Mathematica How Does Thermal Conductivity Affect Heat Distribution in Spherical Sources?

AI Thread Summary
The discussion revolves around solving a heat transfer problem involving a spherical heat source within a solid sphere. The heat transfer is described by Fourier's law, which states that the rate of heat flow is proportional to the temperature gradient and the thermal conductivity of the material. The problem requires determining the temperature at the surface of the heat source, given that it emits heat uniformly and the outer surface of the sphere is maintained at a constant temperature T0. Participants are asked to share their progress on the problem to facilitate further assistance. Key aspects include understanding the implications of thermal conductivity K, the geometry of the sphere, and the heat emission rate Q.
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Homework Statement


For a metal bar of cross sectional area A, the rate of flow of heat along the bar is given by the expression:

Q=-KA(dT/dx)

where K is the thermal conductivity of the material of the bar, and T and x refer to temperature and the distance measured from the high temperature end of the bar respectively. Use this information to solve the following problem.

A spherical heat source of radius a sits at the centre of a solid sphere of radius b>a.

The material of the sphere has thermal conductivity K. The source emits heat equally in all directions at the rate Q per second and the outside of the sphere is held at a constant temperature T0. Determine the temperature T at the surface of the source.


Some help needed please.
 
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