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This investigates the fluid flow, as well as the heat and mass transfer phenomena occurring within a vertical channel housing two immiscible fluids. It focuses particularly on slip effects, encompassing no slip, velocity slip, thermal slip, and multiple slips, each being applied with appropriate boundary conditions. The analysis thoroughly examines crucial characteristics such as variations in thermal conductivity and viscosity. By employing a sixth-order Runge-Kutta numerical method implemented via Mathematica, the study achieves precise solutions for complex scenarios. The extensive findings elucidate the intricate interactions among different slip mechanisms and relevant parameters, providing valuable insights for both theoretical comprehension and practical application in engineering contexts. Furthermore, this research offers significant insights into the dynamics of fluid flow, heat, and mass transfer under various slip effects. Noticeable variations in these slip effects are observed and visually represented. Engineering parameters such as Nusselt number, shear stress, and Sherwood number are meticulously calculated and analyzed using bar charts, offering insights into their impact and behavior.
Gosty et al. (Sun,) studied this question.