Magnetohydrodynamic enhancement of solar collector efficiency using Al ₂ O ₃ –Cu hybrid nanofluids with variable thermal conductivity

Flat plate solar collectors (FPSCs) are valuable for domestic water heating and industrial applications that require low to moderate temperatures. However, their efficiency is often hampered by the low thermal conductivity of conventional working fluids. This study aims to enhance the thermal performance of flat plate solar collectors through the use of hybrid nanofluids under the influence of magnetohydrodynamics (MHD). The governing equations are nondimensionalized, and analytical solutions for the dimensionless momentum and absorber plate energy equations are obtained. The nonlinear dimensionless partial differential thermal energy equation was numerically solved using the bivariate spectral weighted residual method (BSWRM). Our findings indicate that regular nanofluid increases the FPSC heat transfer rate by 4.45%, while hybrid nanofluid increases it by 7.32%. Additionally, the collector efficiency reaches up to 73.15%, demonstrating the effectiveness of hybrid nanofluids under MHD influences. These results offer valuable insights for the design of advanced solar thermal systems.