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

The hydrodynamics of immiscible micropolar fluids is important in a variety of engineering problems, including biofluid dynamics of arterial blood flows, pharmacodynamics, Principle of Boundary layers, lubrication technology, short waves for heat-conducting fluids, sediment transportation, magnetohydrodynamics, multicomponent hydrodynamics, and electrohydrodynamic. Motivated by the development of biological fluid modeling and medical diagnosis instrumentation, this article examines the combined effects of ion slip, viscous dissipation, Joule heating, and Hall current on unsteady generalized magnetohydrodynamic (MHD) Couette flow of two immiscible fluids. Two non-Newtonian incompressible magnetohydrodynamic micropolar and micropolar dusty (fluid-particle suspension) fluids are considered in a horizontal duct with heat transfer. No-slip boundary conditions are assumed at the channel walls and constant pressure gradient. Continuous shear stress and fluid velocity are considered across the interface between the two immiscible fluids. The coupled partial differential equations are formulated for fluids and particle phases and the velocities, temperatures, and microrotation profiles are obtained. Under the physically realistic boundary and interfacial conditions, the Modified cubic B-spline differential quadrature method (MCB-DQM) is deployed to obtain numerical results. The influence of the magnetic, thermal, and other pertinent parameters, i.e. Hartmann magnetic number, Eckert (dissipation) number, Reynolds number, Prandtl number, micropolar material parameters, Hall and ion-slip parameters, particle concentration parameter, viscosity ratio, density ratio, and time on velocity, microrotation, and temperature characteristics are illustrated through graphs. The MCB-DQM is found to be in good agreement with accuracy and the skin friction coefficient and Nusselt number are also explored. It is found that fluids and particle velocities are reduced with increasing Hartmann numbers whereas they are elevated with increment in ion-slip and Hall parameters. Temperatures are generally enhanced with increasing Eckert number and viscosity ratio. The simulations are relevant to nuclear heat transfer control, MHD energy generators, and electromagnetic multiphase systems in chemical engineering.