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The primary focus of this study is to tackle a critical industry issue concerning energy inefficiency. This is achieved through an investigation into enhancing heat transfer in solar radiation phenomena on a curved surface. The problem formulation of governing equations includes the combined effects of thermal relaxation, Newtonian heating, radiation mechanism, and Darcy-Forchheimer to enhance the uniqueness of the model. This research employs the Cattaneo–Christov heat theory model to investigate the thermal flux via utilizing the above-mentioned phenomenon with a purpose of advancing thermal technology. A mixture of silicon dioxide (SiO_2)\ and Molybdenum disulfide (MoS_2) is considered for the nanoparticle’s thermal propagation in base solvent propylene glycol. The simulation of the modeled equations is solved using the Shifted Legendre collocation scheme (SLCS). The findings show that …