This paper presents the theoretical modelling of the microfluidic transport of immiscible, non-Newtonian fluids (specifically, Jeffrey and Casson fluids) through a vertical porous medium by considering magnetohydrodynamic, Hall current, electroosmotic, buoyancy, thermal radiation, and internal heat generation effects all simultaneously. Current literature in this area has primarily focused on Newtonian or single non-Newtonian fluid flows and has not addressed two distinct non-Newtonian fluid flow models in multiphase porous systems with Hall effects and electroosmosis. To accomplish this goal, governing continuity, momentum, and energy equations were formulated for each of the two fluids, the equations were reduced to non-dimensional form through appropriate scaling and analytical solutions for velocity and temperature distributions were obtained. The key findings of this study include that the velocity profile of both fluids is enhanced at high permeability and at high electroosmotic flow parameters and is reduced by the Lorentz force associated with a high magnetic field strength. Theoretical modelling at this level can provide important information on the dynamics of immiscible fluids that can be applied to the design and operation of microfluidic systems and technological applications associated with energy transport and thermal management for cooling systems.
Bhaskar et al. (Tue,) studied this question.