Double diffusive convection in a porous layer saturated with viscoelastic fluid using a thermal non-equilibrium model

Abstract

In this paper, a study of double diffusive convection in an anisotropic porous layer, saturated with viscoelastic fluid, heated form below, and cooled from above, has been performed; the fluid and solid phases are not in thermal equilibrium. Extended Darcy model, which includes the time derivative term in the momentum equation, has been used. For the fluid and solid phase temperature fields, a two-field model has been used separately for energy equation. Linear stability analysis is performed, using normal mode technique, and the expression for Rayleigh number has been obtained. It is found that small inter-phase heat coefficient has substantial effect on the stability of the system. The criterion for both stationary and oscillatory convection is derived analytically. The effects of various parameters on the stability of the system have been investigated. A weak nonlinear stability analysis based on the truncated representation of Fourier series is performed to find Nusselt number and Sherwood number. Further, we studied the transient behavior of the Nusselt number and Sherwood number by solving the finite amplitude equations using a numerical method. The results obtained during the analysis have been presented graphically. A study of streamlines, isotherms, and isohalines has been also made for fluid and solid phases.