Volume 7, Issue 5
Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

Ashok Kumar ,  Pravez Alam and Prachi Fartyal

10.4208/aamm.2014.m632

Adv. Appl. Math. Mech., 7 (2015), pp. 644-662.

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  • Abstract

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, Nub , side Nus) and mass transfer (bottom, Shb , side, Shs) 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 = 2×105 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 (Nub , Sub ) 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.

  • History

Published online: 2018-05

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