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This study examines the heat and mass transfer phenomena that take place in a vertical channel containing immiscible fluids, specifically micropolar and viscous fluids. The main objective is to explore the impact of variable viscosity, velocity slip, and other pertinent parameters on various properties, including velocity, angular velocity, temperature, and diffusion. This investigation reveals a significant correlation between these parameters and the observed effects. Also analyzes the transfer rates of heat, mass, and velocity on both boundaries of the channel. This comprehensive examination provides valuable insights into the intricate mechanisms governing these transfer processes. To solve the complex system of coupled equations, the Runge-Kutta sixth-order method, utilizing the ND Solve Mathematica software is used. This numerical technique offers accurate and reliable solutions for simulating the dynamics of heat and mass transfer in this system. As a result, the velocity slip parameter and thermal conductivity increases, the velocity ,angular velocity and temperature decreases within the system, reverse effect is observed in diffusion. These findings further enhance our understanding of the complex behavior of the immiscible fluids in the vertical channel are depicted graphically.
Gosty et al. (Tue,) studied this question.