Analytical Study of Viscous Heat Generation in Laminar Mixed Convection Flow through a Vertical Porous Channel with Double Pass Configuration

An analytical investigation is conducted to examine fully developed laminar flow and heat transfer in a vertical double-pass channel saturated with a permeable fluid. The flow through the porous medium is modeled using the Brinkman formulation, while both viscous dissipation and Darcy dissipation effects are incorporated into the energy equation. Mixed convection arises from the combined influence of an imposed pressure gradient and buoyancy forces due to temperature differences between the channel walls. The resulting coupled nonlinear governing equations are solved analytically using the regular perturbation method. Particular emphasis is placed on elucidating the effects of the porous medium parameter and the mixed convection parameter on the velocity and temperature distributions in the vicinity of the heated and cooled walls. The analysis reveals that these parameters exert a pronounced influence on the flow and thermal fields, with their impact strongly governed by the baffle position separating the two flow passages. The results demonstrate that appropriate placement of the baffle can significantly modify the interaction between viscous dissipation, buoyancy forces, and porous resistance, thereby enhancing or suppressing heat transfer characteristics within the channel. This study provides fundamental insights relevant to the design and optimization of double-pass porous channel systems used in thermal engineering applications.