Solar energy is a clean, abundant, and renewable resource with enormous potential that extends beyond just providing energy access. It plays a significant role in minimizing greenhouse gas emissions. With approximately \(4\times 10^{15}\) MW of solar energy reaching the Earth, its potential far surpasses estimated global utility demands by a factor of 200. This study presents a comprehensive numerical investigation of unsteady magnetohydrodynamic (MHD) flow of a Cu–TiO2/water hybrid nanofluid in a parabolic thermal solar collector. The fluid properties such as thermal conductivity and dynamic viscosity, are considered to vary linearly with fluid temperature. A variable magnetic field is applied. The governing partial differential equations were transformed to ordinary differential equations using similarity transformation. The resulting first-order system of ODEs was then solved numerically using the collocation method which was implemented in MATLAB’s bvp4c solver. The profiles of various flow variables were determined, and the impact of different flow parameters on wall shear stress, heat and mass fluxes were investigated by computing the skin friction coefficient, Nusselt number, and Sherwood number, respectively. Key findings include: increasing Reynolds number by 28.6% led to a 12% increase in temperature profiles; increasing mass Grashof number by 60% led to a 10% decrease in temperature profiles; Schmidt number and Soret number positively influenced temperature profiles; the Joule heating parameter had a negative effect on temperature profiles; skin friction coefficient decreased by 15% with a 15% increase in Reynolds number; Nusselt number increased by 6% with a 20% increase in magnetic Reynolds number and by 10% with a 15% increase in Schmidt number; and Sherwood number increased by 10% with a 15% increase in Schmidt number. These findings provide valuable insights into the behavior of hybrid nanofluids in solar energy applications and can be used to optimize the design and operation of solar collectors for enhanced efficiency and sustainability.
