Optimizing thermal performance in advanced microfluidic energy systems via 3D rotating (MoS ₂ -SiO ₂ /PAO) hybrid nanofluid flow past a stretching/s

In this study, the high-resolution numerical simulation of the three-dimensional radiative rotating flow of polyalphaolefins (PAOs)-based nanolubricant with synergistic dispersion of molybdenum disulfide (MoS ₂ ) and silicon dioxide (SiO ₂ ) hybrid nanoparticles over a permeable surface expansion is presented. Motile bioconvection microorganisms are incorporated in the hybrid nanofluid to maximize the convective thermal performance and to stabilize the matrix of the multiphase solutions. The computational fluid dynamics framework considers the multiphysical coupled effects of the Darcy–Forchheimer porous medium, thermal radiation, heat sources and convective Biot boundary conditions with an aligned magnetic angle. The numerical approach, BVP4c is used to solve the transformed nonlinear equations of the boundary layer, and response surface methodology is applied to the surface topologies for the statistical mapping of the interactive limits of the parameters. It is found from the quantitative evaluations that the dominance of the porosity parameter is that it exactly gives a 67.4012% increase in the secondary skin friction as the porosity factor increases from 0.5 to 2.5. Moreover, the effect of an aligned magnetic field improves the energy transfer rate by 77.47%. The results of a rigorous grid independence matrix test show that when the number of discrete grid nodes is increased beyond ( N  = 320), all boundary layer fluxes are asymptotically stabilized to within six decimal places. Consequently, absolute convergence results show that the absolute error residuals are always kept within a stable micro-band until 10 ⁻⁸ , demonstrating the unprecedented numerical accuracy, stability and reliability of the present simulation for advanced microfluidic thermal management systems.