Efficiency at arbitrary power for the Curzon-Ahlborn heat engine in linear and nonlinear heat transfer processes

Abstract

The optimal performance of heat engine is an important issue in thermodynamics, but the heat transfer between the working medium and two heat reservoirs induces the irreversibility during the operation of heat engine. Based on two important parameters introduced in this paper(namely, the power gain and the efficiency gain), for heat engine operating in the linear and nonlinear heat transfer processes, the formula for the efficiency at arbitrary power is achieved in terms of a simplified Curzon-Ahlborn heat engine model and the componendo and dividendo rule. The features of heat engine at arbitrary power output are also discussed in detail based on the numerical calculations. It is indicated that the parameter as a function of the power gain P contains two branches:the efficiency shows the monotonous variation on the first branch (the favorable case); the efficiency exhibits the non-monotonous characteristics and has the maximum value on the second branch(the unfavorable case). The working region of the heat engine is reduced as the heat transfer exponent increases, which results from the radiative contribution in the nonlinear heat transfer process. For the first branch, the contour-line plot of versus TL/TH and P clearly demonstrates that has the decreasing trend with increasing TL/TH and|P|; for the second branch, monotonically deceases as TL/TH increases, but shows the non-monotonic behaviors as|P|increases. The efficiency has the maximum value in the region where TL/TH and|P|have the small values, and the working regime of heat engines in the nonlinear heat transfer process is relatively small due to the complexity of the nonlinear heat transfer process. The curves of the efficiency in two heat transfer processes are loop-shaped, when|P| 0 and|P| 1, the curves of ~P in two heat transfer processes are same. But in other regimes, the efficiency of the heat engine with the linear heat transfer process is bigger than in the nonlinear heat transfer process. Furthermore, it is found that a considerably larger efficiency can be obtained when heat engine working close to the maximum power. This implies that there exists the trade-off working point where the heat engine can perform the most effective heat-work conversion. In addition, the curves of the power gain vs. the efficiency gain also display the loop-shaped characteristics, but there is the weak difference on the second branch. Our results are very conducive to understanding the optimal performance of heat engines in different heat transfer processes.