11-53
11-73 The outer surfaces of a large cast iron container filled with ice are exposed to hot water. The time
before the ice starts melting and the rate of heat transfer to the ice are to be determined.
Assumptions 1 The temperature in the container walls is affected by the thermal conditions at outer
surfaces only and the convection heat transfer coefficient outside is given to be very large. Therefore, the
wall can be considered to be a semi-infinite medium with a specified surface temperature. 2 The thermal
properties of the wall are constant.
Properties The thermal properties of the cast iron are given to be k = 52 W/m.qC and D = 1.70u10-5 m2/s.
Analysis The one-dimensional transient temperature distribution in the wall for that time period can be
determined from
§ x ·
¸
erfc¨¨
¸
© 2 Dt ¹
T ( x, t ) Ti
Ts Ti
Hot water
60qC
Ice chest
But,
T ( x, t ) Ti
Ts Ti
0.1 0
60 0
0.00167 o 0.00167
erfc(2.226) (Table 11-4)
Ice, 0qC
Therefore,
x
2 Dt
2.226 
o t
x2
(0.05 m) 2
4 u (2.226) 2 D
4(2.226) 2 (1.7 u 10 5 m 2 /s)
The rate of heat transfer to the ice when
steady operation conditions are reached
can be determined by applying the
thermal resistance network concept as
Rconv,i
R wall
Rconv,o
Rtotal
Q
1
hi A
T1
Rconv
Rwall
7.4 s
Rconv
T2
1
0.00167qC/W
(250 W/m .qC)(1.2 u 2 m 2 )
0.05 m
L
0.00040qC/W
kA (52 W/m.qC)(1.2 u 2 m 2 )
1
1
# 0qC/W
ho A (f)(1.2 u 2 m 2 )
Rconv,i R wall Rconv,o 0.00167 0.00040 0 0.00207qC/W
T2 T1
Rtotal
2
(60 0)qC
0.00207 o C/W
28,990 W
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