Role of Heat and Mass Transfer on Time Dependent Natural Convection Flow in a Vertical Channel with Adiabatic and Isoflux Thermal Boundary Conditions

Abstract

This study investigates transient natural-convection flow with coupled heat and mass transfer in a vertical porous channel subject to adiabatic and isoflux thermal boundary conditions. A mathematical model is formulated to describe the evolution of the velocity, temperature, and concentration fields for a two-dimensional, incompressible, laminar flow through a homogeneous and isotropic porous medium. The governing continuity, momentum, energy, and concentration equations are nondimensionalized and solved analytically using the Laplace transformation technique. The resulting solutions are inverted through the Riemann-Sum Approximation (RSA), while MATLAB PDEPE is employed to validate the analytical results. The effects of thermal and solutal buoyancy, heat generation or absorption, and wall suction/injection on the transport characteristics are examined. The results indicate that increasing thermal and solutal buoyancy enhances the fluid velocity and strengthens the associated heat and mass transfer. Higher Prandtl and Schmidt numbers reduce the temperature and concentration distributions, respectively, leading to thinner thermal and solutal boundary layers. Heat generation increases the fluid temperature and wall heat-transfer rate, whereas heat absorption produces the reverse effect. Suction suppresses the velocity, mass flow, and mass-transfer characteristics, while injection enhances them. The skin-friction coefficient increases with buoyancy forces and injection but decreases with suction. The analytical solutions obtained using the Laplace-transform and RSA procedures show close agreement with the numerical results from MATLAB PDEPE. The study demonstrates that buoyancy, thermal transport, and mass diffusion significantly influence transient natural-convection behaviour in porous channels and provides useful insights into coupled heat and mass transfer under adiabatic and isoflux boundary conditions.