Consider a homogeneous spherical piece of radioactive material of radius ro = 0.04 m that is generating heat at a constant rate of 5×10 W/m. 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. Assume steady one dimensional heat transfer in radial direction, constant thermo-physical properties with heat generation, (a) Write the differential equation and the boundary conditions for heat conduction through sphere (b) Find the temperature distribution based on the given conditions. (c) Evaluate the temperature at the center of the sphere.

Consider a homogeneous spherical piece of radioactive material of radius ro = 0.04 m that is generating heat at a constant rate of 5×10 W/m. 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. Assume steady one dimensional heat transfer in radial direction, constant thermo-physical properties with heat generation, (a) Write the differential equation and the boundary conditions for heat conduction through sphere (b) Find the temperature distribution based on the given conditions. (c) Evaluate the temperature at the center of the sphere.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.36P

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