TY - JOUR T1 - Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall AU - Kumar , Ashok AU - Alam , Pravez AU - Fartyal , Prachi JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 644 EP - 662 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2014.m632 UR - https://global-sci.org/intro/article_detail/aamm/12068.html KW - AB -

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.