The objective of this paper is to investigate natural convection for the temperature dependent viscosity of fluids inside porous media between two vertically eccentric spherical annuli. Brinkman-Darcy-Forchheimer (B-D-F)model and energy equation are used to simulate the fluid and heat transfer inside the porous domain. Employing the modified Sorenson's method produces orthogonal grid along all the boundaries. The grid system and weighting function scheme (WFS) are applied to discretize the governing equations. Nusselt numbers were calculated for a range of Raleigh number (1.0 x 10(3)-8.0 x 10(4)), dimensionless vertical eccentricity of the outer sphere (-0.65, 0, 0.65), porosity of the media (0.4 and 0.9) and Darcy number (0.1 and 0.001) for varying viscosity fluids at different Prandtl numbers (158, 405 and 720) when the radius ratio kept constant at 2.0. The results show how the Raleigh number, the eccentricity, and porosity affect mean Nusselt number whereas the Darcy number does not influence it. (C) 2015 Elsevier Ltd. All rights reserved.