### Unsteady Temperature Distribution in a Sphere

## by Kalan Brinkley

Submitted : Fall 2011

The purpose of my project was to calculate the dimensionless temperature of the center of a sphere. In my problem, it states that through the use of infinite series, one will be able to calculate dimensionless temperature for any radial position of a sphere as time *t* increases. My solution involved the use of L’Hopital’s rule followed by the evaluation of the infinite series in order to calculate the point of convergence for any given time. I looked over several cases of thermal conductivity *k* in order to observe how when τ increases, the convergence rate of a dimensionless temperature decreases, and vice-versa. In my conclusion, I found that heat traveling through an object depends on the thermal conductivity of the object which is useful for calculating temperature distribution within any object.

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