On solute dispersion in an oscillatory magneto-hydrodynamics porous medium flow under the effect of heterogeneous and bulk chemical reaction

Abstract

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 nonmetallic) mix with the water, and they cause several diseases such as cholera, typhoid, and 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 and real concentration distributions, transverse concentration distribution, and transverse uniformity rate of the concentration are obtained. Also, the effect of various flow parameters such as Péclet 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 is 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 seen that the dispersion coefficient ([Formula: see text]) corresponding to the purely time-dependent flow increases with the enhancement of the Darcy number ( Da). Moreover, it is found that as the Hartmann number ( M) enhances, the total dispersivity ( DT) decreases. Also, the transverse concentration distribution becomes flat for larger values of the Hartmann number. It is noticed that when [Formula: see text], the transverse variation curve turns into a trimodal distribution from a bimodal. This model may be helpful for separating various metallic and nonmetallic particles from the water to reduce the water pollution.