Consider a homogeneous spherical piece of radioactive material of radius r0 = 5 cm that is generating heat at a constant rate of q.= 3.8x107 W/m3 The heat generated is dissipated to the environment T∞=27°C and h = 110 W/m2°C steadily. The outer surface of the sphere is maintained at a uniform temperature (Ts) and the thermal conductivity of the sphere is k = 25 W/m°C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere
Consider a homogeneous spherical piece of radioactive material of radius r0 = 5 cm that is generating heat at a constant rate of q.= 3.8x107 W/m3 The heat generated is dissipated to the environment T∞=27°C and h = 110 W/m2°C steadily. The outer surface of the sphere is maintained at a uniform temperature (Ts) and the thermal conductivity of the sphere is k = 25 W/m°C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere
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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Consider a homogeneous spherical piece of radioactive material of radius r0 = 5 cm that is generating heat at a constant rate of q.= 3.8x107 W/m3 The heat generated is dissipated to the environment T∞=27°C and h = 110 W/m2°C steadily. The outer surface of the sphere is maintained at a uniform temperature
(Ts) and the thermal conductivity of the sphere is k = 25 W/m°C. Assuming steady one-dimensional heat transfer,
(a) express the differential equation and the boundary conditions for heat conduction through the sphere,
(b) obtain a relation for the variation of temperature in the sphere by solving the differential equation,
and (c) determine the temperature at the center of the sphere
Transcribed Image Text:Ts
k = 25("/wc)
T = 27°C
h=110(W
m² °C)
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