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The study of 2D non-Newtonian Sutterby nanofluid flow under the effects of magneto-hydro-dynamics (MHD) over the paraboloid surface is investigated here. The upper part of aircraft, submarine, bullet, and car's bonnet are some samples of the paraboloid surface. The movement of these things depends in boundary layer which is formed within the space on it. The reaction between catalyst at the surface and Sutterby nanofluid yields substantial temperature differences consequently made buoyancy-driven flow in the boundary layer region. First-order activation energy is assumed to model the reaction on the catalyst surface that is sited on the paraboloid surface which starts the free convection. The main prevailing equations are reduced by using appropriate dimensionless variables. The numerical solutions of the dimensionless determining equations are achieved by adopting the Runge-Kutta Fehlberg ("RKF") method. The graphical outcomes of the velocity field depend on the dimensionless quantities such as the Deborah number De ,Hartmann number Ha , temperature and concentration-dependent buoyancy parameters i.e. (G t , G s). The contribution of the thermophoresis coefficient Nt , Prandtl number Pr and Brownian motion parameter Nb is examined for the temperature field. Also the effects of Schmidt number Sc are analyzed for the concentration field. We found that both Deborah number and Hartmann number (De , Ha) provide a decrease in the velocity field. The extreme velocity of the fluid is calculated when the fluid flow is categorized as Newtonian fluid i.e. (De = 0). The numerical outcomes of skin friction, local mass transfer rate and local heat transfer rate are also calculated. A detailed comparison with the numerical method is also given to validate the current results. [ABSTRACT FROM AUTHOR]