Response surface-based optimization and sensitivity analysis of MHD tetra hybrid nanofluid flow over a shrinking disk

This work presents a novel numerical and statistical framework for analyzing tetra hybrid nanofluid flow over a shrinking disk with the influence of magnetohydrodynamic (MHD), thermal radiation, and suction effects, integrating both computational and optimization techniques. The fluid comprises water-based tetra hybrid nanofluid containing aluminium oxide (Al2O3), copper (Cu), silicon dioxide (SiO2), and titanium dioxide (TiO2) nanoparticles. The governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs) using similarity transformations and solved numerically via the bvp4c solver in the Matlab software. Validation of the numerical approach is carried out by comparing results with existing literature, showing excellent agreement for limiting cases. Response Surface Methodology (RSM) with central composite design is applied to analyze interactions between the key parameters. The results reveal that increasing the magnetic parameter by 0.1 leads to a 17.3% increase in the skin friction coefficient and an 1.4% enhancement in heat transfer rate. Conversely, raising the radiation parameter by 0.1 reduces the Nusselt number by up to 9.5%, indicating weakened thermal gradients at the wall. In addition, with a 2% increase in suction parameter improving heat transfer and skin friction by approximately 26.6% and 8.8%, respectively. Analysis of variance (ANOVA) confirms that suction and magnetic parameters are the most influential on thermal and flow responses. Sensitivity analysis further highlights strong linear and interaction effects. These findings offer valuable guidelines for the design of advanced thermal management systems using multi-nanoparticle-enhanced fluids, particularly in applications such as rotating heat exchangers, MHD pumps, and electromagnetic cooling devices operating under radiative conditions.

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