Influence of a magnetic field on the flow of a micropolar fluid sandwiched between two Newtonian fluid layers through a porous medium

Abstract

The present problem is concerned with the flow of micropolar/Eringen fluid sandwiched between two Newtonian fluid layers through the horizontal porous channel. The flow in both the regions is steady, incompressible and the fluids are immiscible. The flow is driven by a constant pressure gradient and a magnetic field of uniform strength is being applied in the direction perpendicular to the flow. The flow of electrically conducting fluids, in the three regions, is governed by the Brinkman equation with the assumption that the effective viscosity of each fluid is the same as the viscosity of the fluid. No-slip conditions at the end of the plates, continuity of velocity, continuity of shearing stress and constant rotational velocity at the interface have been used as the boundary conditions to get the solution of the problem considered. The numerical values of the solution obtained are used to analyse the effect of various transport parameters, such as permeability of porous region, magnetic number, viscosity ratio etc. on the velocity profile and micro rotational velocity profile graphically. Also, the variations in the flow rate and the wall shear stress, with respect to the governing parameters, are presented in tabular form.

Micromagnetorotation of MHD Micropolar Flows

“…Moreover, the volumetric flow rate was calculated, while the microrotation parameter, geometric parameter and Hartmann number effects on the flow were investigated. Yadav et al [19] studied the flow of a micropolar fluid between two Newtonian fluid layers through a horizontal porous channel. The flow was driven by a constant pressure gradient and a uniform magnetic field was applied in the direction perpendicular to the flow.…”

Heat and mass transfer analysis for MHD non‐miscible micropolar and Newtonian fluid flow in a rectangular porous channel

“…\end{align}$$Linear momentum equation [36, 38, 39]— $$$$\begin{align} \frac{(\mu _1+\kappa )}{\phi _1}\nabla ^2{\bf v}_1+\frac{\kappa }{\phi _1} \nabla \times {\bf \omega }-\nabla p+{{\bf J}}\times {{\bf B}}-\frac{\mu _1+\kappa }{K_1}{\bf v}_1=0. \end{align}$$$$Equation of angular momentum [36, 38, 40]— $$$$\begin{align} \gamma \nabla ^2\omega -\kappa(2\omega -\nabla \times {\bf v}_1)=0. \end{align}$$$$Energy equation [36, 39]— $$$$\begin{align} k_1\nabla ^2 T_1+2\frac{\mu _1}{\phi _1}(D:D)+4\frac{\kappa }{\phi _1} {...$$…”

“…At the centreline (interface) of non‐miscible fluid that is, $$y=0$$, the flow velocity component as well as shear stress component of micropolar and Newtonian fluid are continuous [40]. $$$$\begin{equation} \begin{split} u_1(y)=u_2(y), \end{split} \end{equation}$$$$ $$$$\begin{equation} \begin{split} \frac{(1+\alpha )}{\phi _1}\frac{du_1}{dy}+\frac{\alpha }{\phi _1}\omega = \frac{n_\mu }{\phi _2}\frac{du_2}{dy}.$$…”

“…Yadav et al. [40–43] have presented a number of works on non‐miscible fluid flow. Devakar and Raje [44] investigated the magnetohydrodynamic (MHD) unsteady flow and heat transmission of two non‐miscible types of Newtonian and micropolar fluids in a horizontal channel filled with a porous material.…”

Differential transform method for couple stress fluid flow in a channel with a porous base

“…Tiwari et al 29 studied stokes flow through an assemblage of nonhomogeneous porous cylindrical particles using the cell model technique. Yadav et al 30 examined the influence of a magnetic field on the flow of a micropolar fluid sandwiched between two Newtonian fluid layers through a porous medium. Yadav and Jaiswal 31 investigated the influence of an inclined magnetic field on the Poiseuille flow of immiscible micropolar‐Newtonian fluids in a porous medium.…”