A Magnetohydrodynamic Time Dependent Model of Immiscible Newtonian and Micropolar Fluids through a Porous Channel: a Numerical Approach

Abstract

The objective of the present article is to study the magnetohydrodynamic(MHD) unsteady flow and heat transfer of two immiscible micropolar and Newtonian fluids through horizontal channel occupied with porous medium. Initially, fluids in both regions as well as both plates are at rest. At an instant of time, the flow in both regions is generated by a constant pressure gradient. The governing non-linear and coupled partial differential equations of Eringen's micropolar fluid and Newtonian fluid are solved subject to suitable initial, boundary and interface conditions. The numerical results for velocity, microrotation and temperature are obtained using Crank-Nicolson finite difference approach. The results obtained for velocities, microrotation and temperatures are presented through figures. The analysis regarding volume flow rate, skin-friction co-efficient and Nusselt number is also done and is presented through tables. It is explored that, velocity, microrotation and temperature are increasing with time and accomplishing steady state at higher time level. Velocity is decreasing with micropolarity parameter and Hartmann number, and increasing with Darcy number. Temperature enhances with increasing Brinkmann number, and declines with Prandtl number and ratio of thermal conductivities.

Role of electromagnetic analysis in radiative immiscible Newtonian and non‐Newtonian fluids through a microchannel with chemical reactions

“…Hence the clear medium provides less resistance and allows the fluid to flow which leads to an increase in the velocity of a fluid. The obtained results are matched with the existing literature 50 . The impact of Hartmann number ( M ) on the velocity profile is plotted in Figure 2B.…”

“…Hasnain et al 49 studied the MHD boundary layer flow of a viscoelastic dusty fluid between the porous stretching sheet and reveals that rising effective viscosity uplifts the velocity of both dust particles and fluid. Devakar and Raje 50 studied the MHD unsteady flow of two immiscible Newtonian fluids and Eringen's micropolar fluid between a horizontal channel with a porous medium and concluded that velocity declines with increasing Hartmann number. Devakar et al 51 discussed the pressure‐driven unsteady flow of two immiscible micropolar and Newtonian fluids across the horizontal channel and observed that velocity increases with an increase in Reynolds number.…”

Ion Slip and Hall Effects on Generalized Time-Dependent Hydromagnetic Couette Flow of Immiscible Micropolar and Dusty Micropolar Fluids with Heat Transfer and Dissipation: A Numerical Study

“…This data represents real MHD generator duct flows and is consistent with relevant publications-see Refs. [35][36][37][38]. The simulation results are verified for the velocity profile by comparing them with the limiting case (the non-MHD, non-dusty, single Newtonian Couette flow for which Ha 2 = 0 Be = 0 Bi = 0 R = 0 1 = 0 2 = 0 r 1 = 1 r 2 = 1Ge = 0).…”

“…The power-law stream with heat transfer and the magnetohydrodynamic impact was examined by Prasad et al 35 Devakar et al 36 presented the unsteady MHD flow of immiscible micropolar and Newtonian fluids inside the parallel plate and found the effect of numerous fluid parameters on flow velocity and temperature profile. Some more remarkable studies on Ion slip and Hall effect on MHD flow can be seen in Refs.…”

Steady magnetohydrodynamic Poiseuille flow of two immiscible non‐Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

“…Nagaraju and Mahesh 22 elucidate the MHD viscous motion of fluid with heat transport in a circular pipe. MHD time‐dependent model of immiscible Newtonian alongside micropolar fluids has been investigated by Devakar and Ankush Raje 23 . Idowu and Falodun 24 recently discussed heat along with mass transport motion of MHD.…”