关键词: 内可逆热机, 线性唯象传热定律, 最优构型, 最优控制

Abstract: Optimal configuration of an endoreversible heat engine with fixed duration and linear phenomenological heat transfer law is determined. The optimal cycle that maximizes the power output of the engine is obtained by using optimal control theory. It is shown that the optimal cycle has six branches including two isothermal branches, four maximum power branches, and no adiabatic branches. The interval of each branch and the temperature of heat reservoirs and working fluid are obtained. The maximum power and the corresponding efficiency of the engine are obtained. The calculation results show that the process time of the maximum power branch, the maximum power output, the input energy and the efficiency of the cycle decrease with the decrease of the heat source tem-perature. The process time of the maximum power branch and the input energy increase and the maximum power output and the efficiency of the cycle decrease with the decrease of the change rate of cylinder volume. The process time of the maximum power branch, the maximum power output and the input energy decrease and the efficiency of the cycle increase with the decrease of the heat conductivity. The obtained results are compared with those obtained with the Newton’s heat transfer law. The compared results show that the optimal cycles with two heat transfer laws both contain two isothermal branches and four maximum power branches, and no adiabatic branches. For two different heat transfer laws, the temperature of their isothermal branches is different, and the process paths of four maximum power branches are different as well. The process times are different for different branches under two different optimal configurations, the maximum work outputs, the required input energies and the thermal efficiencies of the cycles are different.

Key words: Endoreversible heat engine, Linear phenomenological heat transfer law, Optimal configuration, Optimal control