Purpose This study aims to present a novel numerical investigation of steady two-dimensional boundary-layer flow and heat transfer of a Casson–Williamson tri-hybrid nanofluid over a permeable stretching surface, incorporating quadratic thermal radiation and velocity slip effects. The tri-hybrid nanofluid is formed by dispersing gold (Au), zinc (Zn) and iron oxide (Fe2O3) nanoparticles into human blood, enabling enhanced thermal transport while preserving the non-Newtonian rheological behavior of the base fluid. Design/methodology/approach The mathematical model accounts for yield stress and shear-rate-dependent viscosity, making it more realistic for biomedical flow applications. By using suitable similarity transformations, the governing nonlinear partial differential equations are reduced to a coupled system of ordinary differential equations and solved numerically using MATLAB’s bvp4c solver. Findings The results indicate that increasing Casson and Williamson parameters significantly retards fluid motion due to stronger non-Newtonian resistance, whereas the inclusion of tri-hybrid nanoparticles markedly enhances temperature distribution and heat transfer rates. Casson parameter reduces the dimensionless wall shear by approximately 18%–25%, confirming the dominant influence of yield stress on momentum transport. Thermally, the inclusion of quadratic radiation enhances the wall-temperature gradient and increases the Nusselt number by up to 12% compared with the classical linear Rosseland model, particularly at higher wall-temperature ratios (θw 1). Furthermore, the addition of tri-hybrid nanoparticles (φ = 0.01–0.10) improves the heat transfer rate by nearly 15%–22% relative to pure blood, thereby justifying the adoption of a multi-nanoparticle model over mono- or hybrid suspensions. Suction through the permeable surface further augments heat transfer while stabilizing the boundary layer structure. A normalized sensitivity analysis reveals that the quadratic radiation parameter significantly enhances the heat transfer rate, while the Casson and Weissenberg parameters predominantly influence the wall shear stress characteristics. An artificial neural network based on the Levenberg–Marquardt algorithm predicts the skin-friction coefficient and Nusselt number with excellent agreement (R ≈ 1), confirming the robustness of the computational framework. Practical implications The findings of this study provide valuable insights for biomedical thermal management and the design of advanced bio-integrated device applications. Originality/value The novelty of this work lies in the unified treatment of Casson–Williamson rheology, bio-based tri-hybrid nanofluids, quadratic thermal radiation and machine-learning-assisted prediction.
Mandal et al. (Mon,) studied this question.