Multi‐Objective RSM Optimization of Coupled Momentum–Microrotation–Thermosolutal Transport in Double‐Stratified MHD Micropolar Fluid Flow With Suction and Injection

ABSTRACT This study presents a coupled numerical–statistical investigation of steady, laminar, incompressible magnetohydrodynamic (MHD) free convective heat and mass transfer in an electrically conducting micropolar fluid over a semi‐infinite vertical plate, incorporating double stratification, wall suction/injection, and combined thermal–solutal buoyancy effects. Micropolar behavior is modeled using Eringen's theory, which accounts for both translational and microrotational dynamics. The governing equations are reduced through Lie group similarity transformations into coupled nonlinear ordinary differential equations. These are solved using the Keller–box scheme to accurately resolve near‐wall gradients and asymptotic far‐field behavior. Parametric analysis reveals that increasing the micropolar coupling parameter K enhances the peak velocity (10%) and microrotation (100%) while marginally reducing the thermal and solutal fields via stronger convective removal. The magnetic parameter M suppresses velocity (up to 18%) and microrotation (40%), thickens boundary layers, and lowers Nusselt and Sherwood numbers. Thermal stratification ε 1 and solutal stratification ε 2 diminish buoyancy, lowering velocity by over 40% and 15%–20%, respectively. Suction ( f 0 > 0) improves transport, increasing Nusselt and Sherwood numbers by 15%–30%, while injection ( f 0 < 0) produces the opposite effect. Response surface methodology (RSM) is applied for multi‐objective optimization of Nu x , Sh x , C f *, and g peak . Quadratic models ( R 2 > 0.99, Adeq Precision > 79) capture significant linear, interaction, and quadratic effects of K , M , and f 0 . The optimal solution, with overall desirability 0.751, occurs at K ≈ 1.60, M ≈ 0.96, and f 0 ≈ −0.27, yielding Nu x = 1.3047, Sh x = 1.1433, C f * = 0.5001, and g peak = 0.7087, all within the 95% prediction intervals. The integrated findings demonstrate that strategic tuning of micropolar coupling, magnetic field strength, and wall mass flux can enhance thermal and mass transport while controlling frictional and microrotational effects, offering valuable design guidance for MHD micropolar systems in energy, materials processing, and thermal management applications.