Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines

The efficiency at maximum power (EMP) of irreversible Carnot-like heat engines is investigated based on the weak endoreversible assumption and the phenomenologically irreversible thermodynamics. It is found that the weak endoreversible assumption can reduce to the conventional one for the heat engines working at maximum power. Carnot-like heat engines are classified into three types (linear, superlinear, and sublinear) according to different characteristics of constitutive relations between the heat transfer rate and the thermodynamic force. The EMPs of Carnot-like heat engines are proved to be bounded between $η_C/2$ and $η_C/(2-η_C)$ for the linear type, 0 and $η_C/(2-η_C)$ for the superlinear type, and $η_C/2$ and $η_C$ for the sublinear type, respectively, where $η_C$ is the Carnot efficiency.

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