Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

Abstract

AbstractThis article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number (Da), heat source intensity i.e., thermal Rayleigh number (Ra), permeability ratio (K*), orientation angle (ϕ). The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom,Nub, sideNus) and mass transfer (bottom,Shb, side,Shs) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value ofK*, the heat and mass transfer rates are negligible for 10−7≤Da≤ 10−5,Ra= 2 × 105andϕ= 45°. However a significant impact appears on Nusselt and Sherwood numbers whenDalies between 10−5to 10−4. The maximum bottom heat and mass transfer rates (Nub, Sub) is attained atϕ= 45°, whenK*=0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number (Ra) for all the values ofK*. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.