This study considers numerical simulations of the combustions of hydrogen and various hydrocarbons with air, including 21% oxygen and 79% nitrogen, in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The combustion is simulated for the fuel mass flow rates providing the same heat transfer rate (Q) to the combustion chamber in the each fuel case. The effects of Q (only in the case of H-2 fuel) and equivalence ratio (phi) on the combustion and entropy generation rate are investigated for the different Qs (from 5,000 to 10,000 W) and phi s (from 0.5 to 1.0). The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to numerically calculate the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the maximum reaction rates decrease with the increase of phi (or the decrease of lambda). The large positive and negative temperature gradients occur in the axial direction, nonetheless, the increase of phi significantly reduces them. The calculations bring out also that with the increase of phi from 0.5 to 1.0, the volumetric local entropy generation rates decrease about 4% and that the merit numbers increase about 16%.