Temperature distribution in a hoolow sphere subject to arbitary time dependent boundary conditions

In this investigation an analytical solution for the temperature distribution in a hollow sphere, which is subjected to arbitrary time-dependent boundary conditions is presented. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. The solution is based on the separation of variables method and Duhamel’s principle. The temperature distribution is obtained for the case of a sinusoidal boundary condition. For the latter situation, the dimensionless charts of the amplitude and the phase difference of the steady temperature oscillations, at the outer and the inner surfaces of the sphere, are presented.