RSM and Sensitivity Analysis of Hydromagnetic Couette Flow With MoS ₂ Nanofluid and Variable Fluid Properties

The novel theoretical insights into the time‐dependent hydromagnetic Couette flow of engine‐oil based MoS 2 nanofluid under the effects thermal radiation, energy dissipation, Dufour, and Soret effects including temperature‐dependent fluid properties are analyzed. Unlike the conventional persistent property models, this study integrates the variable viscosity and thermal conductivity to accurately model the nanofluid performance in high‐temperature lubrication and regulation systems. The models nonlinearly coupled PDEs governing momentum, energy, and species transport are tackled numerically using an efficient implicit finite difference scheme with stable and convergent structure. The comprehensive parametric analysis of the problem reveals that momentum profiles are significantly enhanced by increasing the Dufour and Soret numbers and thermal Grashof number, whereas they decrease with by the magnetic parameter and variable viscosity effects. The temperature distribution noticeably increases with radiation parameter, nanoparticle volume fraction, and Eckert number, but decreases with thermal absorption. The primary wall friction decreased by magnetic and thermal and mass buoyancy effects but the secondary wall‐friction increased by these parameters. Sensitivity analysis and optimization accomplished via response surface methodology (RSM) identified that the thermal radiation and nanoparticle concentrations are most influential parameters in maximization of thermal transport performance. Remarkably, in comparison to the base fluid, the dispersion of 4% MoS 2 nanoparticles yields a significant 7.13% increase in the heat transport rate. Further, findings of the study offer novel revelations into the combined influences of the radiative thermal transport, cross‐diffusion, and variable properties in nanofluid lubrication, with direct implications for advanced thermal management in automotive engines, aerospace components, and industrial cooling systems.