Numerical simulation of double-diffusive natural convection in a porous cavity : opposing flow

Abstract EN

The aim of this paper is to simulate numerically the two-dimensional double diffusive opposing flow in a porous cavity.

Both the temperature and solute gradients are imposed horizontally, and the two-buoyancy effects can either augment or counteract each other.

The Darcy equation, including Brinkman–Forchheimer terms to account for viscous and inertia effects, is used for the momentum equation, and the SIMPLER algorithm, based on the finite volume approach is used to solve the pressure–velocity coupling.

An extensive series of numerical simulations is conducted for Rat = 3 × 106 and 3 × 107, 10–6 ≤ Da ≤ 1, 1 ≤ N ≤ 20, and for Le = 10 and 100, where Rat, Da, N, and Le are the thermal Rayleigh number, the Darcy number, the buoyancy ratio, and the Lewis number, respectively.

This study is limited to Pr = 0.149 which corresponds to a titanium based alloy.

It is shown that the main effect of the porous medium is to reduce the heat and mass transfer as well as the flow field when the permeability is reduced.

Isotherms and streamlines are plotted for several values of thermal Rayleigh number (Ra), Darcy number (Da), Lewis number (Le), and buoyancy ratio (N).

Comprehensive graphs of Nusselt and Sherwood numbers are presented as a function of the governing parameters.