Mixed Convection in a Vertical Channel Containing Porous and Viscous Fluid Regions With Viscous Dissipation and Inertial Effects: A Perturbation Solution

In this paper, combined forced and natural convection in a vertical channel containing both porous and viscous regions taking into account the influences of inertial force and viscous dissipation has been studied. In this regard, fully developed fluid flow in the porous region was modeled using the Brinkman–Forchheimer extended Darcy model. To solve governing equations of both the porous and viscous regions including thermal energy and momentum equations, a two-parameter perturbation method was applied. The velocity and temperature distributions of both the regions were obtained in terms of various parameters such as inertial force, Grashof, Reynolds, and Brinkman numbers, as well as various types of viscous dissipation models. In addition, numerical solution was conducted using finite difference method to compare the results. The predicted results clearly indicate that the type of viscous dissipation model has significant effect on the temperature and velocity distributions. The acquired knowledge in this study can be used by designers to control channel flow as suitable for a certain application.