In the present work, a numerical analysis has been done to calculate the heat and mass transfer during boiling based on the two-phase annular single component refrigerants in a vertical pipe. The conservation equations of mass, momentum, energy and turbulence models of k-e for each phase have been solved through a numerical finite volume method. A specific wave model has been used for considering the effects of interfacial wavy instabilities in the transport phenomena. The numerical results of heat transfer for R–113 show a good agreement with the available experimental results reported by the others investigators. To compare the R-12 with its suggested alternative, R-134a, the numerical results have been achieved at the same boundary conditions for both of them. Results show that the behaviors of these refrigerants are similar. In addition, the heat transfer coefficient in the case of R-134a is greater than that of R-12, nearly 30 percent.