Parametric sensitivity assessment of slip flow and thermophoretic effects on a vertical stretching surface using response surface methodology

Abstract This study investigates the effect of velocity slip on magnetohydrodynamic boundary-layer flow, emphasizing energy slip and thermophoresis under steady-flow conditions. While Magnetic Resonance Imaging (MRI) employs specialized equipment to generate detailed internal images through proton alignment, the present work focuses on fluid-dynamic mechanisms governing heat and mass transfer. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and solved with MATLAB’s bvp4c solver. A sensitivity analysis is performed to optimize heat transfer performance, representing a key novelty of the study. The results reveal that increasing the velocity slip parameter from 0.7 to 1.9 significantly alters the velocity and temperature profiles, leading to an enhancement of the Nusselt number by approximately 3.3% and a reduction in skin friction by nearly 19.3%. The influence of the dipole effect on flow characteristics is also examined. Furthermore, Artificial Neural Networks (ANN) demonstrate superior predictive accuracy compared to Response Surface Methodology (RSM). Comparison with earlier studies confirms the validity of the results. Overall, the findings demonstrate the potential of velocity slip to enhance heat transfer more effectively than energy slip and thermophoresis in advanced thermal management systems.