Example 19-1
A roughly spherical potato of diameter 3” is placed in an
oven at 350
°
F.
If the potato is initially at 50
°
F, how long will
it take for it to reach 300
°
F?
Assume:
Btu
0.29
hr ft R
k
=
⋅
⋅
2
Btu
2.5
hr ft
R
h
=
⋅
⋅
3
lbm
52
ft
ρ
=
3
4
3
sph
V
r
π
=
Btu
0.825
lbm °F
p
c
=
2
4
sph
A
r
π
=
Solution:
Using the lumped system approximation
( )
ln
p
f
i
f
mc
T t
T
t
h A
T
T
⎛
⎞
−
= −
⎜
⎟
⎜
⎟
−
⎝
⎠
3
4
3
m
V
r
ρ
ρ
π
=
=
(
)
3
2
4
( )
3
ln
4
p
f
i
f
r
c
T t
T
t
T
T
h
r
ρ
π
π
⎛
⎞
⎜
⎟
⎛
⎞
−
⎝
⎠
= −
⎜
⎟
⎜
⎟

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