This article demonstrates the examination of magnetic nanofluid hydrothermal pattern on a sheet, including thermal radiation. Runge–Kutta method is applied to achieve solutions of ordinary differential equations acquired from a resemblance solution. Considering the influences of Brownian movement, Koo–Kleinstreuer–Li equation is utilized for simulating the CuO–water's features. The impact of significant factors including magnetic factors, speed ratio factors, temperature index, radiation and nanofluid mass fraction on hydrothermal pattern is expressed. The results confirm that the factors of surface friction are increased with growing magnetic factors, whereas they are decreased with growing speed ratio factor. It is also found that there is a direct dependency among Nu and the temperature index factors and the speed ratio, while it has a reverse correlation with the radiation as well as magnetic factors.