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It is well known to all of us that there is a shortage of pure drinking water across the globe. Different types of pollutants (metallic and non-metallic) mix with the water and they cause several diseases like cholera, typhoid, various kinds of skin diseases and even, it is found that these kinds of particles may cause skin cancer. In the current study, an analytical solution of a two-dimensional convection-diffusion equation is obtained using Mei's multi-scale homogenization technique to investigate the influences of homogeneous and heterogeneous reactions on dispersion phenomena of the solute in an oscillatory magneto-hydrodynamics porous medium flow. In the appearance of the applied transverse magnetic field and oscillatory pressure gradient, a mathematical model of magneto-hydrodynamics dispersion between two parallel plates is presented. The analytical expressions of Taylor dispersivity, longitudinal mean \& real concentration distributions, transverse concentration distribution and transverse uniformity rate of the concentration are obtained. Also, the effect of various flow parameters such as P\'eclet number, Hartmann number, Schmidt number, Darcy number, oscillatory Reynolds number, porous parameter, dispersion time, downstream and upstream locations, chemical heterogeneous boundary reaction and bulk reaction are discussed. How the transport phenomena of the solute display different natures with the various ranges of Darcy and Hartmann numbers with the aid of homogeneous and heterogeneous boundary reactions are highlighted. To show the effect of the absorption parameters on the transport coefficient, the third-order approximation of concentration is performed.

It is well known that the widely applied Taylor diffusion model predicts the longitudinal distribution of tracers. Some recent studies indicate that the transverse concentration distribution is highly significant for large dispersion times. The present study describes an analytical approach to explore the two-dimensional concentration dispersion of a solute in the hydromagnetic laminar flow between two parallel plates with boundary absorption. The analytical expressions for the transverse concentration distribution and the mean concentration distribution of the tracers up to second-order approximation are derived using Mei's homogenization technique. The effects of the Péclet number and Hartmann number on the Taylor dispersivity are shown. It is also observed how the transverse and longitudinal mean concentration distributions are influenced by the magnetic effect, dispersion times, and boundary absorption. It is remarkable to note that the boundary absorption creates a large non-uniformity on the transverse concentration in a hydromagnetic flow between two parallel plates.

The present paper explores an analytical solution to study the two-dimensional concentration distribution of a solute in a conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. Mei’s homogenization technique is used to acquire the mean concentration distributions up to the second-order approximation and the transverse concentration distributions up to third order. An uneven form of the concentration cloud and the transverse variation of the concentration distribution in a hydromagnetic flow are illustrated for the initial stage. The rate of progress towards uniformity of a solute cloud seems much slower than that of normality. It is observed that the peak of the transverse mean concentration and transverse variation of the concentration distribution of the solute significantly decrease with the increase in the magnetic field for small dispersion times. This is because, with an increase in the magnetic field, the velocity profiles flatten at the central core region between the parallel plates. The research proposes a time scale of 10 δ 2 / D (where δ is half the distance between two parallel plates and D is the molecular diffusivity) to characterize the dispersion process to approach the transverse uniformity.

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