2 Chapter Heat Conduction Equation
T (r ) =
37,894r 2
+ 98.34 ln r + 257.2 = 257.2 473.68r 2 + 98.34 ln r
4(20)
The temperature at the center surface of the pipe is determined by setting radius r to be 17.5 cm, which is
the average of the inner radius and outer radius.
T (r ) = 257.2 473.68(0.175) 2 + 98.34 ln(0.175) = 71.2C
2-137 A spherical ball in which heat is generated uniformly is exposed to iced-water. The temperatures at
the center and at the surface of the ball are to be determined.
Assumptions 1 Heat transfer is steady since there is no indication of change any with time. 2 Heat transfer
is one-dimensional., and there is thermal symmetry about the center point. 3 Thermal conductivity is
constant. 4 Heat generation is uniform.
Properties The thermal conductivity is given to be k = 45 W/mC.
Analysis The temperatures at the center and at the surface of the ball are
determined directly from
T s = T +
&
gr0
(2.6 10 6 W/m 3 )(0.15 m)
= 0C +
= 108.3C
3h
3(1200 W/m 2 .C)
T0 = T s +
&
gr0 2
(2.6 10 6 W/m 3 )(0.15 m) 2
= 108.3C +
= 325C
6k
6(45 W/m.C)
2-138 .... 2-141 Design and Essay Problems
2-80
D
g
h
T