On dispersion of solute in a hydromagnetic flow through a channel subject to asymmetric wall temperature and slip velocity

Abstract

With the influence of asymmetric wall temperature and inclined magnetic field under a constant pressure gradient, the present study explores the transport process of solute in a magneto-hydrodynamics (MHD), viscous, incompressible, electrically conducting fluid through a porous channel. The coupled heat and velocity equations are solved to obtain the explicit expressions for the temperature and velocity profiles. The slip velocity has been taken at the lower wall of the channel and the first order boundary absorption is applied at both the channel walls. Aris’s moment method is employed to obtain the first four central moments and the governing time-dependent advection-diffusion equation is solved, using an implicit finite-difference technique. The axial distribution of mean concentration of the solute is determined by the Hermite polynomial representation. For the first time, the various dispersion characteristics are observed for various parameters, such as the absorption parameter ($\beta$), angle of inclined magnetic field ($\alpha$), Prandtl number ($Pr$), Hartmann number ($M$), suction Reynolds number ($R$), injection Reynolds number ($R^{\prime }$), Darcy number ($Dn$), Grashof number ($Gr$), Navier slip parameter ($\gamma$), thermal radiation parameter ($\delta$) and dispersion time ($t$), simultaneously. It is prominent that when $\gamma$ increases from 0.1 to 0.2, the dispersion of solute increases 28.68% and when it increases from 0.2 to 0.3, $D_a$ increases by 22.75%. Conversely, when $\delta$ increases from 1 to 2, the dispersion of solute enhances more rapidly by 154.95% and when $\delta$ rises from 2 to 3, $D_a$ increases 39.33%. It is significant to note that, the amplitude of the mean concentration $C_m(x,t)$ reduces as $\gamma$, $Gr$ and $Pr$ enhances. On the other hand, the amplitude of the mean concentration rises as $\alpha$ and $M$ reduces. Both experimental and numerical validations are performed for the present work with the existing literature and an excellent agreement is achieved. For experimental validation, a combination of an artanh transformation and a piece-wise uniform mesh is utilized. Also, the two dimensional distribution of mean concentration is obtained analytically for various values of $\gamma$, $Gr$, $Pr$ and $\delta$. The obtained results from the current study are helpful for purification of crude oil, to understand the various hemodynamic conditions and for separation of matter from fluids etc.