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

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

Entropy analysis of the MHD Jeffrey fluid flow in an inclined porous pipe with convective boundaries

The present work deals with entropy generation analysis of a non-Newtonian Jeffrey fluid flow through an inclined pipe of circular cross section in the presence of uniform porous medium. The flow is subjected to constant pressure gradient and uniform magnetic field. The boundaries of circular pipe are assumed to be convective. Due to the presence of mixed convection, the underlying governing equations are nonlinear and coupled. The numerical solution of the system of governing equations is obtained. The analysis of roles played by the transport properties viz. fluid velocity and temperature is done to explore the thermodynamic entities like entropy generation number and Bejan number. The study of irreversibilities in the considered flow is analysed taking several sets of parameters, i.e., the Jeffrey fluid parameter, the Hartmann number, the Darcy number, the Grashof number, suction/injection parameter, the Brinkman number, the Prandtl number and the Biot number appearing in the problem