Consider a homogeneous spherical piece of radioactive material of radius r-0.04 m that is generating heat at a con- stant rate of g = 4 x 10' W/m'. The heat generated is dissi- pated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 80°C and the thermal conductivity of the sphere is k = 15 W/m. "C. As- suming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat con- duction through the sphere. (b) obtain a relation for the varia- tion of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere. so'C
Consider a homogeneous spherical piece of radioactive material of radius r-0.04 m that is generating heat at a con- stant rate of g = 4 x 10' W/m'. The heat generated is dissi- pated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 80°C and the thermal conductivity of the sphere is k = 15 W/m. "C. As- suming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat con- duction through the sphere. (b) obtain a relation for the varia- tion of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere. so'C
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Consider a homogeneous spherical piece of radioactive
material of radius r = 0.04 m that is generating heat at a con-
stant rate of g = 4 x 10' W/m'. The heat generated is dissi-
pated to the environment steadily. The outer surface of the
sphere is maintained at a uniform temperature of 80°C and
the thermal conductivity of the sphere is k = 15 W/m. C. As-
suming steady one-dimensional heat transfer, (a) express the
differential equation and the boundary conditions for heat con-
duction through the sphere, (b) obtain a relation for the varia-
tion of temperature in the sphere by solving the differential
equation, and (c) determine the temperature at the center of the
sphere.
80°C
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