The direct coupling of a thermally stabilized combustor and a steam generator has previously been shown by Strenger and Churchill to result in minimal concentrations of NO and CO and exceptionally high rates of heat transfer relative to conventional processes. Across the flame front, the Reynolds number falls from above to below 2100, leading to decaying turbulence and laminarization in the stream of hot burned gas. In the heat exchanger the cooling increases the Reynolds number and results in a sudden transition back to turbulent flow. The development and transition in the flow as well as the confinement are responsible for the high rates of heat transfer. The k-ϵ model has been adapted successfully to predict this complex behavior by using a controlled perturbation to trigger the transition at the experimentally observed point. The predictions not only agree well with experimental measurements of heat transfer but also provide insight into the fluid-mechanical and thermal behavior.