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

Published online by Cambridge University Press:  21 July 2015

Ashok Kumar ,
Pravez Alam  and
Prachi Fartyal
Ashok Kumar*
Affiliation:
Department of Mathematics, HNB Garhwal University (A Central University), Srinagar–246174, Uttarakhand India
Pravez Alam
Affiliation:
Department of Mathematics, HNB Garhwal University (A Central University), Srinagar–246174, Uttarakhand India
Prachi Fartyal
Affiliation:
Department of Mathematics, HNB Garhwal University (A Central University), Srinagar–246174, Uttarakhand India
*
*Corresponding author. Email: [email protected] (A. Kumar)
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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.

Keywords

65M1078A48Spectral element methodanisotropic porous mediumnon-Darcy Brinkmann modelnon-uniform heating
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 5 , October 2015 , pp. 644 - 662
Copyright
Copyright © Global-Science Press 2015 

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