The onset of Darcy–Brinkman–Rayleigh–Benard convection in a composite system with thermal diffusion

Abstract

AbstractThe effect of thermal diffusion on the onset of double‐diffusive convection is analyzed by considering a composite system of the fluid‐saturated porous layer. The porous layer of the composite system is modeled employing the Darcy–Brinkman–Rayleigh–Benard model. The boundaries of the composite system are assumed to be rigid‐rigid under normal gravitational force. The governing equations satisfying the Darcy–Brinkman–Rayleigh–Benard model are solved using the regular perturbation method. A mathematical expression is derived for the critical thermal Rayleigh number by solving the coupled equation. The impact of various physical parameters on the onset of convection is graphically represented under the influence of the Soret effect and the stability of the system is analyzed.