A theoretical-numerical analysis based on the second law of thermodynamics is used to examine the propagation of laminar H(2)-enriched CH(4)-air flames. The analysis is based on computing the various entropy generation terms in a transient reacting flow field. A comprehensive, time-dependent computational model, which employs a detailed description of chemistry and transport, is used to simulate the transient ignition and flame propagation in this reacting flow field. Flames are ignited in a jet-mixing layer far downstream of the burner. Following ignition, a well-defined triple flame is formed that propagates upstream with nearly constant flame displacement speed along the stoichiometric mixture fraction line. As the flame approaches the burner, it transitions to a double flame, and subsequently to a burner-stabilized nonpremixed flame. The triple point exhibits the maximum entropy generation, indicating that this point is characterized by high chemical reactivity, as well as large temperature and mass fraction gradients. The volumetric entropy generation is the highest in the two premixed reaction zones, and the lowest in the nonpremixed reaction zone. In the premixed zones, the volumetric entropy generation due to chemical reaction is the highest, followed by heat conduction, and then mixing. The converse is true for the nonpremixed zone. However, the integrated entropy generation rate indicates that heat conduction is the major contributor, followed by chemical reactivity, and then mixing. As H(2) addition to methane fuel is increased, the integrated entropy generation increases primarily due to enhanced heat conduction and chemical reactivity. However, the contributions of heat conduction, chemical reactivity, and mixing to total entropy generation weakly depend on the fuel being burned. While the flame propagates upstream entropy generation increases and reaches a maximum when the flame exhibits a well-defined triple flame structure, and then decreases as the flame approaches the burner. The second law efficiency of the system remains nearly constant with H(2) addition, since the increased irreversibilities due to H(2) addition are compensated by the increase in the flow availability in the fuel blend. (c) 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.