Analytical Solution for Three-Dimensional Transient Heat Conduction in a Multilayer Sphere

Abstract

An analytical solution is obtained for the problem of three dimensional heat conduction in sphere with multiple layers in the radial direction, spatially non-uniform but time independent volumetric heat sources are assumed in each layers, separation of variables method is used to obtain transient temperature distribution. The solution obtained is valid for any combination of homogeneous first and second kind boundary conditions in the angular and axial direction of the sphere and for the non-homogeneous third kind boundary condition in the radial direction. Proposed solution is also applicable to multiple layer with zero inner radius. An illustrative example problem for the three layer quarter-spherical region is solved.