Convective energy transport in a vertical porous channel: Effects of triple diffusion and Newtonian heating/cooling

Abstract

The effect of triple diffusion on convection of viscous liquid in a vertical channel saturated with permeable material is explored subject to Robin conditions on the boundaries. Inside the duct, the salts of distinct compositions are diffused. Non‐Darcy approach is used to describe the porous material influence on transport processes. Symmetric and asymmetric heating conditions are considered for the ambient temperatures close to the vertical channel borders. Heat is exchanged between the vertical plates and the external fluid. Initially, the solutions are found without an influence of viscous dissipation and buoyancy forces. Inclusion of these two effects leads to nonlinear equations and adopting Brinkman parameter as the perturbation characteristic for the solutions is procured. Owing to the limitation on the perturbation characteristic, the conservation relations are solved numerically using the Runge–Kutta procedure combined with shooting technique. The flow patterns are depicted for the properties of the heat and mass Grashof numbers, porous parameter, inertial parameter, Brinkman number, Biot numbers, and chemical reaction characteristics. The effects of these parameters are explored on the skin frictions and Nusselt numbers. In the case of dissipations caused by viscosity and Forchheimer drag term, the perturbation results and numerical solutions are equal for low magnitudes of perturbation characteristic.