A computational investigation of the effects of external burning on the performance of single expansion ramp nozzles (SERN) operating at transonic speeds is presented. The study focuses on the effects of external heat addition and introduces a simplified injection and mixing model based on a control volume analysis. This simplified model permits parametric and scaling studies that would have been impossible to conduct with a detailed CFD analysis. The CFD model is validated by comparing the computed pressure distribution and thrust forces, for several nozzle configurations, with experimental data. Specific impulse calculations are also presented which indicate that external burning performance can be superior to other methods of thrust augmentation at transonic speeds. The effects of injection fuel pressure and nozzle pressure ratio on the performance of SERN nozzles with external burning are described. The results show trends similar to those reported in the experimental study, and provide additional information that complements the experimental data, improving our understanding of external burning flowfields. A study of the effect of scale is also presented. The results indicate that combustion kinetics do not make the flowfield sensitive to scale.