Boundary Element Method for double diffusive natural convection in a horizontal porous layer

Abstract

A numerical study of double-diffusive natural convection in porous media using the Boundary Element Method is presented. The studied configuration is a horizontal layer filled with fluid saturated porous media, where different temperature and concentration values are applied on the horizontal walls, while the vertical walls are adiabatic and impermeable. Transport phenomena in porous media are described with the use of modified Navier-Stokes equations in the form of conservation laws for mass, momentum, energy and species. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared with those in published studies.

Natural convection in porous media under cross temperature and concentration gradients with Boundary Element Method

“…Transport phenomena in porous media is mathematically described with conservation equations for mass, momentum, energy and species, which are written at the macroscopic level considering the fact that only a part of the volume, expressed with porosity φ, is available for the fluid flow [4]. The general set of equations is given as:…”

“…Since the integral equations are given in terms of variables on the integration boundaries, as well as within the integration domain, the discretization of the solution boundary and domain is required. The whole numerical scheme was already presented at BEM/MRM the details are given in [5], [4]. The main steps to obtain a solution of the described problem with BDIM are:…”