Variable porosity and Hall–ion slip effects on MHD micropolar nanofluid flow over a paraboloid surface: A sensitivity analysis

This study investigates the magnetohydrodynamic (MHD) micropolar nanofluid flow over a paraboloid surface with variable porosity, a subject of great importance for advanced thermal and fluid systems such as MHD generators, nuclear cooling units, and aerospace thermal control devices. While previous research has largely focused on uniform porosity and overlooked Hall–ion slip effects, this work addresses a critical gap by analyzing the combined influence of Hall–ion interactions, micropolar fluid behavior, and spatially varying porosity on the flow, heat, and mass transfer characteristics. The aim of this study is to perform a comprehensive sensitivity analysis of flow and transport phenomena by varying key physical parameters α1,α2, and α3 and assessing their impact on field profiles. The governing nonlinear partial differential equations are reduced to a system of ordinary differential equations using similarity transformations and are numerically solved using the Galerkin finite element method. In addition, response surface methodology is employed to optimize local wall couple stress and evaluate the sensitivity of parameters. Under sensitivity analysis, α2 is identified as an influential parameter affecting K1. The results show that an increase in the Da and the Be enhances the velocity profile, whereas a higher M reduces it. The microrotation profile increases with α1, while the temperature field rises with Df. Conversely, increases in the Pr, Sr, and Le reduce the thermal and solutal boundary layer thicknesses. The model demonstrates high predictive accuracy, with R2 = 99.9% and adjusted R2 = 98.9%. To ensure numerical accuracy and stability, a detailed grid independence test is conducted, confirming that the solution remains unchanged with further mesh refinement. This study provides new insights into the optimization and accurate modeling of MHD nanofluid flows in porous media, which are highly relevant to plasma applications, MEMS technologies, and advanced energy systems.