The transient natural convection has been analyzed for the temperature dependent viscosity of fluids in spherical annulus and between two vertically eccentric spheres. Using the modified Sorenson's method to generate the grid line can get the grid system with orthogonality along all boundaries. The grid system goes along with weighting function scheme to discretize the general governing equation. Numerical solutions were obtained for Rayleigh numbers (5.0 x 10(3) -6.5 x 10(4)) at a radius ratio of 2.0 with the dimensionless vertical eccentricity of the outer sphere (0- +/- 0.65) for variable viscosity fluids at different Prandtl numbers (158, 405 and 720). The results of this analysis show that heat and flow patterns vary with the Rayleigh number and the eccentricity; besides, the effect of variable viscosity is investigated. The present calculations applied to constant viscosity are compared with the results of other papers, and these comparison results are agreeable. (C) 2003 Elsevier Ltd. All rights reserved.