Heat conduction equation through a heat generated eccentric cylindrical annulus with the inner surface kept at a constant temperature and the outer surface subjected to convection is analytically solved in bipolar coordinates using the Green's function method. Since it is not possible to find an analytical Green's function to the conduction equation in bipolar coordinates for an eccentric annulus subject to boundary condition(s) of third type (convection), a novel method treating the same problem as a. second type boundary value problem is devised. The method has first been applied to heat generating eccentric annuli and results have been compared to the results of computational fluids dynamics (CFD) code FLUENT. Perfect agreement was observed for various geometrical configurations and a wide range of Biot number. Then, heat transfer through eccentric annuli without heat generation was considered. Variation of heat dissipation with radii ratio was studied and a very good agreement with the literature has been observed. A simple approximate analytical expression for the heat transfer rate is derived using first term (zero-order) approximation. It has been demonstrated that this expression gives very accurate results for a wide range of geometrical configurations and Blot number. (C) 2014 Elsevier Masson SAS. All rights reserved.