This study investigates the heat and mass transmission behavior in an unsteady magnetohydrodynamic (MHD) movement of nanofluids over an inclined permeable surface, with applications in enhancing thermal management systems such as automotive cooling and industrial heat exchangers. The model specifically examines the consequence of thermal diffusion (Soret effect) and buoyant forces on Cu and TiO2 nanoparticles dispersed in engine oil. The governing equations, comprising velocity, energy, and concentration equations, are recast into nonlinear ODEs manipulating similitude adaptations. These ODEs are then solved through a standard perturbation method under appropriate boundary conditions. The key findings indicate that enhancing thermal radiation diminishes the velocity and temperature profiles, while raising chemical reaction rates decrease concentration levels. Additionally, higher Soret parameter values are associated with increased velocity and concentration. Quantitatively, TiO2-engine oil nanofluids exhibit a 15% higher velocity compared to Cu-engine oil nanofluids, highlighting the superior performance of TiO2 in dynamic thermal systems. Furthermore, numerical outcomes for the local skin contention, Nusselt numeral, and Sherwood digit are tabulated to illustrate the consequence of material properties. The outcomes of this study are particularly beneficial in optimizing the design of heat exchangers, improving fuel efficiency in automotive engines, and enhancing industrial processes where precise thermal control is critical.