Double Diffusive Natural Convection in a Porous Rhombic Annulus

Abstract

This article reports on an investigation performed to study laminar steady state double diffusive natural convection in a two-dimensional porous enclosure of rhombic cross-section. Solutions are obtained numerically using a finite volume method for the case when the inner wall is uniformly heated to a temperature T _h while subjected to a high solute concentration S _h , and the outer wall is evenly cooled to a temperature T _c while exposed to a low solute concentration S _c . Simulations are conducted for several values of Rayleigh number (Ra), Darcy number (Da), Prandtl number (Pr), porosity (ϵ), and enclosure gap (E _g ) for fixed values of Lewis number (Le = 10) and buoyancy ratio (N = 10). The results are displayed in terms of streamlines, isotherms, isoconcentrations, mid-height velocity, temperature, concentration profiles, and local and average Nusselt and Sherwood number values. Predictions indicate that for the Lewis number and buoyancy ratio considered, the flow field is more affected by mass transfer than by heat transfer. Moreover, convection effects increase with an increase in Ra, Da, E _g , and/or ϵ. The porosity of the porous matrix has no effect on the flow, temperature, and concentration fields at low values of Darcy number. Furthermore, the total heat and mass transfer increases as Pr increases and/or as the enclosure gap decreases due to an increase in the wall area over which heat and mass transfer occur. Values of and indicate dominant diffusion at low Ra number values with convection affecting the total heat and mass transfer at high Ra values.

Acknowledgments

The financial support provided by the University Research Board of the American University of Beirut is gratefully acknowledged.