A non-linear approximation for natural convection boundary layer flow near a vertical wall under the influence of thermal radiation is analysed. The governing equation comprises of the set of non-linear partial differential equations is transformed into ordinary differential equations via the similarity transformation. The final dimensionless equations are solved numerically using the Runge Kutta Ferlberg fourth-fifth order (RKF45) method. The effects of the embedded parameters affecting the flow formation, temperature distribution, Nusselt number and the Skin friction are thoroughly examined. It is found that the temperature gradient is proportional to the thermal radiation near the plate whereas inversely proportional to the temperature gradient far away from the plate. The flow formation in the boundary enhanced near the vertical wall with thermal radiation parameter increase but remain constant in the free stream region. The rate of heat transfer enhanced with the thermal radiation whereas decreases with other embedded parameters under consideration.