Transient Double-Diffusive Convection in a Vertical Channel with Soret–Dufour Effects, Viscous Dissipation, Heat Generation and Chemical Reaction

Abstract

This paper investigates transient double-diffusive free convection flow in a vertical channel, incorporating the combined effects of Soret and Dufour cross-diffusion, viscous dissipation, internal heat generation/absorption, and first-order chemical reaction. The governing equations for momentum, energy, and species concentration are formulated under the Boussinesq approximation and non-dimensionalized to identify the key governing parameters: Prandtl number, Schmidt number, Dufour number, Soret number, Eckert number, buoyancy ratio, heat source parameter, chemical reaction parameter, Reynolds number, and thermal Grashof number. Analytical solutions are obtained using Olayiwola's Generalized Polynomial Approximation Method (OGPAM), a robust technique for solving parabolic partial differential equations with constant or variable coefficients. The solutions are validated against numerical results computed via Maple 2015's Dsolve numeric function, with excellent agreement confirming the accuracy and reliability of the analytical approach. The results demonstrate that increasing the Dufour and Soret numbers enhances temperature, concentration, and velocity fields through cross-diffusion mechanisms, while viscous dissipation substantially increases temperature and velocity in high-velocity flows. The Prandtl number reduces temperature, velocity, Nusselt number, and skin friction, but enhances species concentration and Sherwood number. The Schmidt number reduces all transport quantities, whereas the thermal Grashof number enhances temperature and velocity through strengthened buoyancy. The chemical reaction parameter significantly reduces species concentration, acting as a sink for the concentration field. The heat generation/absorption parameter reduces temperature while increasing concentration, revealing complex coupling between thermal and concentration fields.