<p>This study offers a numerical assessment of Maxwell hybrid nanofluid flow around an unsteady vertical cylinder, integrating the principles of magnetohydrodynamics (MHD) and the Cattaneo–Christov model. The research elucidates their profound effects on the velocity, temperature, and concentration profiles by meticulously considering critical parameters such as Brownian motion, thermophoresis, variable thermal conductivity, and non-uniform heat generation/absorption. The transformation of governing partial differential equations (PDEs) into nonlinear coupled ordinary differential equations (ODEs) was achieved through the adept application of similarity transformations, with the resulting ODEs solved using the three-stage Lobatto IIIa method complemented by MATLAB’s bvp4c scheme. The inquiry rigorously investigates the influence of nanoparticle morphology on the fluid's resistance as it traverses the vertical cylinder, with particular emphasis on the rates of heat and mass transfer. The findings indicate that an increase in the Maxwell parameter markedly diminishes velocity, temperature, and concentration profiles due to enhanced fluid elasticity yet paradoxically augments the heat transfer rate. Additionally, elevated thermal and solutal relaxation times intensify temperature and concentration fields, while the solutal relaxation time explicitly reduces mass transfer efficiency. Crucially, the study highlights the superior thermal performance of lamina-shaped nanoparticles, while spherical nanoparticles are found to optimise shear stress and mass transfer. Notably, the Fe₃O₄-Cu Maxwell hybrid nanofluid exhibits a remarkable 38% enhancement in absolute skin friction, a 23% increase in the Nusselt number, and an average 3% improvement in the Sherwood number compared to the Cu Maxwell nanofluid. These insights offer invaluable contributions to optimising fluid behaviour and transport properties in advanced thermal systems.</p>