Magnetic nanofluids (MNFs) have recently piqued the interest of many experts because of their capability and significance in various real applications. Hence, in this study, we want to numerically highlight the influence of convective boundary conditions and radiation on the magnetic nanofluids (MNFs) flowing past a permeable moving plate. The governing flow model in partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) using suitable similarity variables. The ODEs are solved by implementing the built-in solver in Matlab called bvp4c. The relevant specification of the parameters led to the execution of two numerical outputs. We have finalized the investigation by incorporating a stability analysis to confirm the stability qualities conveyed by the outputs. The stability analysis has supported our initial presumption that only one of the outputs is stable. In this present study, the thermal performance between cobalt ferrite nanofluid and manganese-zinc ferrite nanofluid is compared, and it appears that cobalt ferrite nanofluid has a slightly better performance in heat transportation compared to manganese-zinc ferrite nanofluid. We also considered a higher amount of thermal radiation and Biot number to scrutinize the heat transfer performance of MNF. We found that the immense value of these parameters effectively improves the heat transfer rate. The skin friction coefficient is magnified when the plate moves towards the slit, but the heat transportation performance is higher when the plate moves out from the slit. This research is significant because it simulates the thermal performance of MNFs when greater radiation and convective heat are applied to a moving plate; therefore, it could be used as a guide for actual applications that involve the heat transfer process.