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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. [ABSTRACT FROM AUTHOR]

An investigation has been undertaken as Soret and Schmidt outcomes on the mixed convection flow using Robin boundary conditions. The results use a vertical channel being kept at constant cold temperature and concentration at the left wall and hot temperature and concentration at the right wall. The exchange of heat is done by help of plates with a fluid. We consider the external fluid with equal and different temperatures. This physical problem is solved by using nondimensional parameters with the corresponding boundary conditions. To find analytical solution, the regular perturbation series method is used, and for finding the numerical solution, the well‐known Runge–Kutta method with shooting technique is employed. Comparison of the current study is favorable with the previous published results. The obtained results depend on the governing parameters such as thermal Grashof number, solutal Grashof number, Biot numbers, symmetric and asymmetric wall temperatures, Schmidt number, Soret number, and Brinkman number. An influence of these parameters on the fields of velocity, temperature, and concentration is reported. Further, the numerical results for the Nusselt number, mean value of the velocity, dimensionless bulk temperature, skin friction, and molecular diffusion coefficient are tabulated for different parametric conditions and explained. For small value of Brinkman number, the obtained values agree with other published results for all considered cases. [ABSTRACT FROM AUTHOR]

The unsteady mixed convective flow in a long vertical channel containing porous and fluid layer bounded by a smooth and corrugated wall is studied. Nonlinear equations governing the motion have been solved by linearization technique wherein the flow is assumed to be in two parts: a mean part and a perturbed part. Exact solutions are obtained for the mean part, and the perturbed part is solved using long wave approximation. Separate solutions are matched at the interface using suitable matching conditions. Results for a wide range of governing parameters such as Grashof number, viscosity ratio, width ratio, conductivity ratio, and frequency parameter are plotted for different values of porous parameter. Closed-form expressions for the Nusselt number and skin friction at both left and right channel walls are also derived. It is found that the Grashof number, width ratio, and conductivity ratio promote the velocity parallel to the flow direction and reduce the velocity perpendicular to the flow direction. The presence of porous matrix and viscosity ratio suppresses the velocity parallel to the flow direction and promotes the velocity perpendicular to the flow direction. The validity of the results obtained for the two-fluid model is compared with the available one-fluid model in the absence of porous matrix for steady flow, and the values agree very well. [ABSTRACT FROM AUTHOR]