Intricacies of coupled molecular diffusion on double diffusive viscoelastic porous convection

Abstract

The effect of cross-diffusion on the onset of convective instability in a horizontal porous layer saturated with double diffusive viscoelastic fluid is investigated. A modified Darcy–Oldroyd-B model is used to describe the viscoelastic fluid flow in a porous medium. A linear instability analysis has been performed to obtain the condition for the onset of stationary and oscillatory convection and the numerical results for NaCl–MgCl2system are presented. Besides, the eigenvalues are computed numerically using a Galerkin method and the results are found to compare well with those obtained analytically. The simultaneous effect of viscoelasticity and the cross diffusion has led to significant changes in the convective pattern. The cross-diffusion terms induce stabilizing or destabilizing influence on the system depending on the magnitude as well as stabilizing/destabilizing impact of one of the stratifying components. The range of strain retardation parameter beyond which oscillatory convection ceases to occur is found to increase with increasing stress relaxation parameter irrespective of cross diffusion effects. The cross over boundary between stationary and oscillatory convection is demarcated by identifying a codimension-two point in the viscoelastic parameters plane. The results of Maxwell fluid are highlighted as a particular case.

Keywords

• Instability
• Double-diffusive convection
• Cross-diffusion terms
• Oldroyd-B fluid
• Porous media