Energy conversion for conjugate conduction, convection and radiation analysis have been performed for free convection heat transfer with radiation effect of a steady laminar boundary-layer flow that pass a non-linearly flow field over extrusion stretching sheet by two kinds of boundary-layer conditions. The well-known Boussinesq approximation has been used to represent the buoyancy term adding to the governing equation. All of the important parameters m, Nr, Pr, G, Bi are represented the dominance of the non-linearly effect, radiation effect, free convection effect and conduction convection effect which have been presented in governing equations, respectively. The similarity transformation and the finite-difference method have been used to analyze the present problem. The results were shown that the free convection effect will be produced a larger heat transfer effect better than the forced convection. On heat conduction processing, the convection conduction number Ncc or free convection parameter G will be provided a good effect with a larger value. The results are shown by graphics, so that it is a physical multimedia technique features study also. (C) 2013 Elsevier Ltd. All rights reserved.