F S
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w
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or
Spe
cifi
c V
olum
e (m
3 /kg
) E
nth
alp
y (
kJ/
kg
) E
ntr
op
y (
kJ/
kg
·K)
O"l
Tem
per
atu
re
Pre
ssu
re
>%j
(C)
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a)
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apor
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7045
Sou
rce:
Abr
idge
d fr
om J
.H.
Kee
nan,
F.G
. Key
es,
P.G
. H
ill,
an
d J
.G.
Moo
re, S
team
Ta
ble
s-M
etri
c U
nits
. N
ew Y
ork:
Jo
hn
Wil
ey
&
Son
s, I
nc.,
196
9. W
ith
per
mis
sion
of
the
auth
ors
an
d p
ubli
sher
s.
>
'"1:1
'"1:1
t.%j
Z o ~
w
CD
--
l
TA
BL
E A
.7.
PR
OP
ER
TIE
S O
F S
UP
ER
HE
AT
ED
ST
EA
M (
ST
EA
M T
AB
LE
), S
I U
NIT
S (
u, s
pe
cif
ic v
olu
me
, m
3 Ik
g; H
, en
tha
lpy,
kJ I
kg;
S,
en
tro
py,
kJ I
kg
·K)
w
<.D
A
bsol
ute
Pre
ssur
e,
kP
a T
emp
erat
ure
(C)
00
(Sat
. Tem
p., C
) 1
00
15
0 20
0 25
0 3
00
3
60
4
20
5
00
>
rj
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8
Sou
rce:
Abr
idge
d fr
om
J.H
. K
een
an,
F.G
. Key
es, P
.G. H
ill,
an
dJ.
G. M
oore
, Ste
am
Ta
ble
s-M
etri
c U
nits
. New
Yor
k: J
oh
n W
iley
&
Son
s, I
nc.,
1969
. W
ith
per
mis
sion
of
the
auth
ors
an
d p
ubli
sher
s.
T A
BL
E A
.B.
RH
EO
LO
GIC
AL
PR
OP
ER
TIE
S O
F F
LU
ID F
OO
DS
Con
sist
ency
C
oeff
icie
n t
Flo
w
Tem
per
atu
re
(m)
Beh
avio
r M
easu
rem
ent
Pro
du
ct
(C)
Com
posi
tion
(P
a so
) In
dex
(n)
M
eth
od
R
efer
ence
Oli
ve o
il 20
no
rmal
0.
084
1.0
un
kn
ow
n
Mo
hse
nin
(9
70
) H
on
ey
24
norm
al
5.6
1.0
Cap
illa
ry
Ch
arm
(19
78)
tub
e S
oy b
ean
oil
30
norm
al
0.04
1.
0 u
nk
no
wn
M
oh
sen
in (
97
0)
Ho
ney
24
no
rmal
6.
18
1.0
sing
le
Ch
arm
(9
78
) cy
lind
er
Who
le m
ilk
20
norm
al
0.02
12
1.0
un
kn
ow
n
Mo
hse
nin
(9
70
) S
kim
mil
k 25
no
rmal
0.
0014
1.
0 u
nk
no
wn
M
oh
sen
in (
97
0)
Cre
am
3 20
'/cf
at
0.00
62
1.0
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kn
ow
n
Mo
hse
nin
(9
70
) C
ream
3
30%
fat
0.
0138
1.
0 u
nk
no
wn
M
oh
sen
in (
97
0)
App
le ju
ice
27
200
Bri
x 0.
0021
1.
0 C
apil
lary
S
arav
aco
s (1
968)
tu
be
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le ju
ice
27
600
Bri
x 0.
03
1.0
Cap
illa
ry
Sar
avac
os
(196
8)
tub
e G
rap
eju
ice
27
200
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x 0.
0025
1.
0 C
apil
lary
S
arav
aco
s (1
968)
tu
be
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pe
juic
e 27
60
0 B
rix
0.11
1.
0 C
apil
lary
S
arav
aco
s (1
968)
tu
be
To
mat
o c
on
cen
trat
e 32
5.
8%T
.S.
0.22
3 0.
59
Coa
xial
H
arp
er a
nd
cy
lin
der
E
I S
ahri
gi (
1965
) T
om
ato
co
nce
ntr
ate
32
30
%T
.S.
18.7
0.
4 C
oaxi
al
Har
per
an
d
cyli
nder
E
I S
ahri
gi (
1965
) T
om
ato
pu
ree
un
kn
ow
n
unkn
own
0.92
0.
554
Coa
xial
C
har
m (
1978
) cy
lind
er
Cor
n sy
rup
27
48
.4%
T.S
. 0.
053
1.0
Coa
xial
H
arp
er (
1960
) cy
lin
der
>
A
pric
ot p
ure
e 21
17
.7%
T.S
. 5.
4 0.
29
Coa
xial
H
arp
er(1
96
0)
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cyli
nder
'i:
i A
pric
ot p
ure
e 25
1
9%
T.S
. 20
.0
0.3
Coa
xial
W
atso
n (
1968
) t<:
l Z
cy
lin
der
t:
l n
arro
w g
ap
......
Apr
icot
pu
ree
27
13.8
% T
.S.
7.2
0.41
C
apil
lary
S
arav
aco
s (1
968)
:x:
tub
e w
A
pric
ot c
one.
25
2
6%
T.S
. 67
.0
0.3
Coa
xial
W
atso
n (
1968
) C
D
cyli
nd
er
CD
nar
row
gap
T A
BLE
A.B
. (C
on
tin
ued
) """ 0 0
Con
sist
ency
C
oeff
icie
nt
Flo
w
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Tem
per
atu
re
(m)
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avio
r M
easu
rem
ent
0 0 P
rodu
ct
(C)
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posi
tion
(P
a sn
) In
dex
(n)
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ho
d
Ref
eren
ce
t::l
App
lesa
uce
24
unkn
own
0.66
0.
408
Cap
illa
ry
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arm
(197
8)
'"d
tub
e ~
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lesa
uce
25
31.7
%T
.S.
22.0
0.
4 C
oaxi
al
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son
(19
68)
0 n cy
lind
er
t:%j
r:n
nar
row
gap
r:n
A
pple
sauc
e 27
11
.6%
T.S
. 12
.7
0.28
C
apil
lary
S
arav
aco
s (1
968)
t:%
j tu
be
Z
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lesa
uce
24
unkn
own
0.5
0.64
5 C
oaxi
al
Ch
arm
(197
8)
q cy
lind
er
......
Ch
arm
(197
8)
Z
App
lesa
uce
unkn
own
unkn
own
5.63
0.
47
Coa
xial
t:%
j
cyli
nder
t:%
j
Pea
r pur
ee
27
14.6
%T
.S.
5.3
0.38
C
apil
lary
S
arav
aco
s (1
968)
~
......
tub
e Z
P
ear
pure
e 27
15
.2%
T.S
. 4.
25
0.35
C
oaxi
al
Har
per
(19
60)
q
cyli
nder
P
ear
pure
e 32
18
.31%
T.S
. 2.
25
0.48
6 C
oaxi
al
Har
per
an
d
cyli
nder
L
eber
man
n (
1964
) P
ear
pure
e 32
45
.75%
T.S
. 35
.5
0.47
9 C
oaxi
al
Har
per
an
d
cyli
nder
L
eber
man
n (1
964)
P
each
pur
ee
27
10.0
%T
.S.
4.5
0.34
C
apil
lary
S
arav
acos
(196
8)
tub
e P
each
pur
ee
27
10.0
%T
.S.
0.94
0.
44
Coa
xial
H
arp
er (1
960)
Ban
ana
pure
e 24
un
know
n 6.
5 cy
lind
er
0.45
8 C
oaxi
al
Ch
arm
(197
8)
Ban
ana
pure
e 24
un
know
n 10
.7
cyli
nder
0.
333
Cap
illa
ry
Ch
arm
(19
78)
tub
e B
anan
a pu
ree
20
unkn
own
6.89
0.
46
Cap
illa
ry
Ch
arm
(19
78)
tub
e B
anan
a pu
ree
42
unkn
own
5.26
0.
486
Cap
illa
ry
Ch
arm
(19
78)
tub
e B
anan
a pu
ree
49
unkn
own
4.15
0.
478
Cap
illa
ry
Ch
arm
(197
8)
tub
e N
ote:
Thi
s ta
ble
is
no
t in
ten
ded
to
pro
vide
a
com
plet
e li
st
of
rheo
logi
cal
prop
erti
es a
vail
able
for
li
quid
fo
od
prod
ucts
. V
aria
bili
ties
wit
h t
emp
erat
ure
an
d c
once
ntra
tion
may
be
illu
stra
ted
mor
e ac
cura
tely
in
ref
eren
ces
prov
ided
.
TA
BL
E A
.9.
SP
EC
IFIC
HE
AT
S O
F F
OO
DS
Com
posi
tion
S
peci
fic
Hea
t W
ater
P
rote
in
Car
bo
hy
dra
te
Fat
Ash
E
q. (
3.31
) E
q. (
3.32
) E
q. (
3.33
) E
x&er
imen
tall
Pro
du
ce
(%)
(%)
(%)
(%)
(%)
(kJ/
kg
K)
(kJ I
kg K
) (k
J Ikg
K)
kJ/
kg
K)
Bee
f 68
.3
20.7
0.
0 10
.0
1.0
3.39
3.
35
3.35
3.
52
(Ham
bu
rger
) F
ish,
can
ned
70
.0
27.1
0.
0 0.
3 2.
6 3.
43
3.31
3.
35
Sta
rch
12
.0
0.5
87.0
0.
2 0.
3 1.
976
1.61
2 1.
754
Ora
ng
e ju
ice
87.5
0.
8 11
.1
0.2
0.4
3.87
3 3.
818
3.82
2 L
iver
, raw
bee
f 74
.9
15.0
0.
9 9.
1 1.
1 3.
554
3.52
1 3.
525
Dry
mil
k,
3.5
35.6
52
.0
1.0
7.9
1.76
3 1.
365
1.52
0 n
on
fat
Bu
tter
15
.5
0.6
0.4
81.0
2.
5 2.
064
2.39
0 2.
043
2.0
51
-2.1
35
M
ilk,
who
le
87.0
3.
5 4.
9 3.
9 0.
7 3.
860
3.76
8 3.
831
3.85
2 p
aste
uri
zed
B
lueb
erri
es,
73.0
0.
4 23
.6
0.4
2.6
3.50
8 3.
073
3.44
5 sy
rup
pac
k C
od, r
aw
82.6
15
.0
0.0
0.4
2.0
3.75
1 3
.63
0
3.69
7 S
kim
mil
k 90
.5
3.5
5.1
0.1
0.8
3.94
8 3.
935
3.93
5 3
.97
7-4
.01
9
To
mat
o s
oup,
81
.4
1.8
14.6
1.
8 0.
4 3.
718
3.47
1 3.
676
con
cen
trat
e B
eef,
lean
77
.0
22.0
1.
0 3
.55
9
3.51
2 3.
579
Egg
yol
k 49
.0
13.0
11
.0
1.0
2.90
5 2.
457
2.44
9 2.
810
Fis
h, f
resh
76
.0
19.0
1.
4 3.
617
3.43
7 3.
500
3.6
00
B
eef,
lea
n 71
.7
21.6
0.
0 5.
7 1.
0 3.
458
3.40
4 3.
437
3.43
3 P
ota
to
79.8
2.
1 17
.1
0.1
0.9
3.6
80
3
.59
6
3.63
4 3.
517
App
le, r
aw
84.4
0.
2 14
.5
0.6
0.3
3.7
93
3.
734
----
-.. 3.759·~ 3
.72
6-4
.01
9
Bac
on
49
.9
27.6
0.
3 17
.5
4.7
2.92
6 2.
864
2.85
1 2.
01
Cu
cum
ber
96
.1
0.5
1.9
0.1
1.4
4.09
0 4.
073
4.06
1 4.
103
Bla
ckb
erry
, 76
.0
0.7
22.9
0.
2 0.
2 3.
588
3.48
7 3.
521
syru
p p
ack
P
ota
to
75.0
0.
0 23
.0
0.0
2.0
3.5
59
3.
429
3.48
3 3.
517
Vea
l 68
.0
21.0
0.
0 10
.0
1.0
3.38
3 3.
056
3.34
9 3.
223
Fis
h
80.0
15
.0
4.0
0.3
0.7
3.68
4 3.
408
3.65
1 3.
60
:>
Che
ese,
65
.0
25.0
1.
0 2.
0 7.
0 3.
307
2.77
6 3.
215
3.26
5 '"t:
1 '"t:
1 co
ttag
e t<:
l S
hri
mp
66
.2
26.8
0.
0 1.
4 0.
0 3.
337
3.11
1 3.
404
3.01
4 Z
t:1
S
ard
ines
57
.4
25.7
1.
2 11
.0
0.0
3.11
5 2.
972
3.00
2 3.
014
~
Bee
f, r
oas
t 60
.0
25.0
0.
0 13
.0
0.0
3.08
1 3.
098
3.11
5 3
.05
6
Car
rot,
fre
sh
88.2
1.
2 9.
3 0.
3 1.
1 3
.88
9
3.83
1 3.
864
3.8
1-3
.93
5
.... 'R
eid
y,
G.A
. 19
68.
Th
erm
al P
rope
rtie
s of
Foo
ds a
nd
Met
ho
ds
of
Th
eir
Det
erm
inat
ion
. M
.S.
Th
esis
Fo
od
Sci
ence
Dep
artm
ent,
0 .....
. M
ichi
gan
Sta
te U
nive
rsit
y, E
ast
Lan
sing
, M
ichi
gan.
402 FOOD PROCESS ENGINEERING
TABLE A.10. THERMAL CONDUCTIVITY OF SELECTED FOOD PRODUCTS
Moisture Content Temperature Thermal Conductivity Product (%) (C) (W!mK)
Apple 85.6 2 to 36 0.393 Applesauce 78.8 2 to 36 0.516 Beef, freeze dried
- 1000 mm Hg pressure 0 0.065 - 0.001 mm Hg pressure 0 0.037
Beef, lean - perpendicular to fibers 78.9 • 7 0.476 - perpendicular to fibers 78.9 62 0.485 - parallel to fibers 78.7 8 0.431 - parallel to fibers 78.7 61 0.447
Beef fat 24 to 38 0.19 Butter 15 46 0.197 Cod 83 2.8 0.544 Corn, yellow dent 0.91 8 to 52 0.141
30.2 8 to 52 0.172 Egg, frozen whole -10 to-6 0.97 Egg, white 36 0.577 Egg, yolk 33 0.338 Fish muscle o to 10 0.557 Grapefruit, whole 30 0.45 Honey 12.6 2 0.502
80 2 0.344 14.8 69 0.623 80 69 0.415
Juice, apple 87.4 20 0.559 87.4 80 0.632 36.0 20 0.389 36.0 80 0.436
Lamb - perpendicular to fiber 71.8 5 0.45
61 0.478 - parallel to fiber 71.0 5 0.415
61 0.422 Milk 37 0.530 Milk, condensed 90 24 0.571
78 0.641 50 26 0.329
78 0.364 Milk, skimmed 1.5 0.538
80 0.635 Milk, nonfat dry 4.2 39 0.419 Olive oil 15 0.189
100 0.163 Oranges, combined 30 0.431 Peas, black-eyed 3 to 17 0.312 Pork
- perpendicular to fibers 75.1 6 0.488 60 0.54
- parallel to fibers 75.9 4 0.443 61 0.489
Porkfat 25 0.152 Potato, raw flesh 81.5 1 to 32 0.554 Potato, starch gel 1 to 67 0.04 Poultry, broiler muscle 69.1 to 74.9 4 to 27 0.412 Salmon
- perpendicular to fibers 73 4 0.502 Salt 87 0.247 Sausage mixture 64.72 24 0.407 Soybean oil meal 13.2 7 to 10 0.069 Strawberries -14t025 0.675
APPENDIX 403
TABLE A.10. (Continued)
Moisture Content Temperature Thermal Conductivity Product (ei) (C) (W/mK)
Sugars 29 to 62 0.087 to 0.22 Turkey, breast
- perpendicular to fibers 74 3 0.502 - parallel to fibers 74 3 0.523
Veal - perpendicular to fibers 7f> 6 0.476
62 0.489 - parallel to fibers 7f> 5 0.441
60 0.452 Vegetable & Animal oils 4 to 187 0.169 Wheat flour 8.8 43 0.45
65.5 0.689 1.7 0.542
Whey 80 0.641
Reidy, G.A. 1968. Thermal Properties of Foods and Methods of Their Determination. M.S. Thesis Food Science Dept. Michigan State University, East Lansing, Michigan.
404 FOOD PROCESS ENGINEERING
TABLEA.11. ENTHALPY OF FROZEN FOODsa
Mean Specific
Water Heath Content 4 to 32C
Product %(wt) kJ/kgC Temp.C -40 -30 -20 -18 -16
Fruits and Vegetables
Applesauce 82.8 3.73 Enthalpy kJ Ikg 0 23 51 58 65 % waterunfrozenc 6 9 10 12
Asparagus, peeled 92.6 3.98 Enthalpy kJ/kg 0 19 40 45 50 % water unfrozen
Bilberries 85.1 3.77 Enthalpy kJ/kg 0 21 45 50 57 % water unfrozen 7 8
Carrots 87.5 3.90 Enthalpy kJ/kg 0 21 46 51 57 % water unfrozen 7 8
Cucumbers 95.4 4.02 Enthalpy kJ/kg 0 18 39 43 47 % water unfrozen
Onions 85.5 3.81 Enthalpy kJ/kg 0 23 50 55 62 % water unfrozen 5 8 10 12
Peaches 85.1 3.77 Enthalpy kJ/kg 0 23 50 57 64 without stones % water unfrozen 5 8 9 11
Pears, Barlett 83.8 3.73 Enthalpy kJ/kg 0 23 51 57 64 % water unfrozen 6 9 10 12
Plums without 80.3 3.65 Enthalpy kJ/kg 0 25 57 65 74 stones % water unfrozen 8 14 16 18
Raspberries 82.7 3.73 Enthalpy kJ/kg 0 20 47 53 59 % water unfrozen 7 8 9
Spinach 90.2 3.90 Enthalpy kJ/kg 0 19 40 44 49 % water unfrozen
Strawberries 89.3 3.94 Enthalpy kJ/kg 0 20 44 49 54 % water unfrozen 5 6
Sweet cherries 77.0 3.60 Enthalpy kJ/kg 0 26 58 66 76 without stones % water unfrozen 9 15 17 19
Tall peas 75.8 3.56 Enthalpy kJ/kg 0 23 51 56 64 % water unfrozen 6 10 12 14
Tomato pulp 92.9 4.02 Enthalpy kJ/kg 0 20 42 47 52 % water unfrozen 5
Eggs Egg white 86.5 3.81 Enthalpy kJ/kg 0 18 39 43 48
% water unfrozen 10 Egg yolk 40.0 2.85 Enthalpy kJ Ikg 0 19 40 45 50
% water unfrozen 20 22 Whole egg 66:4 3.31 Enthalpy kJ/kg 0 17 36 40 45
with shelld
Fish and Meat Cod 80.3 3.69 Enthalpy kJ/kg 0 19 42 47 53
% water unfrozen 10 10 11 12 12 Haddock 83.6 3.73 Enthalpy kJ Ikg 0 19 42 47 53
% water unfrozen 8 8 9 10 11 Perch 79.1 3.60 Enthalpy kJ/kg 0 19 41 46 52
% water unfrozen 10 10 11 12 12 Beef, lean 74.5 3.52 Enthalpy kJ/kg 0 19 42 47 52 Freshe % water unfrozen 10 10 11 12 13 Beef, lean dried 26.1 2.47 Enthalpy kJ/kg 0 19 42 47 53
% water unfrozen 96 96 97 98 99 Bread
White bread 37.3 2.60 Enthalpy kJ/kg 0 17 35 39 44 Wholewheat 42.4 2.68 Enthalpy kJ/kg 0 17 36 41 48
bread
a Above -40C. b Temperature range limited to 0 to 20C for meats and 20 to 40C for egg yolk. C Total weight of unfrozen water = (total weight offood)(% water content/lOO)(waterunfrozen/l00).
APPENDIX 405
-14 -12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
73 84 95 102 110 120 132 152 175 210 286 339 343 14 17 19 21 23 27 30 37 44 57 82 100 55 61 69 73 77 83 90 99 108 123 155 243 381 5 6 7 8 10 12 15 17 20 29 58 100
64 73 82 87 94 101 110 125 140 167 218 348 352 9 11 14 Hi 17 18 21 25 30 38 57 100
64 72 81 87 94 102 111 124 139 166 218 357 361 9 11 14 15 17 18 20 24 29 37 53 100
51 57 64 67 70 74 79 85 93 104 125 184 390 5 11 14 20 37 100
71 81 91 97 105 115 125 141 163 196 263 349 353 14 16 18 19 20 2:1 26 31 38 49 71 100 72 82 93 100 108 118 129 146 170 202 274 348 352 13 16 18 20 22 25 28 33 40 51 75 100 73 83 95 101 109 120 132 150 173 207 282 343 347 14 17 19 21 23 26 29 35 43 54 80 100 84 97 111 119 129 142 159 182 214 262 326 329 333 20 23 27 29 33 37 42 50 61 78 100 65 75 85 90 97 105 115 129 148 174 231 340 344 10 13 16 17 18 20 23 27 33 42 61 100 54 60 66 70 74 79 86 94 103 117 145 224 371
6 7 9 11 13 16 19 28 53 100 60 67 76 81 88 95 102 114 127 150 191 318 367
7 9 11 12 14 16 18 20 24 30 43 86 100 87 100 114 123 133 149 166 190 225 276 317 320 324 21 26 29 32 36 40 47 55 67 86 100 73 84 95 102 111 121 133 152 176 212 289 319 323 16 18 21 23 26 28 33 39 48 61 90 100 57 63 71 75 81 87 93 103 114 131 166 266 382
6 7 il 10 12 14 16 18 24 33 65 100
53 58 65 68 72 75 81 87 96 109 134 210 352 13 18 20 23 28 40 82 100
56 62 68 72 76 80 85 92 99 109 128 182 191 24 27 28 29 31 33 35 38 45 58 94 100 50 55 61 64 67 71 75 81 88 98 117 175 281
59 66 74 79 84 89 96 105 118 137 177 298 323 13 14 16 17 18 19 21 23 27 34 48 92 100 59 66 73 77 82 88 95 104 116 136 177 307 337 11 12 13 14 15 16 18 20 24 31 44 90 100 58 65 72 76 81 86 93 101 112 129 165 284 318 13 14 15 16 17 18 20 22 26 32 44 87 100 58 65 72 76 81 88 95 105 113 138 180 285 304 14 15 16 17 18 20 22 24 31 40 55 95 100 62 66 70 74 79 84 89 93
100
49 56 67 75 83 93 104 117 124 128 131 134 137 56 66 78 86 95 106 119 135 150 154 157 160 163
d Calculated for a weight composition of 58% white (86.5% water) and 32% yolk (50% water). e Data for chicken, veal, and venison very nearly matched the data for beef of the same water content."
From Dickerson (1981)
406 FOOD PROCESS ENGINEERING
TABLE A.12. INITIAL FREEZING TEMPERATURE OF FRUITS, VEGETABLES AND JUICES
Product
Apple juice Apple juice concentrate Applesauce Asparagus Bilberries Bil berry juice Carrots Cherry juice Grape juice Onions Orange juice Peaches Pears Plums Raspberries Raspberry juice Spinach Strawberries Strawberry juice Sweet cherries Tall peas Tomato pulp
Water content
(% by weight)
87.2 49.8 82.8 92.6 85.1 89.5 87.5 86.7 84.7 85.5 89.0 85.1 83.8 80.3 82.7 88.5 90.2 89.3 91.7 77.0 75.8 92.9
TABLE A.13. HEAT TRANSFER COEFFICIENTS
Condition
Naturally circulating Air blast Plate contact freezer Slowly circulating brine Rapidly circulating brine
Liquid nitrogen low side of horizontal plate where gas
blanket forms upper side of horizontal plate
Boiling water
Initial freezing
temperature (C)
-1.44 -11.33
-1.67 -0.67 -1.11 -1.11 -1.11 -1.44 -1.78 -1.44 -1.17 -1.56 -1.61 -2.28 -1.22 -1.22 -0.56 -0.89 -0.89 -2.61 -1.83 -0.72
Heat Transfer Coefficient (W/m2K)
5 22 56 56 85
170 425 568
APPENDIX 407
TABLE A.14. VARIOUS FORMS OF GAS CONSTANT
0.0821 1.987 1.987 8.314
1546 10.n
18,510 0.7302
848,000 8,314.34
62,36:3.32
atmliter/g-mole K cal/g-mole oK BTU/lb-mole R joules/g-mole K ft Ibs/lb-mole R Ob,/in'l ft' /Ib-mole R Ob,/in'lin'/lb-mole R atm ft'/Ib-mole R (Kg/m'lcml/lb-mole K m'Pa/kg mole K cm'mm Hg/mole K
TABLE A.1S. FREQUENTLY USED CONVERSION FACTORS FOR ENGLISH TO STANDARD INTERNATIONAL UNITS
Area 1 ft' = 0.0929 m'
Density Ilbm/ft'l = 16.0185 kg/m'
Diffusivity 1 ft'/hr = 2.581 X 10-' m'/s
Energy 1 BTU = 1055 J = 1.055 kJ 1 kcal = 4.184 kJ
Enthalpy 1 BTU/Ibm = 2.3258kJ/kg
Force lib, = 4.4482N 1 N = 1 kgm/s'
Heat flux 1 BTU/hr = 0.29307 W 1 BTU/min = 17.58 W 1 kJ/hr = 2.778 X 1O- 4kW 1,]/s=IW
Heat Transfer Coefficient 1 BTU/hr ft'F = 5.6783 W /m'K
Length 1 ft = 0.3048 m 1 micron = 10-6 m
Mass 1 Ibm = 0.4536 kg
Mass Transfer Coefficient 1 Ib mole/hr ft' mole fraction
= 1.3562 X 10-:< kg mole/s m'mole fraction
Pressure 1 psia = 6.895 kPa 1 psia = 6.895 X lO:J N/m'
Specific Heat 1 BTU/lbmF = 4.1865 J/gK
Temperature rF = 1.8'C
Thermal Conductivity 1 BTU/hrft F = 1.731 W /mK
Viscosity Ilbm/ft h = 0.4134 cp Ilbmft s = 1488.16 cp lcp=10-'Pas llbrs/ft' = 4.7879 X 10' cp 1 Ns/m' = 1 Pas 1 kg/ms = 1 Pas
Volume 1 W = 0.02832 m' 1 gal = 3.785 X 10-3 m3
408 FOOD PROCESS ENGINEERING
BIBLIOGRAPHY
CHARM, S.E. 1978. The Fundamentals of Food Engineering, 3rd Edition. The A VI Publishing Co., Westport, Conn.
CLARY, B.L., G.L. NELSON, and R.E. SMITH. 1971. The application of the geometry analysis technique in determining the heat transfer rates from biological materials. ASAE Trans. 14(3)386.
CRANK, J. and G. PARK. 1968. Diffusion in Polymers, Academic Press, New York, NY.
DICKERSON, R.W., Jr. 1981. Enthalpy of frozen foods. In Handbook and Product Directory Fundamentals. American Society of Heating, Refrigeration and Air Conditioning Engineers. New York.
DICKERSON, R.W., Jr. 1969. Thermal properties of foods. In The Freezing Preservation of Foods, 4th Ed., Vo!' 2. D.K. Tressler, W.B. Van Arsdel and M.J. Copley. The AVI Publishing Co., Westport, Conn.
HARPER, J.C. 1960. Viscometric behavior in relation to evaporation of fruit purees. Food Techno!. 14:557.
HARPER, J.C. and A.F. EL SAHRIGI. 1965. Viscometric behavior of tomato concentrates. J. Food Sci. 30:470.
HARPER, J.C. and KW. LEBERMANN. 1964. Rheological behavior of pear purees. Proc. 1st Intern. Congr. Food Sci. & Techno!. 719-728.
KEENAN, J.H., F.G. KEYES, P.G. HILL, and J.G. MOORE. 1969. Steam Tables - Metric Units. John Wiley & Sons, Inc., New York, NY.
MOHSENIN, N.N. 1978. Physical Properties of Plant and Animal Materials. Vol. I, Part II. Gordon and Breach Science Publishers. New York, NY.
RAZNJEVIC, K. 1978. Handbook of Thermodynamic Tables and Charts. McGraw-Hill Book Co., New York.
REIDY, G.A. 1968. Thermal Properties of Foods and Methods of their Determination. M.S. Thesis. Food Science Dept., Michigan State University. E. Lansing, MI.
SARAVACOS, G.D. 1968. Tube viscometry of fruit purees and juices. Food Techno!. 22(12)1585-1588.
WATSON, E.L. 1968. Rheological behavior of apricot purees and concentrates. Can. Agri. Engr. 10(1)8-12.
Answers to Selected Problems
Chapter 1
1.1. 105.6 kj/kg 1.3. 0.288 mg/l
Chapter 2
2.1. m = 2.236 kPa; n = 0.295 2.3. m = 1.8676 X 10-3 kPa;
n = 0.399 2.5. f = L::.PR/ pu2 L 2.7. L::.P = 17.7 kPa (water)
L::.P = 468.9 kPa (puree) 2.9. L::.P = 1.53 (L::.P for water) 2.11. D = 2.93 em
Chapter 3
3.1. 23 em 3.3. 6.18 W /m2C 3.5. 1 - exp(UA/Wep )
3.7. 30.6 C 3.9. 60.5 C 3.11. 0.79 hr 3.13. 109.7 C
Chapter 4
4.1. 86.5%
APPENDIX 409
4.3. 350 kj/kg; 88.5% 4.5. tF = 3.49 min 4.7. tF = 6.02 hr; d = 23.87 m
Chapter 5
5.1. 2689 W /m2K 5.3. F = 58.878 kg/hr
Chapter 6
6.2. 0.1166 kgH20/kg dry solids 6.4. 82.5 mieron 6.6. 9.1% MC
Chapter 7
7.1. 55.56 kg/min 7.3. 8.1 min 7.5. 2 stages
Chapter 8
8.1. 36 hr 8.3. 10.03 em
Index
Absolute humidity, 264 Activation energy, 10 Adia ba tic calorimeter, 173 Agitated container, 144 Air-blast freezing, 198 Angle of internal friction, 70 Angle of repose, 71 Angle of slide, 70 Anomalous objects, 137
heat transfer, 137 Answers, problems, 410 Apparent specific hea( 193 Arching, 71 Arrhenius equation, 14
plot, 14 Atomizers, 287
centrifugal pressure, 287 droplet size, 292 energy requirement, 291 fan spray, 288 rotary, 289
BET equation, 275 Belt dryer, 283 Biot number, 124 Boiling point elevation, 218 Boundary layer, 18, 49 Brownian motion, 10 Bulk density, 66
Cabinet dryer, 279 Calandria evaporator, 231 Capillary tube rheometer, 32
Centrifugal separation, 377 basic equations, 377 liquid-liquid, 379 particle-gas, 381 rate, 378 system design, 377
Characteristic dimension, 93 Chemical potential, 6, 159 Chemical reaction, 10 Clausius-Clapeyron equation, 7, 218,
221 Coaxial cylinder rheometer, 37 Concentrated product properties, 58 Cone and plate rheometer, 41 Consistency coefficient, 28 Conveyor dryer, 282 Cooling processes, 87
agitated container, 144 radiation, 99 steady-state, 108 unsteady-state, 124
Count mean diameter, 292
Dehydration, 261 air-suspended, 283 constant-rate, 266, 269 diffusion controlled, 271 drum, 310 falling-rate, 268, 269, 272 fixed-tray, 279
cabinet, 279 tunnel, 279
freeze, 315 fluidized bed, 310 moving bed, 281
411
412 FOOD PROCESS ENGINEERING
belt, 283 conveyor, 282
pneumatic, 308 spray, 284
Diffusion coefficients, 16 mass diffusivity, 17 molecular, 333
Diffusivity, 193 Drag coefficient, 298 Droplet evaporation, 296
drag coefficient, 298 heat and mass transfer, 298 time, 303
Drying curve, 265 rate of, 265
Duhring's rule, 221
Effective molecular weight, 163 Elasticity, 26 Enthalpy, 4 Enthalpy balance, 238
evapora tion, 241 Entropy, 5 Equilibrium curve, 334, 336, 337 Equilibrium moisture content, 274
BET equation, 275 isotherms, 276 Langmuir equation, 275
Equilibrium processes, 332 Evaporation, 216
boiling point elevation, 218 Duhring's rule, 221 heat transfer, 223 low-temperature, 254 mechanical recompression, 252 multiple effect systems, 240
backward feed, 246 forward feed, 246 parallel feed, 246
retention time, 233 single-effect systems, 237 steam economy, 238 system design, 231
agitated film, 232 Calandria, 231 forced circulation, 232 long-tube vertical, 232 plate, 233 rising-falling film, 233
thermal-recompression, 248 suction pressure, 249
Evaporative cooling, 265 Extraction, 339
leaching, 339, 343
rate, 340 right-triangle system, 347
Fick's first law, 16 second law, 16
Filtration, 365 constant-pressure, 368 constant-rate, 366 mechanisms, 370 operating equation, 365 system design, 370
Flow, 44 liquids, 44 powder, 65, 70 slurries, 61
Flow behavior index, 28 Flow number, 293 Fluidized-bed drying, 310 Fluidized-bed freezing, 200 Food engineering, 1 Forced circulation evaporator, 232 Fourier equation, 89 Fourier modulus, 125 Free energy, 5, 159 Freezing, 158
air blast, 198 curves, 162 effective molecular weight, 163 equipment design, 198 fluidized bed, 200 immersion, 204 IQF,200 plate, 201
Freeze drying, 315 atmospheric, 322 drying times, 317 heat and mass transfer, 315 system design, 318
Freezing rates, 176 factors which influence, 178 finite element analysis, 195 freezing point depression, 159 Mott procedure, 190 Neumann problem, 185 numerical solution, 191 Plank's equation, 178 refrigeration requirement, 166, 171,
175 slowest cooling location, 177 Tao solution, 187 thermal arrest time, 177 thermal center, 177 Tien solution, 188
Frequency factor, 14
Friction, 44 contractions, 55 entrance regions, 54 equivalent lengths, 56 expansions, 55 factor, 44, 51, 53 laminar flow, 46 non-Newtonian flow, 52 pneumatic conveying, 64 suspensions, 61 turbulent flow, 48
Frozen foods, 159 apparent specific heat, 193 enthalpy change, 165 unfrozen water fraction, 170
Frozen storage, 205 changes during, 205 crystallization, 205 desiccation, 205 temperature fluctuation, 206 time-temperature-tolerance, 206
Generalized Reynold's number, 47 Geometric index, 137 Graetz-number, 95 Granular food properties, 65 Grashof number, 95, 98
Heat exchangers, 115 direct contact, 122 plate, 118 scraped-surface, 121 steam infusion, 122 stream injection, 122 triple-tube, 117 tubular, 117
Heat of respiration, 91 Heat generation, 91 Heat transfer, 87
conduction, 88 convection, forced, 93 convection, free, 98 finite objects, 136 radiation, 99
absorptivity, 99 emissivity, 99 Stefan-Boltzmann, 99
Heat transfer coefficient, 228 convective, 92 evaporation, 228
in freezing, 196 overall, 99
Heating processes, 87 agitated container, 144 non-Newtonian flow, 108 radiation, 99 steady-state, 108 unsteady-state, 124
Heating-rate constant, fh' 131 Heat-sensitivity, 87
INDEX 413
Heat transfer in laminar flow, 95, 108 circular tube, 95 external flow, 96 fully-developed parabolic velocity
flow, 110 fully-developed velocity profile for
power law fluid, 111 internal flow, 95 non -circular ducts, 96 piston flow, 109
Heat transfer in transition region, 96 Heat transfer in turbulent flow, 96,
115 circular tubes, 96 noncircular ducts, 96
Hooke's law, 26 HTU, 338
Ice crystals, 163 growth, 163, 164 nucleation, 163
Ideal solution, 9 gas, 9
Immersion freezing, 204 Individual quick freezing, 200 Initial freezing point, 195 Insulation, 90
Kelvin model, 75 Kinetic energy, 44, 48
theory, 10 Kinetics, 10 Kopelman equations, 103
Lag factor, j, 131 Laplace equation, 89 Langmuir equation, 275
414 FOOD PROCESS ENGINEERING
Latent heat, 7, 160 fusion, 161 vaporization, 7, 218
Leaching, 339, 343 multi-stage, 347
Lewis number, 268 Log mean temperature difference, 95 Log-normal distribution, 69
geometrie standard deviation, 69 log geometric mean, 68
Mass flow rate equation, 52 Mass mean diameter, 292 Mass transfer, 16, 333
coefficients, 18, 268, 316 overall coefficients, 341 two-film theory, 333
Material balance 334 contact equilibrium, 334 evaporation, 237, 241 extraction, 343
Maxwell equation, 102 Maxwell model, 72 Mechanical energy balance, 52 Mechanical recompression, 252 Mechanical separation, 364 Molality, 161 Mole fraction, 160 Mott procedure, 190 Multiple-effect evaporator, 240
backward feed, 246 forward feed, 246 parallel feed, 246
Neumann problem, 317 Newtonian flow, 26 Non-Newtonian flow, 27 NTU, 338 Nucleation, 164
homogenous, 164 Heterogenous, 164
Nucleation boiling, 226 Numerical methods, 142 Nusselt number, 93
Operating line, 337 Order of reaction, 10
first-order, 10 second-order, 11
Othmer plot, 8
Peclet number, 118 Phase change, 6, 218, 164
diagram, 6 Plank's equation, 178 Plasticity, 25 Plate freezing, 201 Plate evaporator, 233 Plate heat exchanger, 118 Pneumatic drying, 308 Porosity, 66 Powder properties, 65
angle of internal friction, 70 angle of repose, 71 angle of slide, 70 arching, 71 bridging, 71 bulk density, 66 particle density, 66 porosity, 66 Sauter diameter, 67 size, 66 size distribution, 66 void,66
Power law equation, 28 Prandtl number, 93 Pressure, 264
partial, 264 saturation vapor, 265
Pseudoplastics, 28 Psychrometries, 264
absolute humidity, 264 relative humidity, 264
Pump design, 52 power requirement, 52
Pressure-composition diagram, 9
R-value,90 Raoult's law, 9, 159, 333 Rate constant, 10 Recrystallization, 205 Relative humidity, 264 Reynolds number, 19, 93
generalized, 47 Rheological properties, 27
consistency coefficients, 27
flow behavior index, 28 Rheology, 25 Rheometers, 32
capillary tube, 32 coaxial cylinder, 36 cone and plate, 41 rotational, 36
Rising-falling film evaporator, 233 Rotational rheometer, 36
Sauter mean diameter, 292 Schmidt number, 19 Scraped-surface heat exchanger, 121 Sedimentation, 373
high concentration, 375 low concentration, 373
Sherwood number, 18 Single-effect evaporator, 237 Slurry properties, 59 Solid food properties, 65 Specific heat, 4, 100 Spray dryers, 284
co-current, 285 counter current, 285 mixed flow, 286 parallel flow, 287
Steam economy, 238 Steam infusion, 122 Steam jacket, 144 Stefan-Boltzmann's constant, 99 Stoke's law, 375 Storage, 20, 205
prediction of food quality, 20 Supercooling, 162 Survivor curve, 12
spores, 12 thiamine, 14
Suspension properties, 58
Tao solution, 187 Temperature distribution, 124
anomalous objects, 137 finite objects, 135 finite surface and internal resistance,
127
INDEX 415
negligible internal resistance, 125 negligible surface resistance, 126 numerical method, 142 tube flow, laminar, 108
Terminal velocity, 374 Texture, 76
parameters, 77 Texture profile analysis, 77 Thermal arrest time, 177 Thermal conductivity, 103
anisotropic system, 103 fibrous system, 103 isotropic system, 103 parallel to fibers, 105 perpendicular to fibers, 105 powdered food in a packed bed, 107 variable in freezing, 181
Thermal properties, 100 apparent specific heat, 193 diffusivity, 193 specific heat, 100 thermal conductivity, 93, 102
Thermodynamics, 4 potential, 5
Thermal-recompression, 248 Tien solution, 188 Triple-tube heat exchanger, 117 Tubular heat exchanger, 117 Tunnel dryer, 279
Unfrozen water fraction, 170 Uniformly retreating ice front, 317 Unsteady-state heat transfer, 124
agitated containers, 144 finite surface and internal resistance,
127 negligible internal resistance, 125 negligible surface resistance, 126
Viscoelastic, 75 parameter measurement, 76
Viscosity, 26 apparent, 43 concentrates, 59 suspensions, 59
Other A VI Books
AGRICUL TURAL ENERGETICS Fluck and Baird
DRYING CEREAL GRAINS Brooker, Bakker-Arkema, Hall
ENCYCLOPEDIA OF FOOD ENGINEERING Hall, Fa rrall, Rippen
ENCYCLOPEDIA OF FOOD TECHNOLOGY Vol. 2 Johnson and Peterson
FOOD DEHYDRATION Vol. 1 and 2 2nd Edition Van Arsdel, Copley, Morgan
FOOD ENGINEERING SYSTEMS Vol. 1 and 2 Farrall
FOOD PROCESSING WASTE MANAGEMENT Green and Kramer
FUNDAMENTALS OF ELECTRICITY FOR AGRICULTURE Gustafson
FUNDAMENT ALS OF FOOD ENGINEERING 3rd Edition Charm
GRAIN STORAGE: PART OF A SYSTEM Sinha and Muir
HANDLING, TRANSPORTATION AND STORAGE OF FRUITS AND VEGETABLES
Vol. 1 2nd Edition Ryall and Lipton Vol. 2 Ryall and Pentzer
AN INTRODUCTION TO AGRICULTURAL ENGINEERING Roth, Crow, Mahoney
NUTRITIONAL EVALUATION OF FOOD PROCESSING 2nd Edition Harris and Karmas
POSTHARVEST BIOLOGY AND HANDLING OF FRUITS AND VEGETABLES
Haard and Salunkhe POTATOES: PRODUCTION, STORING, PROCESSING
2nd Edition Smith PRINCIPLES OF FARM MACHINERY
3rd Edition Kepner, Bainer, Barger PROCESSING EQUIPMENT FOR AGRICULTURAL PRODUCTS
2nd Edition Hall and Davis SOYBEANS: CHEMISTRY AND TECHNOLOGY
Vol. 1 Revised Edition Smith and Circle THE TECHNOLOGY OF FOOD PRESERVATION
4th Edition Desrosier and Desrosier
aMlta 330 340
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