Impact of Thermophoresis on Fully Developed Combined Buoyancy Forces in a Vertical Channel Filled With Porous Materials: Homotopy Perturbation Method

Abstract

This work develops a comprehensive mathematical model to analyze heat and mass transfer in a vertical porous channel under the influence of internal heat source/sink, chemical reaction, and buoyancy-driven flow. The model comprises a set of coupled second-order nonlinear ordinary differential equations describing temperature, concentration and velocity fields. The energy equation incorporates the heat source/sink parameter, while the concentration equation features the thermophoresis, Schmidt number effects and a chemical reaction term. The momentum equation includes thermal and solutal buoyancy effects and accounts for the resistance of the porous medium through the Darcy number. The system is subject to mixed boundary conditions that simulate shear-driven flow with specified temperature and solute concentration at the heated plate and convective cooling and solute depletion at the cold plate. The governing equations were solved using the homotopy perturbation method (HPM). The analysis reveals that internal heat generation enhances fluid temperature, which, in turn, drives buoyancy-induced acceleration of the flow, while heat absorption suppresses temperature and slows the flow. The thermophoresis effect strongly influences solute distribution by coupling it with Schmidt number, and chemical reactions. The velocity field is found to be highly sensitive to the combined thermal and solutal buoyancy effects and the medium's permeability. It is observed that the temperature profile decreases with increase in Biot number while concentration and velocity profiles increase with increase in Biot number.