The growing need for reliable energy supply to enhance productivity in industrial and residential sectors underscores the importance of conserving solar energy. This can be achieved through measures such as optimizing solar collector coatings and optical heat processes. The environmental risks posed by fossil fuels, like coal and diesel, for electricity generation, further highlight the urgency of seeking alternative solutions. Solar energy has emerged as a highly promising option, capturing global attention for its potential to improve productivity and sustainability. The study focuses on examining aluminum alloy-titanium alloy/ethylene glycol hybrid nanofluid in the flow of non-Newtonian Oldroyd-B through a parabolic trough surface collector located in the solar water pumps (SWP). The Galerkin weighted residual method was utilized to solve the group of equations that describe momentum, energy, and entropy generation. The findings show that the hybrid nanofluid leads to better thermal radiative performance compared to the ordinary nanofluid. Therefore, the implications of these findings are substantial, particularly in the fields of thermal engineering and renewable energy. By offering insights into the efficient utilization of solar energy in water pumping systems and the reduction of entropy generation, this research has the potential to drive innovations that enhance the sustainability and performance of such systems.