Free convection in spherical annular sectors filled with a porous medium

Calculated free convection flows and heat transfer are presented for concentric spherical annular sectors, filled with a porous medium. Two isothermal walls and an adiabatic radial wall at the sector angle define the sectors. The governing equations (in the stream function and temperature formulation) are solved numerically using ADI (alternative direction implicit) finite-difference method. Over the range of geometric parameters examined, the obtained results for spherical annuli and low Rayleigh number Ra. As Ra increases, multicellular flows develop for small values of the aspect ratio parameter gamma. In addition, analytical solutions of the governing equations were obtained for small values of Ra (<1) and it was shown that these solutions agree well with those obtained numerically. Significant differences in the local heat transfer rates on the inner and outer walls of the spherical annuli were observed from these solutions.