Multi-scale analysis of solute dispersion in free and forced convection flow between two parallel plates filled with a porous medium

This study investigates the transverse concentration distribution of contaminant transport in free and forced convective flow within a parallel plate filled with a porous medium. The solute undergoes irreversible boundary reactions at the plates. Most previous studies explored similar configurations in free and forced convective flows by incorporating magnetic effects. However, our study introduces a porous medium, which more accurately reflects real-world scenarios, such as pores in particles within flowing rivers or other environments. We develop an analytical solution of the dispersion coefficient, mean and transverse concentration using a multi-scale technique. The present study examines the effects of Grashof number ( G ), porous parameter and relative viscosity in the presence of boundary absorptions on the solute dispersion. Higher porous parameter values reduce permeability, limit solute spreading, and maintain a peak in the mean concentration distribution. In porous media, a negative G enhances solute dispersion near the upper boundary, whereas a positive G influences dispersion when the lower boundary absorbs. The buoyancy forces dominate for G > 0 or G < 0 , driving the flow toward the heating or cooling plates and intensifying non-uniformity in the transverse concentration distribution. This effect becomes more significant with higher porosity and viscosity, as the porous medium reduces permeability and increases resistance to fluid motion. When boundary reactions are considered in the presence of a porous medium under free and forced convection, they cause uneven solute distribution as the walls absorb solute. A higher porous parameter increases resistance to fluid flow, which amplifies concentration gradients and enhances non-uniformity. • Solute transport in free and forced convection flow in a porous medium. • Includes boundary absorption effects in the parallel plate channel. • Uses multiscale homogenization to obtain the analytical transverse concentration. • A higher porous parameter reduces permeability, which limits solute spreading. • Solute transport in free and forced convection aids understanding groundwater contamination processes.