Consider a homogeneous spherical piece of radioactive material of radius ro = 0.04 m that is generating heat at a constant rate of ėgen = 5 x 107 w/m3 . the heat generated is dissipated to the environment

asked Oct 16, 2023 108k views

Consider a homogeneous spherical piece of radioactive material of radius ro = 0.04 m that is generating heat at a constant rate of ėgen = 5 x 107 w/m3 . the heat generated is dissipated to the environment steadily. the outer surface of the sphere is maintained at a uniform temperature of 110°c and the thermal conductivity of the sphere is k = 15 w/m·k. 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.