Stability Analyses of Brinkman–Bénard Convection in Hybrid-Nanoliquid Saturated-Porous Medium Using Local Thermal Non-equilibrium Model

This paper carries out linear and weakly non-linear stability analyses of natural convection in a Newtonian hybrid-nanoliquid saturated porous medium. The Boussinesq approximation is assumed to be valid in the study, and a two-phase energy model is used. The weighted residual Galerkin technique is employed to obtain the expression for the Rayleigh number and Lorenz model by using a truncated double Fourier series solution. The quadratic non-linear Lorenz model is solved numerically by using the Runge–Kutta–Fehlberg method. Water is considered as a carrier liquid, and copper and alumina nanoparticles are considered with dilute concentration. Linear stability analysis reveals the onset of convection prepones in a hybrid nanoliquid-saturated porous medium. The amount of heat transport is maximum in a hybrid nanoliquid saturated porous medium and minimum in a liquid-saturated porous medium. Local thermal non-equilibrium situation ceases at higher rates of interphase heat transfer coefficient. The assumption of local thermal non-equilibrium is prominent in hybrid nanoliquid saturated porous medium. The results of the hybrid-nanoliquid channel, a hybrid nanoliquid saturated porous medium with the local thermal assumption, are presented as a limiting case of the study.