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The flows of non-Newtonian fluid over upper horizontal surfaces of rockets, over bonnets of cars, and pointed surfaces of aircraft are of great importance to the experts in the field of space sciences, automobile construction, and aerodynamic industry where efficiency is dependent on the thickness of paraboloid of revolution, buoyancy, and autocatalysis. The purpose of this study is to present not only the nonlinear governing equation which models the transport phenomenon, but also to analyze the non-Newtonian Erying–Powell fluid flow within a thin layer formed on an object which is neither a perfect horizontal nor a vertical, and neither an inclined surface nor a cone/wedge. The governing equation suitable to model the transport phenomenon above for the case of equal diffusivity during quartic autocatalytic kind of chemical reaction was non-dimensionalized and solved numerically. The velocity of the flow along x − direction can be enhanced when thickness increases negligible but buoyancy forces increase significantly. The rate of increase in the velocity of the flow along the y − direction from the wall to the free stream is optimal when the thickness of the paraboloid of revolution is zero (objects with a uniform thickness) and buoyancy force is sufficiently large. The concentration of Erying–Powell fluid at the wall G (0) is a decreasing function of Prandtl number but an increasing property of Schmidt number. [ABSTRACT FROM AUTHOR]