An unsteady magnetohydrodynamic boundary-layer model was developed for a Sutterby penta-hybrid nanofluid flowing over an extending catalytic surface, with particular emphasis on transport mechanisms relevant to wastewater treatment. Water was employed as the base fluid, while polystyrene, poly (acrylic acid), poly (acrylic acid)-block-polystyrene (PAA-b-PS), cerium oxide, and copper oxide were incorporated to represent complementary functionalities associated with colloidal stabilization, contaminant adsorption, photocatalytic degradation, and antimicrobial activity. The coupled conservation equations governing momentum, energy, and species concentration were formulated in Cartesian coordinates, together with a Poisson equation for the pressure field. Appropriate similarity transformations were subsequently introduced to reduce the governing partial differential equations to a coupled system of nonlinear ordinary differential equations. Surface-catalyzed contaminant degradation was represented through reaction boundary conditions parameterized by Damköhler numbers. The resulting boundary-value problem was solved numerically using the MATLAB bvp5c solver. The computed results demonstrated that the hydrodynamic, thermal, and concentration boundary layers were strongly governed by the combined effects of magnetic forcing, Sutterby rheological behavior, nanoparticle loading, unsteadiness, and reaction kinetics. The effects of the magnetic field, Sutterby rheological parameters, nanoparticle loading, reaction kinetics, and pressure variations on the velocity, temperature, and contaminant-concentration distributions were systematically evaluated. The numerical results demonstrated that the coupled effects of magnetohydrodynamic forcing, Sutterby rheology, and penta-hybrid composition substantially modified momentum, thermal, and mass transport within the boundary layer. In particular, appropriate combinations of the governing parameters were shown to intensify thermal and solutal transport and promote contaminant degradation at the catalytic surface. Pressure variations were additionally demonstrated to influence boundary-layer development and species transport, thereby affecting the predicted contaminant-removal characteristics. These findings establish a theoretical framework for understanding coupled magnetohydrodynamic, non-Newtonian, heat-transfer, and reactive mass-transfer phenomena in multifunctional nanofluid systems and provide potential guidance for the development and optimization of advanced wastewater-treatment processes.
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