Optimization of heat transfer in non-Newtonian double immiscible fully developed fluid flow

Stratified immiscible fluid flows are central to functional gradient material fabrication, where thermal and hydrodynamic interactions strongly influence the final material performance; however, the combined roles of non-Newtonian rheology, nanoparticle dispersion, and magnetic field effects remain insufficiently explored. This study focuses on mixed convection heat transfer with double impermeable layers inside a vertical channel, consisting of a Jeffrey fluid in region I and a Casson nanofluid in region II, and a transverse magnetic field in steady uniform flow. A transformation-based computational approach is employed to resolve the coupled momentum and energy transport. The main focus shows that increasing the nanoparticle loading has similar effects in both regions, significantly increasing the heat transfer efficiency and reducing the velocity by increasing the flow resistance. Furthermore, the Jeffrey and Casson parameters provide improved flow rates and thermal uniformity in fluid layers, which inhibit convective motion but provide good stability and control of the flow. These observations provide good physical information and useful suggestions for improving the thermal and hydrodynamic properties in complex functional gradient material processing systems.