Combined effects of viscous and Darcy dissipation on mixed convection flow in a composite vertical channel partially filled with a porous material: Analytical approach

In this paper, the combined influence of thermal dissipation and Darcy dissipation on the steady motion of a fully developed mixed convection flow of viscous, incompressible fluid through a vertical composite channel partially filled with porous material is investigated in depth. The motion of the fluid within the channel is triggered by the sudden application of a pressure gradient in the direction of flow as well as natural convection due to the temperature gradient caused by applied heat through the channel boundaries. The setup of the system is done in such a way that the clear fluid and porous regions are separated by an interface between the two regions. The Brinkman-extended Darcy model is used to simulate momentum transfer. By matching their velocities and accounting for shear stress jump situations at the interface, the clear fluid and porous areas are linked. In addition, the thermal energy equation in the clear fluid region considers the viscous dissipation effect, whereas, in the porous region, the Darcy dissipation effect is considered in addition to the viscous dissipation effect. The homotopy perturbation method (HPM) was applied to solve the momentum and energy equations. The effects of various flow parameters introduced into the problem are discussed using line graphs. The study discovered that increasing the Brinkmann number increased both the temperature and velocity profiles. Furthermore, as the thickness of the porous medium increases, so does the pressure gradient, whereas increasing the porosity reduces the pressure gradient within the composite channels. Also, when the viscosity ratio goes up, the pressure gradient needed to move the flow through the channel goes up as well.