Theoretical study of cross diffusion effects on convective instability of Maxwell fluid in porous medium

Abstract

The onset of double diffusive convection in a layer of Maxwell viscoelastic fluid in porous medium with cross diffusion effects is studied using linear and nonlinear stability analysis. The previous study has focused on linear stability analysis only. Therefore, in the present study, we have focused on oscillatory convection and nonlinear stability theory. The linear analysis is based on the classical normal mode technique. The expressions for stationary, oscillatory convections are obtained as a function of governing parameters such as solute Rayleigh number, Soret parameter, Dufour parameter and Lewis number and their effects on the stability of a system are shown graphically. The nonlinear analysis is based on the truncated Fourier series which provides the quantification of heat and mass transfer. The transient behavior of Nusselt and Sherwood numbers is studied by solving numerically a fifth order Lorentz type system using Runge-Kutta method. © 2016 Columbia International Publishing.