(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
This 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, Nu_b, side Nu_s) and mass transfer (bottom, Sh_b, side, Sh_s) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of K^∗, the heat and mass transfer rates are negligible for 10^-7≤Da≤10^−5, Ra=2×10^5 and ϕ=45^◦. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between 10^−5 to 10^−4. The maximum bottom heat and mass transfer rates (Nu_b, Su_b) is attained at ϕ=45^◦, when K^∗= 0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number (Ra) for all the values of K^∗. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.