11-34
11-50 A hot dog is dropped into boiling water, and temperature measurements are taken at certain time
intervals. The thermal diffusivity and thermal conductivity of the hot dog and the convection heat transfer
coefficient are to be determined.
Assumptions 1 Heat conduction in the hot dog is one-dimensional since it is long and it has thermal
symmetry about the centerline. 2 The thermal properties of the hot dog are constant. 3 The heat transfer
coefficient is constant and uniform over the entire surface. 4 The Fourier number is W > 0.2 so that the oneterm approximate solutions (or the transient temperature charts) are applicable (this assumption will be
verified).
Properties The properties of hot dog available are given to be U = 980 kg/m3 and cp = 3900 J/kg.qC.
Analysis (a) From Fig. 11-16b we have
T Tf
T0 Tf
r
ro
88 94
59 94
ro
ro
1
½
0.17 °
° 1
¾
° Bi
°¿
k
hro
0.15
Water
94qC
The Fourier number is determined from Fig. 11-16a to be
1
Bi
T0 Tf
Ti Tf
k
hro
½
0.15
°
°
¾W
59 94
0.47 °
°¿
20 94
Dt
ro 2
Hot dog
0.20
The thermal diffusivity of the hot dog is determined to be
Dt
ro2
0.20 
o D
0.2ro2
t
(0.2)(0.011 m) 2
120 s
2.017 u 10 7 m 2 /s
(b) The thermal conductivity of the hot dog is determined from
k
DUc p
(2.017 u 10 7 m 2 /s)(980 kg/m 3 )(3900 J/kg.qC)
(c) From part (a) we have
k
h
0.15ro
1
Bi
k
hro
0.771 W/m.qC
0.15 . Then,
(0.15)(0.011 m)
0.00165 m
Therefore, the heat transfer coefficient is
k
h
0.00165 
o h
0.771 W/m.qC
0.00165 m
467 W/m 2 .qC
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