<p>Heat transport over curved porous surfaces is essential for biomedical applications, such as targeted medicinal heating and thermal management in implanted devices. In this work, the effects of Darcy–Forchheimer resistance and an angled magnetic field on the constant two-dimensional boundary layer flow of an incompressible Casson fluid containing a Cu–Al₂O₃–TiO₂/H₂O a trihybrid nanoparticle combination across a curved permeable stretching sheet are studied. The energy model incorporates linear thermal radiation and a non-uniform heat source/sink. Velocity, temperature, skin friction, Nusselt number, entropy generation, and Bejan number are obtained by solving the governing equations with MATLAB’s bvp4c solver after transforming them into nonlinear ordinary differential equations via similarity transformations. A feedforward ANN trained using the Levenberg–Marquardt algorithm is employed for prediction. The ANN predictions are in very good agreement with the numerical solutions. The results show that the velocity profile is suppressed by the magnetic and porosity parameters and the Forchheimer number, while the fluid motion is enhanced by increasing the curvature parameter. Thermal radiation and heat generation increase the temperature field, but thermal relaxation decreases the thermal boundary layer thickness. The entropy generated by viscous heating increases with the Brinkman number. Additionally, the entropy generation and the Bejan number are shown to increase with the temperature ratio parameter, indicating an increase in thermodynamic irreversibility dominated by heat transfer effects. The ANN model can accurately estimate the skin friction coefficient and the Nusselt number. In comparison to more straightforward nanoparticle formulations, the Cu–Al₂O₃–TiO₂/H₂O trihybrid nanofluid has higher overall thermal performance in the development of biomedical heat transfer applications.</p>