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# International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

8 Issues per year

IMPACT FACTOR 2016: 0.890

CiteScore 2016: 0.84

SCImago Journal Rank (SJR) 2016: 0.251
Source Normalized Impact per Paper (SNIP) 2016: 0.624

Mathematical Citation Quotient (MCQ) 2016: 0.07

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2191-0294
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Volume 17, Issue 5

# Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media

Akil J. Harfash
Published Online: 2016-07-19 | DOI: https://doi.org/10.1515/ijnsns-2015-0139

## Abstract

A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as ${R}_{c}$ increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as $Rc$ increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

MSC 2010: 76S05; 76Rxx; 35B35

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Accepted: 2016-06-06

Published Online: 2016-07-19

Published in Print: 2016-08-01

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 17, Issue 5, Pages 205–220, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339,

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