High-temperature reactors are employed to produce key intermediates within the chemical value chain such as synthesis gas and hydrogen cyanide. The drawback of those reactors is their high energy consumption. In practice, intensive simulations, know-how based on experience, as well as heuristics are used to optimize those reactors. Knowledge of the key transport phenomena that govern the reactor behavior, however, enables a systematic reactor design and optimization. Using a simplified but effective rigorous two-dimensional reactor model, modeling assumptions are scrutinized and key flow and heat transfer phenomena are identified using the case study of synthesis of hydrogen cyanide (HCN). Following the model validation, it is shown that buoyant forces are significant near the walls whereas turbulent flow is negligible. In contrast to estimates using dimensionless numbers both conduction accounting for 81.9% and radiation with 18.1% are significant in providing the energy to the reacting gas mixture inside the synthesis compartments. The results demonstrate the importance of a careful model selection for high-temperature reactors and enable a targeted reactor design optimization.