Heat transfer optimization in MHD Casson ternary hybrid nanofluid flow using CPC fractional modeling

Efficient thermal management in microchannel systems is essential for modern cooling devices, biomedical systems, energy units, and compact heat exchangers. In this study, the unsteady heat transfer and flow behavior of a Casson-type ternary hybrid nanofluid in a parallel-plate microchannel are investigated under generalized magnetohydrodynamic (MHD) effects. Water is used as the base fluid, while gold [Formula: see text], copper [Formula: see text], and silver [Formula: see text] nanoparticles are uniformly suspended to improve the thermal transport capacity of the fluid. The main motivation of this work is to examine how memory effects, magnetic field strength, and enhanced nanoparticle properties influence the velocity and temperature distributions in a non-Newtonian microchannel flow. To describe the memory and hereditary characteristics of the flow, the governing equations are modeled using the Constant Proportional Caputo (CPC) fractional derivative. An implicit finite-difference scheme is also developed to support thus study results numerically. The model is validated by comparing the present profiles with the previous study results, and a close agreement is observed. In addition, a magnitude-based sensitivity analysis is carried out to identify the most influential physical parameters. The results show that the thermal Grashof number has the strongest effect on the velocity response, while the effective Prandtl number is the dominant parameter controlling the temperature field. The CPC fractional model provides smoother and more flexible transient behavior compared with the classical integer-order model. Furthermore, the ternary hybrid nanofluid shows better heat transfer performance than simple nanofluid and hybrid nanofluid cases because of its improved effective thermal conductivity.