Analytical Solution of Temperature Field in Hollow Sphere under Periodic Boundary Condition

This paper presents an analytical investigation of the temperature distribution in a hollow sphere subjected to a periodic boundary condition. The material is assumed to be homogenous and isotropic with time-independent thermal properties. Assuming the temperature field to be two-dimensional, use was made of Fourier series to decompose the periodic boundary condition into harmonic oscillations. In order to check the validity of the results, the technique was also applied to a solid sphere under harmonic boundary condition for which theoretical results were available in the literature. The agreement between our results and those reported by others in this particular geometry under harmonic boundary condition was realized to be very good confirming the applicability of the technique utilized in the present work.

Keywords:

Heat Conduction , Sphere , Periodic Boundary Condition