On dispersion of solute in a hydromagnetic flow between two parallel plates with boundary absorption

Abstract

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.

Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel

“…They derived analytical expressions of mean and transverse concentrations up to third order. Dispersion of a solute between parallel plate channel in the presence of a magnetic field without and with boundary absorption was investigated by Poddar et al [24] and Dhar et al [25], respectively. The aforementioned studies focused on the dispersion phenomena for onedimensional unsteady flow.…”

“…Roy et al [38] discussed Taylor dispersion phenomena in non-Darcy porous medium and showed its applications on drug transport in impeded blood vessels. Numerous fields of research and engineering, such as metallurgy, earth science and nuclear engineering, are involved in the study of the flow of an electrically conducting fluid through a porous media in the presence of a magnetic field [25,39]. Very recently, Poddar et al [40] studied a more complex model of solute transport process in a MHD porous medium with the aid of oscillatory pressure gradient under the influence of heterogeneous and bulk chemical reactions.…”

“…[24] and Dhar et al. [25], respectively. The aforementioned studies focused on the dispersion phenomena for one-dimensional unsteady flow.…”

“…[38] discussed Taylor dispersion phenomena in non-Darcy porous medium and showed its applications on drug transport in impeded blood vessels. Numerous fields of research and engineering, such as metallurgy, earth science and nuclear engineering, are involved in the study of the flow of an electrically conducting fluid through a porous media in the presence of a magnetic field [25,39]. Very recently, Poddar et al.…”

Exact moment analysis of transient/asymptotic dispersion properties in periodic media with adsorbing/desorbing walls

“…36 The exact moment method can be applied to any steady or time-periodic velocity field, 27,52 be it solenoidal, irrotational, or a superposition of the two. Therefore, it allows to investigate transient and asymptotic dispersion properties in hydromagnetic/electrokinetic flows 53,54 as well as Casson fluid flows 35,55 usually adopted in hemodynamics.…”