Natural convection in the boundary layer of a constant temperature and concentration vertical wall embedded in a darcy doubly stratified porous medium

Abstract

This paper presents the succession of heat and/or mass driven natural convection processes along a uniform temperature and concentration vertical wall embedded in a Darcy doubly stratified porous medium. Using the scale analysis of the governing equations, three possible heat transfer regimes are discovered, presented and quantified through the temperature, concentration and velocity boundary layer thickness, magnitude and location. If ST and SC are the porous medium thermal and concentration stratification coefficients and if N is the
buoyancy ratio, then we can encounter these possibilities: a heat driven convection regime (HDC) along the wall if SC > ST ; a mass driven convection regime (MDC) along the wall if
ST > SC > N > 1; a HDC−MDC succession in all the other cases. The finite difference method is used to solve the governing equations and to verify the results on the heat transfer regimes succession for one particular case.