Double-diffusive convection in a porous layer subjected to an inclined temperature gradient incorporating Soret effect

Abstract

In several commonly occurring natural convection phenomena, the system is subjected to non-uniform heating that causes an inclined thermal gradient. As a result, the natural convection problem deviates from the classical Rayleigh–Bénard problem, in which the thermal gradient has only a vertical component. In this study, we present linear and global stability analyses results concerning thermosolutal convection in a Newtonian fluid-saturated Darcy porous layer subjected to an inclined thermal gradient in the presence of the Soret effect (associated with thermophoresis). The thermal gradient is assumed to have horizontal and vertical components, resulting in the formulation having two thermal Rayleigh numbers as system parameters, viz. horizontal and vertical Rayleigh numbers. The horizontal thermal gradient gives rise to a Hadley-type circulation. This circulation can become unstable if the vertical thermal gradient attains a certain threshold. We focus on the effect of the Soret parameter on the system’s stability under non-uniform inclined heating. The analyses reveal that the solutal Darcy–Rayleigh number and Lewis number destabilise the system, while the Soret parameter has a non-monotonic effect on the system’s stability depending on the horizontal Rayleigh number. The energy stability bounds do not coincide with linear ones for the present problem; hence, subcritical instabilities are possible.