In this thesis, numerical simulations were used to investigate forced convection heat transfer through channels with complex internal structures fabricated by rapid prototyping. Numerical investigations of heat conduction through the solid phase of four different designs, flow through them and forced convection heat transfer were conducted. Numerical simulations, providing full flow field information, allow a detailed discussion of flow phenomena and temperature distribution inside the heat exchanger channels. The investigation focuses on understanding the complex interplay between heat conduction in the complex internal open-cell structures and heat transfer by forced convection. This leads to insight on the impact of the open-cell structures on the pressure drop over unit length, fluid mixing and heat transfer.The result of this insight takes the form of concrete design criteria for certain objective functions related to pressure drop or heat transfer.