Maximum power processes for multi-source endoreversible heat engines

The maximum power processes of multi-source endoreversible engines with stationary temperature reservoirs are investigated. We prove that the optimal solution is always time independent with a single hot and a cold engine contact temperature. The heat reservoirs fall into three groups: the hot reservoirs which are connected at all times for heat delivery, the cold reservoirs which are connected at all times for heat drain, and possibly a group of reservoirs at intermediate temperatures which are unused. This phenomenon is demonstrated for a three-source system. We find that for a commonly used class of heat transfer functions, including Newtonian, Fourier, and radiative heat transport, the efficiencies at maximum power are the same as for two-reservoir engines with appropriately chosen properties.