Unsteady Mixed Convective Flow Confined between Vertical Wavy Wall and Parallel Flat Wall Filled with Porous and Fluid Layer

Abstract

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.