Response surface optimization for Minsta-Gherasim hybrid nanofluid flow over a porous surface with varying water temperature levels and magnetic influence.

This work uses the Darcy-Forchheimer model in porous media to study the thermal and flow behaviour of such hybrid nanofluids, monitoring the combined impacts of viscous dissipation, porosity, Forchheimer number, Eckert number, and changing water temperatures. Velocity, temperature, and heat transfer profiles are examined using the BVP4C numerical scheme, which has better accuracy in solving nonlinear boundary value problems. Response Surface Methodology (RSM) is used to optimize system performance, including analysing multi-parameter interactions and how these factors affect the effectiveness of heat transfer to complement the numerical approach. Certain parameter settings resulted in a notable improvement in the hybrid nanofluids' thermal performance. The results indicate that the increasing values of porosity and inertial resistance, instead of accelerating the flow velocity, slow it down, but at the same time, their effect enhances the thermal distribution profile. Viscous dissipation significantly affects thermal energy, and the Eckert number ([Formula: see text]) is essential for figuring out the temperature profile of fluid flows. The increase in kinetic energy to thermal energy, with increasing Eckert number, is also evident, as demonstrated by the increased fluid temperatures. Optimal configurations delineated through RSM reveal improvements in the Nusselt number contingent on specific parametric combinations. Moreover, the study fills the gap in knowing the thermal behaviour of hybrid nanofluids under varied temperature conditions in porous structures. The results provided in this article offer valuable guidelines for designing and operating thermal systems in applications that include advanced cooling technologies, heat exchangers, biomedical devices, and renewable energy systems. A mathematical approach that integrates numerical and statistical methodologies offers a robust framework for advancing the field of hybrid nanofluid research and its emerging applications.