Ecological optimization for general heat engines

• The heat exchanging processes are non-isothermal.
• The internal dissipations are considered.
• The optimization is conducted under the ecological criterion.
• General upper and lower bounds of the optimal efficiency have been deduced.
• The efficiency bounds of different real heat engines have been proposed.

We conducted an analysis of efficiency and its bounds for general heat engines under the maximum ecological criterion. For generality, both nonisothermal heat-exchanging processes and internal dissipation were taken into consideration. When the product of the internal dissipation and the heat capacity ratio is one, the efficiency under the maximum ecological criterion is the same as that of the irreversible Carnot model. However, the efficiencies have different physical meanings and optimization spaces. Furthermore, the efficiency is independent of the time it takes to complete each process and the heat conductance. For other situations, numerical calculations were conducted to investigate the parameters’ effects on optimal efficiency. When the dimensionless contact times approach zero, the irreversible Carnot model is recovered. The general upper and lower bounds of optimal efficiency are obtained by applying the asymmetric heat capacity ratio limits when the dimensionless contact times approach infinity. In addition, the efficiency of general endoreversible heat engines was investigated. The efficiency bounds of different real-life heat engines under the maximum ecological criterion are proposed.