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In this paper heat conduction equation for an eccentric spherical annulus  with the inner surface kept at a constant temperature and the outer surface  subjected to convection is solved analytically. Eccentric problem domain is  first transformed into a concentric domain via formulating the problem in  Bispherical coordinates system. Since an analytical Green’s function for the  heat conduction equation in Bispherical coordinates for an eccentric sphere  subject to boundary condition of third type cannot be found, an analytical  Green's function obtained for Dirichlet boundary condition is employed in  the solution. Utilizing this Green's function yields a boundary integral  equation (BIE) for the unknown normal derivative of the surface temperature  distribution. The resulting BIE is solved analytically using method of  moments. The method has been applied to heat generating eccentric spherical  annuli and results are compared to the simulation results of Fluent CFD  code. A very good agreement was observed in temperature distribution  computations for various geometrical configurations and a wide range of Biot  number. Variation of heat dissipation with radii and eccentricity ratios are  studied and a very good agreement with FLUENT has been observed.

Heat conduction in convectively cooled eccentric spherical annuli: A boundary integral moment method