Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall (Advances in Applied Mathematics and Mechanics, 2018)
This article summaries a numerical study of thermo-solutal natural convectionin a square cavity filled with anisotropic porous medium. The side walls of thecavity are maintained at constant temperatures and concentrations, whereas bottomwall is a function of non-uniform (sinusoidal) temperature and concentration. Thenon-Darcy Brinkmann model is considered. The governing equations are solved numericallyby spectral element method using the vorticity-stream-function approach.The controlling parameters for present study are Darcy number $(Da)$, heat source intensityi.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameterson 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. Numericalresults show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligiblefor $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impactappears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. Themaximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasingRayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the abovestudy that due to anisotropic permeability the flow dynamics becomes complex.