The application of nanofluids has exploded in recent decades to improve the local number, mean Nusselt number, and rate of heat transfer. However, boundary layer equations of nanofluid across a flat plate with radiation have not been studied, and therefore the present paper studies them mathematically for the first time. For water-based copper and aluminium oxide nanofluids, a similarity solution is presented in this study, and the subsequent system of the ordinary differential equation (ODE) is numerically solved by the Runge-Kutta method in MATLAB. Two different hydraulic boundary conditions are used in the simulations. In the first, the flow across a moving plate and the direction of the flow are analyzed, while in the second, the flow over a nonlinearly moving plate in a still fluid is investigated. The nanoparticle’s boundary layer thickness is found less than the thermal and hydraulics boundary layers. The local Nusselt number and friction factor of both the nanofluids are calculated and compared with the base fluid. The results demonstrate that the friction coefficient is high and the Nusselt number is low in the high volume fraction of nanoparticles. Results demonstrate that the friction factor for water-aluminium oxide is 16%greater than that for the water-CuO whereas the local Nusselt number for water-aluminium oxide is only 5% more than that for the water-CuO
