Heat transfer and entropy generation analysis of trihybrid Williamson nanofluid flow over a rotating disk: a numerical study with response surface and sensitivity analysis

Rotating flow systems serve as fundamental platforms for studying enhanced heat and mass transfer in advanced engineering processes. This study primarily aims to investigate the flow, thermal, and bioconvective behaviors of a trihybrid Williamson nanofluid via a rotating disk in the presence of motile microorganisms. The trihybrid nanofluid comprised copper, iron oxide, and aluminum oxide nanoparticles dispersed in a base fluid of water. A mathematical model was developed under steady, incompressible flow conditions, incorporating thermal radiation, heat source/sink effects, Brownian motion, thermophoresis, viscous dissipation, and Darcy-Forchheimer porous media. The governing nonlinear equations were transformed and solved numerically using the MATLAB BVP4C algorithm to ensure accuracy and numerical stability. Additionally, the Response Surface Methodology (RSM) based on a Central Composite Design yielded a high coefficient of determination (99.96%), indicating excellent agreement with the numerical data. A sensitivity analysis was conducted to quantify the effects of key factors on the heat transfer characteristics. The results indicate that the radiation parameter is the most dominant factor, contributing approximately 65–75% to the overall variation in heat transfer, followed by the heat source/sink parameter (25–30%), whereas the Weissenberg number has the least influence (5–10%). These findings provide quantitative insights into parameter sensitivity and offer applications in biomedical rotating devices, bioreactors, rotating disk reactors, rotating machinery cooling, and advanced energy and chemical processing systems.