Two‐Phase Nanofluid Flow in a Non‐Newtonian Model Past a Deformable Sheet With Magnetized Environmental Effects: Statistical Modeling and ANOVA Analysis

ABSTRACT This paper presents a comprehensive numerical analysis of magnetohydrodynamic (MHD) Casson nanofluid movement over a permeable, linearly stretching sheet, integrating the contributions of non‐uniform heat generation or absorption and chemical interaction. The mathematical model integrates the non‐Newtonian attribute of Casson fluids and enhanced thermal conductivity due to nanoparticles. A uniform transverse magnetic field is imposed, and wall permeability is considered to simulate suction or injection. Through similarity variables, the primary nonlinear partial differential equations are reduced to a system of ordinary differential equations, which are then solved numerically. The influences of various physical parameters including the Casson fluid parameter, magnetic field strength, heat source/sink coefficient, and chemical reaction rate on velocity, microrotation, temperature, and concentration profiles are thoroughly investigated. The study reveals that magnetic damping, viscous resistance, and stretching elevate Casson nanofluid motion and thermal transport, with Brownian motion intensifying internal energy and thermal boundary thickness. Increasing chemical consumption actively removes flow species. Using response surface methodology (RSM), model accuracy and significance are assessed through analysis of variance (ANOVA) for different parameters. Using RSM and ANOVA, model accuracy is validated through regression metrics.