Numerical investigation of unsteady MHD immiscible Casson micropolar and Jeffery fluid in a horizontal channel with heat transfer using MCB-DQM approach

Abstract

The dynamics of immiscible Casson micropolar and Jeffery fluid flow offer new possibilities for enhancing momentum and heat transfer efficiencies. Motivated by numerous applications of immiscible fluid flows in natural and industrial systems, the current work presents a numerical investigation of unsteady, incompressible, magnetohydrodynamic (MHD) flow involving two immiscible fluids, namely, Casson micropolar and Jeffery fluid, in a horizontal channel. The flow, driven by a uniform pressure gradient, assumes no-slip conditions at the channel walls and a continuous, nondeformable interface between the immiscible fluids. The well-established rapid converging modified cubic B-spline differential quadrature method (MCB-DQM) is applied to solve the partial differential equations governing the flow. The impact of crucial fluid parameters comprising the Casson micropolar fluid parameter, Jeffery fluid parameter, thermal, magnetic, and various other fluid parameters on temperature, microrotation, and velocity profile is illustrated graphically. Notably, the parameters of each fluid influence the profiles in both fluid zones. The flow dynamics are significantly affected by viscous dissipation, Lorentz force, fluid–wall interactions, and interfacial conditions. Key parameters such as time, Jeffery fluid, Casson micropolar, ion slip and Hall parameters, Reynolds number, Eckert number, the ratio of viscosities, the ratio of densities, and pressure gradient show significant impacts on the velocity, microrotation, and temperature profiles. However, reverse or mixed behavior is observed for other parameters. The novelty of current work lies in modeling the unsteady, immiscible, MHD flow of Casson micropolar and Jeffery fluid and proposing a numerical solution by deploying the MCB-DQM method. The findings have potential applications in various industrial and engineering processes, such as the design of oil extraction, optimizing processes in the food processing and cosmetics industry, and developing effective strategies for environment conservation.