The basic scales of natural convection heat and mass transfer in fluids and fluid-saturated porous media

Abstract

The parallel structure of the fields of natural convection in fluids and natural convection in porous media is reviewed in terms of the most basic scales of flow, heat and mass transfer. In each field, the review includes single vertical boundary layers, enclosures, heat and mass transfer in the presence of temperature and concentration buoyancy effects, Benard flow and new or still unexplored directions of research. In particular, an original scale analysis of the nonDarcy regime in a porous layer heated from below shows that the Darcy-nonDarcy transition occurs when the Darcy-Rayleigh number Ra k exceeds O(Pr p), where Pr p is an important new dimensionless group called “the porous medium Prandtl number.” In the nonDarcy regime the Nusselt number scales as Ra k ½ times Pr p ½.