A radioactive material can be considered as a sphere of ro = 0.04 m. the sphere is generating heat at a constant rate of 4x107 W/m³. The heat generated is dissipated to the environment in a steady state. The thermal conductivity of the sphere is k=15 W/m.°C and the surface of the sphere is maintained at a constant temperature of 80°C. Assuming steady one-dimensional heat transfer, (a) drive the differential equation and the express boundary conditions for heat conduction through the sphere, (b) Get a relation for the variation of temperature in the sphere by solving the differential equation, and (c) Calculate the temperature at the center of the sphere.

A radioactive material can be considered as a sphere of ro = 0.04 m. the sphere is generating heat at a constant rate of 4x107 W/m³. The heat generated is dissipated to the environment in a steady state. The thermal conductivity of the sphere is k=15 W/m.°C and the surface of the sphere is maintained at a constant temperature of 80°C. Assuming steady one-dimensional heat transfer, (a) drive the differential equation and the express boundary conditions for heat conduction through the sphere, (b) Get a relation for the variation of temperature in the sphere by solving the differential equation, and (c) Calculate 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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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

A radioactive material can be considered as a sphere of ro = 0.04 m. the sphere is
generating heat at a constant rate of 4x107 W/m³. The heat generated is dissipated
to the environment in a steady state. The thermal conductivity of the sphere is k=15
W/m.°C and the surface of the sphere is maintained at a constant temperature of
80°C. Assuming steady one-dimensional heat transfer,
(a) drive the differential equation and the express boundary conditions for heat
conduction through the sphere,
(b) Get a relation for the variation of temperature in the sphere by solving the
differential equation, and
(c) Calculate the temperature at the center of the sphere.

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