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.
In this paper, the steady fully developed non‐Darcy mixed convection flow of a nanofluid in a vertical channel filled with a porous medium with different viscous dissipation models is analyzed. The Brinkman‐Forchheimer extended Darcy model is used to describe the fluid flow pattern in the channel. The transport equations for a nanofluid are solved analytically using the seminumerical‐analytical method known as differential transformation method, and numerically with the Runge‐Kutta shooting method. Finally, the influence of pertinent parameters, such as solid volume fraction, different nanoparticles, mixed convection parameter, Brinkman number, Darcy number, and inertial parameter on the velocity and temperature fields are shown graphically. The results show that velocity and temperature are enhanced when the mixed convection parameter, Brinkman number, and Darcy number increases whereas solid volume fraction and inertial parameter decreases the velocity and temperature fields. The obtained results show that the nanofluid enhances the heat transfer process significantly.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.