Convection in a concentric annulus with heat generating porous media and a permeable inner boundary

The effects of a permeable inner boundary on the maximum temperature and the convective flows were investigated numerically for a two-dimensional horizontal annulus containing a uniformly heat generating porous media. The time-dependent governing equations were nondimensionalized and put into an explicit finite difference numerical form. The finite difference equations were obtained from truncated Taylor series expansions using a central differencing scheme. Nondimensional temperatures and streamlines were obtained for heat generation rates ranging from 20 to 1,500 W/m³ corresponding to a range of modified Rayleigh numbers of 324 to 24,340 and for several combinations of isothermally heated wall conditions for annuli of radius ratio of 2. It was found that multi-cellular flows occur at the highest Rayleigh numbers investigated.