Green’s function, temperature in a convectively cooled sphere with arbitrarily located spherical heat sources

Steady state heat conduction in a convectively cooled sphere having arbitrarily located spherical heat sources inside is treated with the method of Green’s function accompanied by a coordinate transform. Green’s function of the heat diffusion operator for a finite sphere with Robin boundary condition is obtained by spherical harmonics expansion. Verification of the analytical solution is exemplified in some generic cases related to the pebbles of South-African PBMR as of year 2000 with 268 MW thermal power. Analytical results for different sectors of the sphere (pebble) are compared with the results of computational fluid dynamics code FLUENT™. This work is motivated through a modest effort to assess the stochastic effects of distribution and volumetric effects of fuel kernels within the pebbles of future-promising pebble bed reactors.