This study explores how wall permeability affects unsteady Couette flow in a nanofluid with convective heating. We developed a flow model to analyze how different parameters influence velocity, temperature, and entropy generation, including the role of magnetic fields. The results show that higher nanoparticle concentration and Reynolds number boost velocity when pressure gradient, MHD effects, and nanofluid fraction stay fixed. Interestingly, Alumina-water nanofluid accelerates flow faster than Copper-water nanofluid. Meanwhile, increasing the Eckert number lowers the temperature profile, with copper-water nanofluid heating up more quickly than Alumina-water. Another key finding is that entropy generation grows with the Eckert number but behaves differently along the channel it raises near the lower wall but drops closer to the upper wall as nanoparticle concentration increases. These insights could help optimize nanofluid applications in thermal systems and magnetic-field-controlled flows.