An optimization methodology for design of compact heat exchangers is formulated with consideration of heat transfer area reservation. The optimal design of 3D-printed high-temperature plate-fin heat exchangers are based on numerical simulation of fluid flow and heat transfer using OpenFoam. The design principles and simulation procedure are explained. The radiation heat transfer in compact heat exchangers is simulated and the effect is discussed. Along the fin height direction, the radiation heat transfer offers an additional path for heat transfer from the fins to the plates, parallel to the thermal conduction through the fins, therefore the total heat transfer rate can be enhanced.