Non-Darcian effects on natural convection in porous media confined between horizontal cylinders

Abstract

The inertia, boundary and velocity-square terms, normally not included in the flow analysis, are included in the study of natural convection between isothermal, concentric cylinders (inner cylinder heated) filled with saturated, porous media. The results show that all of these effects reduce the heat transfer rate with the boundary term being the most significant. It is shown that since at high Rayleigh numbers the flow adjacent to the confining walls becomes of boundary-layer type, with a very thin sublayer over which the velocity reaches its maximum value, then as long as the contribution of the velocity-square term is small, Darcy's model holds for very large Rayleigh and Prandtl numbers. A flow regime diagram showing the pseudo-conduction, Darcy and non-Darcy regimes, is given.