Evolution of concentration distribution and removal of a solute in magnetohydrodynamics channel flow: Effects of buoyancy-driven force and induced magnetic field

The dispersion of reactive solutes in various flow geometries has significant implications for ecological and environmental applications. Researchers such as Poddar et al. (Poddar et al. 2021 Proc. R. Soc. A 477, 20200830 (doi:10.1098/rspa.2020.0830) and Dhar et al. (Dhar et al. 2021 Phys. Fluids. 33, 083609) have extensively studied solute transport in magnetohydrodynamics (MHD) channel flow, focusing on the applied magnetic field. However, the impact of the induced magnetic field on solute dispersion between two parallel plates remains poorly understood. This article presents an analytical investigation using Mei's multi-scale homogenization approach to examine the effects of the Hartmann number, Grashof number and absorption parameter on the multi-dimensional concentration distribution and removal efficiency of a reactive solute in MHD laminar channel flow. The findings provide insights into concentration behaviour, such as the decrease in the Taylor transport coefficient with an increase in the induced magnetic field. These insights have practical implications for improving sewage and wastewater treatment by effectively separating desired particles from contaminants, contributing to advancements in environmental purification techniques.