Trihybrid nanofluids possess promising applications in the biomedical, electronic, cosmetic, and materials processing fields owing to their enhanced thermophysical characteristics. This study examined the flow and thermal characteristics of a tri-hybrid ( \(Au - Ag - TiO_{2}\) )/blood Casson nanofluid over a rotating disk, influenced by nonlinear thermal radiation, focusing on the Darcy-Forchheimer effects, slip phenomena, Biot number, and internal heat generation or absorption. The governing equations were simplified to a system of ordinary differential equations by introducing appropriate similarity variables and solved numerically using the BVP4C solver. The computed Nusselt number values were compared with those from earlier investigations in the literature and showed strong consistency, demonstrating the reliability of the present numerical model. Additionally, a response surface approach was utilized to create a regression model that showed excellent agreement with the numerical data, with a coefficient of determination of (99.99%), indicating high predictive accuracy for the skin friction coefficient. The analysis showed that the nanoparticle concentration had the greatest impact among the studied parameters, contributing approximately (70–75%), while the magnetic parameter accounted for about (14–16%), and the Casson parameter contributed nearly (10–13%) to the variation in skin friction.
