Double diffusive LTNE porous convection with Cattaneo effects in the solid

Abstract

AbstractThe impact of Cattaneo heat flux law in the solid on the onset of double‐diffusive Darcy porous convection with local thermal nonequilibrium temperatures is investigated. The Fourier law of heat transfer is invoked for the fluid, whereas the Cattaneo heat flux law used to transfer heat in solid skeleton alters the temperature equation from parabolic to hyperbolic. The results are obtained for porous skeletons of aluminum and copper oxides. Both Cattaneo and solute concentration effects reinforce in controlling the onset of oscillatory convection and some novel consequences are observed. Compared with the results perceived in the absence of solute concentration, a manifestation of oscillatory convection with scaled‐interphase heat transfer coefficient as well as solid thermal relaxation time parameter initiates earlier in its presence. The effect of increasing interphase heat transfer coefficient and the Lewis number is to delay and hasten the onset of stationary and oscillatory convection. Besides, the increase in the value of solid thermal relaxation time parameter advances the oscillatory onset. Although the increase in the solute Darcy–Rayleigh number is to delay the stationary onset, it shows a twofold behavior on the onset of oscillatory convection. Before the onset of oscillatory convection, the size of the convection cell gets narrower and after which it becomes much wider. The existing results are retrieved as limiting cases from the current study.