Comparative analysis between 36 nm and 47 nm alumina–water nanofluid flows in the presence of Hall effect

White crystalline powder (aluminum oxide\(-\hbox {Al}_2\hbox {O}_3\)) and water are the products often formed after the heating of aluminum hydroxide. In this report, boundary layer flow of two different nanofluids (i.e., 36 nm \(\hbox {Al}_2\hbox {O}_3\)-water and 47 nm \(\hbox {Al}_2\hbox {O}_3\)-water) over an upper horizontal surface of a paraboloid of revolution under the influence of magnetic field is presented. The combined influence of magnetic field strength, electric current density, electric charge, electron collision time, and the mass of an electron in the flows are considered in the governing equations. Three-dimensional transport phenomenon was considered due to the influence of the Lorentz force \((\vec {F})\) along the z-direction as in the case of Hall currents. In this study, the dynamic viscosity and density of the nanofluids are assumed to vary with the volume fraction \(\phi\). The dimensional governing equations were non-dimensionalization and parametrization using similarity variables. The corresponding boundary value problem was transformed into initial value problem using the method of superposition and solved numerically using fourth-order Runge–Kutta method with shooting technique (RK4SM). Magnetic field parameter is seen to have dual effects on the cross-flow velocity profiles of both nanofluids. The maximum cross-flow velocity is attained within the fluid domain when 36 nm nanoparticles alumina is used. The cross-flow velocity gradient at the wall increases with magnetic field parameter (M) and also increases significantly with Hall parameter at larger values of M.