Double diffusive convection in a couple stress fluid saturated porous layer with internal heat source

Abstract

Abstract The onset of double diffusive convection in a couple stress fluid saturated porous layer with an internal heat source is studied using linear and weak nonlinear stability analyses. The linear analysis is based on the classical normal mode technique. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. In the present context, double diffusive convection is of particular interest in the study of extraction of metals from ores where a mushy layer is formed during solidification of a metallic alloy. Further, internal heating of the system is used as an external means to influence the transport process, thereby controlling the quality and structure of the resulting solid. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of governing parameters such as internal Rayleigh number, couple stress parameter, solute Rayleigh number, Darcy-Prandtl number, normalized porosity and Lewis number and their effects on the stability of a system are shown graphically. It is observed that the onset of both stationary and oscillatory convection is advanced by the internal Rayleigh number. The nonlinear analysis is based on the truncated representation of Fourier series which provides the quantification of heat and mass transfer. Heat transport is reinforced while mass transport is suppressed by the internal Rayleigh number. The transient behavior of Nusselt and Sherwood numbers is studied by solving numerically a fifth order Lorenz type system using Runge–Kutta method. Some known results are recovered as the particular cases of the present study.