Numerical investigation of slip effects on heat and mass transfer in a vertical channel with immiscible micropolar and viscous fluids of variable viscosity

Abstract This study investigates the fluid flow, heat, and mass transfer phenomena within a vertical channel containing two immiscible fluids, with a particular focus on slip effects. These effects include no slip, velocity slip, thermal slip, and multiple slips, each analyzed with appropriate boundary conditions. The study thoroughly examines key characteristics, such as variations in thermal conductivity and viscosity. Using a sixth‐order Runge–Kutta numerical method implemented using Mathematica, the study achieves precise solutions for complex scenarios. The detailed results show how the various slip mechanisms and relevant parameters interact with each other in complex ways. These findings are useful for both theoretical understanding and application in real‐life engineering situations. This study also gives important information about how fluid flow, heat transfer, and mass transfer change under different slip effects. It looks at these effects and shows how they change visually. It also carefully calculates and analyzes engineering parameters like the Nusselt number, shear stress, and Sherwood number using bar charts, showing how they affect and behave. The study resulted in velocity slip having a minimal impact on temperature, whereas thermal slip resulted in higher temperatures. Both velocity and thermal slip conditions simultaneously result in the lowest temperatures.