Advanced heating and cooling system design via numerical and data-driven optimization of unsteady MHD tetra-hybrid nanofluid flow

This research establishes a combined numerical-surrogate-design-of-experiments framework for the local-similarity examination of unsteady magnetohydrodynamic stagnation-point flow of Al₂O₃–Cu–TiO₂–Fe₃O₄/water tetra-hybrid nanofluid over an exponentially expanding permeable sheet. Thermal radiation, viscous dissipation, and temperature-dependent Arrhenius species consumption are taken into account. The reduced boundary value issue is solved using MATLAB bvp4c and checked against mesh, domain, tolerance, and limiting case benchmarks. A Bayesian-regularized artificial neural network (BR-ANN) is used to replicate numerical velocity, temperature, and concentration profiles. An L27 Taguchi design and analysis of variance (ANOVA) are used to assess the impact of factors for wall heat and mass transfer. Reanalysis of the 27 tabulated signal-to-noise (S/N) responses indicates that the Froude number accounts for 97.02% of Nusselt-number S/N variance (F = 1272.53, p < 0.001), and the Schmidt number accounts for 93.74% of Sherwood-number S/N variation (F = 1567.52, p < 0.001). The in-sample and test MSEs provided are of order 10-10-10-13. Independent case-wise validation is not demonstrated yet. These contributions of the factors are characterizing the respective parameter domain and are not mean percentage gains of the device efficiency. The approach reveals crucial control parameters for idealized boundary-layer transport; experimental confirmation and more detailed surrogate validation have to be done.