In the presence of convective heat transfer and melting conditions, this work examines the thermal and fluid dynamics of two different nanofluids over a curved, extending sheet under the effects of an exponential heat source, radiation, and an electric field. In this study, the nanofluid contains two types of nanoparticles, \(\textit{MnZnFe}_{2} O_{4}\) and \(\textit{NiZnFe}_{2} O_{4}\) , with water as the base fluid. Similarity transformations reformulate partial differential equations into coupled ordinary differential equations, which are then numerically solved using the combined shooting and 4th-order Runge–Kutta (RK) methods. The study examines how critical parameters influence the velocity and temperature distributions of nanofluids. The variations in thermal conductivity and flow behavior between the two nanofluids are highlighted through comparative analysis. Results reveal that stronger magnetic fields suppress fluid motion, while increased thermal radiation enhances heat transfer. The exponential heat source significantly amplifies temperature gradients, and the melting parameter plays a critical role in altering flow behavior near the surface. Increasing the Eckert number from 0.01 to 0.5 reduces the Nusselt number by approximately 44%, while increasing the Biot number from 0.2 to 0.5 enhances heat transfer by nearly 105%. These results provide valuable insights for optimizing thermal systems using nanofluids under complex boundary conditions, with potential applications in materials processing, energy systems, and advanced heat management technologies. This study demonstrates the effectiveness of the ‘response surface methodology’ (RSM) framework and numerical methods in resolving complex heat transfer issues.
