Soret-driven convection of Maxwell-Cattaneo fluids in a vertical channel

Abstract

The Soret effect, also known as thermal diffusion, plays a crucial role in the phenomenon of double diffusion convection in liquids. This study investigates Soret-driven convection within a vertical double-diffusive layer of Maxwell-Cattaneo (M-C) fluids, where the boundaries maintain constant temperatures and solute concentrations that are distinct from each other. The heat transfer equation for Maxwell-Cattaneo fluids is governed by a hyperbolic rule of heat conduction, rather than the typical Fourier parabolic one. The Chebyshev collocation method is employed to solve the corresponding stability eigenvalue problem. The neutral stability curve shows significant fluctuation responses due to the M-C effect. When the Cattaneo number (C) reaches 0.02, multiple local minima appear in the critical Grashof number (Gr). The instability the thermal convection is found to be amplified by the combined effects of Maxwell-Cattaneo and Soret, along with the Grashof number, while the double diffusion effect appears to suppress the instability of convective system. The influence of Soret effect on convective instability will diminish dramatically as the Gr number rises above 8200.