In this study, we present an innovative and detailed analysis of the motion of a binary nanofluid, specifically copper (Cu - EO) and Magnetite (Fe3O4 - EO), in a porous medium under solar radiation. Our research is driven by the potential to significantly enhance the thermal performance of a Parabolic Trough Solar Collector (PTSC) using a binary nanofluid. The boundary conditions, partial differential restrictions, and the governing PDEs are transformed into the ODEs system with appropriate similarity transformations. The finite element method (FEM) and semi-analytical technique memad Akbari-Ganji's Method (AGM) are used to solve the approximate solutions of ODEs. The findings of evaluating Copper (Cu - EO) and Magnetite (Fe3O4 - EO) were the two different nanofluids based on engine oil that were presented. Furthermore, the model's overall entropy variations are enhanced using Reynolds. Moreover, our study contributes to understanding fluidity and viscosity alterations in such systems. We use the Brinkman number to observe these alterations. We reveal that the thermal efficiency of (Cu - EO) is lower than (Fe3O4 - EO) by a range of 0.005–0.6. This indicates a substantial enhancement in the thermal performance of the PTSC.