Impact of porous material and slip condition on the MHD flow of immiscible Couple stress-Newtonian fluids through an inclined channel: Head loss and pressure difference

Abstract

Nowadays, non-Newtonian and Newtonian non-miscible fluid flow problems are much more effective in real-life physical problems. The understanding of flow behavior of magneto-hydrodynamic non-miscible fluids through a porous region playing an important role in the areas of biochemical sciences, crude oil extraction, transport issues and biomedicine. The aim of the present study is to know the impact of inclination angle of the channel, porous material used in the channel, slip boundary condition and applied magnetic field on the flow variables such as velocity profile, wall shear stress, pressure differences, head loss and volumetric flow rate of the two electrically conducting non-miscible couple stress and Newtonian fluids flowing through an inclined channel occupied with porous material of different porosity and permeability. An inclined channel is divided into two sub-regions of equal width through which the Newtonian and Couple stress fluids flow, respectively. Here, Brinkman’s model has been used to study the flow of immiscible fluid in their respective porous region. The equations that govern the flow of non-miscible fluids are solved using a well-defined analytical method and Mathematica 10.3 software. The present study concludes that the porous materials can be used to control the velocity of immiscible fluids in an inclined channel. It is also concluded from the present study that the use of slip condition promotes the values of velocity, volumetric flow rate, pressure differences and head loss. This work is validated with the previously published research work. Such models can be helpful in industries for filtering or refining immiscible oils.