Thermal performance optimization of Au–Al2O3–TiO2 nanofluids in casson blood flow: a second law analysis and parametric sensitivity study via Keller box method

The current research focuses on optimizing heat transfer and flow behavior of Casson blood based ternary hybrid nanofluid flow around a porous cylindrical surface, targeting biomedical heat transfer applications. The nanofluid consist of gold, aluminium oxide, and titanium dioxide nanoparticles dispersed in a blood based Casson fluid. The governing partial differential equations can be transformed into an equivalent system and solved numerically using the implicit finite difference method. The influence of critical parameters on flow and thermal characteristics, entropy generation and Bejan number shown graphically. Results shows that THNF enhances velocity profile up to 35% and temperature distribution up to 29% compared to hybrid and mono nanofluids. However, THNF also exhibits up to 35% higher entropy generation, while mono nanofluid demonstrate superior Bejan numbers, indicating lower irreversibility and better thermal efficiency. Response Surface Methodology (RSM), combined with a Central Composite Design (CCD) structure, improves heat and flow performance. Three influential input parameters $$\beta ,M,Da$$ and $$\Pr ,Rd,\phi$$ on the output responses is statistically assessed using RSM. The regression analysis demonstrates high accuracy with $$R^{2}$$ values exceeding $$99.9\%$$ both responses. ANOVA confirms the statically significance of main, quadratic and interactions effects, with $$p$$ -values $$\left( {p < 0.01} \right)$$ . Sensitivity analysis reveals that nanoparticle volume fraction $$\left( \phi \right)$$ has the strongest positive impact on heat transfer rate and Casson parameter $$\left( \beta \right)$$ has the lowest negative impact on surface drag. The maximum heat transfer rate is achieved is $$1.33592,$$ corresponding to $$\Pr = 2.0,Rd = 1.5,$$ and $$\phi = 0.05$$ , while the minimum surface drag is $$0.73076,$$ at $$\beta = 3.0,\,M = 2.0,$$ and $$Da = 0.6.$$ optimization yields a desirability score of 0.995, indicating excellent agreement between predicted and actual outcomes.