Numerical investigation of electromagnetic [Cu + TiO₂/H₂O]^h hybrid nanofluid flow with solar radiation over an exponential stretching surface

Abstract The idea of a hybrid nanofluid (HNF) has sparked curiosity among many scientists because of its ability to enhance thermal characteristics, leading to elevated rates of heat transfer (HT). These HNFs are utilized in various engineering and industrial settings, such as electronics cooling, manufacturing, naval structures, biomedical applications, and drug delivery. The current study investigates the analysis of irreversibility in EMHD [Cu + TiO 2 /H 2 O] h flow over a stretching sheet with radiation and viscous dissipation. The governing PDEs are converted into ODEs using similarity variables. These ODEs are then solved using the RKF method along with a shooting technique. The effects of different physical parameters on the velocity and temperature distributions of the HNF, as well as on HT and surface drag force, are thoroughly examined and presented in graphs. The velocity of [TiO 2 /water] n flow declines as the magnetic field strength rises, but it rises with greater electric field values for [Cu + TiO 2 /water] h . The temperature of the [Cu + TiO 2 /water] h increases with elevated levels of radiation, Eckert number, and heat generation strength. Higher Reynolds and Brinkman numbers result in a rise in entropy generation for [Cu + TiO 2 /H 2 O] h , whereas the Bejan number decreases to the same extent. The HT rate in [Cu + TiO 2 /H 2 O] h increases by 3.05% as the Eckert number rises, while it drops by 4.01% when there is significant thermal radiation. Skin friction reduces by 3.21% in [TiO 2 /water] n as the electric field strength increases, whereas it decreases by 4.05% with an increase in magnetic field strength. These discoveries offer valuable perspectives on furthering the utilization of HNFs in engineering and industrial operations.