Critical design parameters on the performance prediction of converging nozzles are the geometric features and the operating conditions, which include the stagnant properties at the inlet, frictional and heat transfer behaviors on the nozzle wall; where the latter two are hard to handle together in compressible high-speed flows. This paper presents a recent computational model, that integrates the axisymmetric continuity, momentum and energy equations, to predict the combined effects of surface roughness and heat flux conditions on the flow and heat transfer characteristics of compressible flows through converging nozzles. To build a comprehensive overview, analyses are conducted at convergence half angles from 0 degrees to 9 degrees and inlet stagnation to back pressure ratios ranged from 1.01 to 2, covering both the un-choked and choked cases. Non-dimensional surface roughness and surface heat flux values are in the order of 0.0025-0.05 and 20-2000 kW/m(2) respectively. The influences of the model parameters on the nozzle performance are discussed through the streamwise variations of Mach number, shear stress, discharge coefficient and Nusselt number; to verify the validity of the model comparisons are made with the numerical and experimental data available in the literature.