A mathematical analysis to investigate the non-linear, isothermal, steady state, free convection boundary layer flows of an incompressible third-grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation, and heat generation/absorption. The transformed conservation equations for linear momentum, heat, and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finitedifference Keller-box method. The numerical code is validated with the previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and lowdensity polymer material processing. © The Brazilian Society of Mechanical Sciences and Engineering 2018.