A Study on the Stability of Darcy–Brinkman–Bénard Convection in a Binary Fluid-Saturated Porous Medium: Rigid–Rigid Boundaries

Abstract

The linear stability analysis of Darcy–Brinkman–Bénard convection (DBBC) in a binary fluid-saturated porous layer is studied numerically using \(n\) term Galerkin approach for rigid–rigid, isothermal boundaries. The occupied binary fluid and porous medium are assumed to be in thermal non-equilibrium. Thus, two energy equations are used for each phase. The critical values of the Darcy–Rayleigh and wave numbers for the onset of convection are obtained by considering ten terms in the Galerkin solution. The effect of the five parameters of the model, namely the Darcy number, Da, the modified ratio of thermal conductivity \(\gamma\), the Lewis number Le, the separation ratio coefficient, \(\chi\), and the inter-phase heat transfer coefficient, H, on the stability of the system is discussed in detail and presented with the aid of plots and tables. The onset of convection in a binary fluid-saturated porous medium is delayed for realistic boundary conditions compared with ideal boundary conditions (stress-free, isothermal boundary conditions). Increasing the values of the Darcy number, inter-phase heat transfer coefficient, and the separation ratio coefficient stabilizes DBBC. In contrast, the thermal conductivity ratio and Lewis number are destabilize the system. Furthermore, convective cell size remains unaltered with increasing \(\chi\). Convection is delayed in the pure fluid medium compared to the binary fluid medium. Local thermal non-equilibrium ceases for small and large inter-phase heat transfer coefficient values.