Unsteady Temperature Distribution in a Sphere

by Frank Beaulieu

Submitted : Spring 2010

The following project is one of multiple problems that entail a solid sphere of uniform temperature being suddenly exposed to a constant temperature. The analytic solution to the heat transfer model is expressed in the form of an alternating infinite series, which incorporates multiple properties of real bodies and heat transfer between such bodies. The aim is to express the dimensionless temperature at the center of the sphere using careful manipulation of this analytic solution, and, using a pre-defined time constant, to plot the change in this dimensionless temperature over time.

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