Exploring the rheology of immiscible non-newtonian fluids in a heated curved channel with thermodiffusion and diffusion-thermo effects

This study examines the heat and mass transfer behavior of two immiscible non-Newtonian Casson and Ree Eyring liquids through a thermally radiative curved pipe. The conduit is divided into two distinct domains: Region I (core) containing Ree–Eyring fluid and Region II (periphery) occupied by Casson fluid. By modifying the Navier–Stokes equations and introducing suitable non-dimensional parameters, a mathematical framework is formulated to capture the complex interaction of fluid properties and transport mechanisms. The perturbation method is employed to obtain analytical solutions of the resulting nonlinear differential equations. The analysis incorporates the combined effects of Soret and Dufour phenomena to assess how coupled temperature and concentration gradients influence energy and mass transport. The findings demonstrate that curvature, viscosity and density ratios, Prandtl and Reynolds numbers, thermal radiation, and thermal conductivity parameters significantly alter the velocity, thermal, and concentration profiles. Results reveal that increasing the viscosity ratio enhances the axial velocity of both fluids, while a higher conductivity ratio suppresses fluid temperature. Streamlines and isotherms are provided to visualize variations in velocity and temperature fields, and performance indicators such as skin friction, Nusselt number, and volumetric flow rate are quantified. These insights underline the crucial role of immiscible fluid dynamics in optimizing processes such as chemical reactors, thermal management systems, and separation technologies, where coupled heat and mass transfer under complex conditions governs efficiency and stability.