Numerical investigation and optimization of unsteady micropolar nanofluid flow over a stretching surface using response surface methodology

This study analyzes the micropolar nano liquid flow over an obliquely stretched, porous surface with a focus on energy transport. The model incorporates magnetic effects, porosity, and slip conditions in velocity and concentration, under thermal convective boundaries. Using similar transformations, the governing equations are reduced and answered statistically via the bvp4c approach in MATLAB, along with the shooting method, is devoted to obtaining the calculations, which are addressed via graphs and tables. The influence of key material parameters on flow and heat transfer characteristics is examined using response surface methodology (RSM). This approach is employed to analyze and optimize the effects of principal controlling factors on skin-friction, Nusselt number, and related transport quantities. The numerical findings, verified against previously published results, demonstrate strong sensitivity of the flow behavior to variations in magnetic field intensity, permeability, and thermophysical properties. These insights contribute to improved design strategies in thermal management systems and micro-scale fluidic technologies. For the two evaluated scenarios, the adjusted R-squared and R-squared values for skin-friction are obtained as 98.39 % and 98.92 %, respectively, indicating excellent predictive accuracy of the statistical models. The Sherwood number exhibits greater sensitivity to Brownian motion, thermophoresis, and Dufour effects compared to heat generation parameters. The outcomes of this study provide practical design guidance for thermal management systems, nanofluid-based cooling technologies, micro-scale fluidic devices, biomedical transport systems, porous media reactors, electromagnetic flow control devices, and energy conversion systems, highlighting the engineering significance of the present investigation.