A general property of endoreversible thermal engines

Abstract

In this work we propose that endoreversible Carnot–type heat engines have a general property independent of the heat transfer law used to describe heat exchanges between the working fluid and its thermal reservoirs. This property has to do with the so-called ecological function [F. Angulo–Brown, J. Appl. Phys. 69, 7465 (1991)]. According to this property, the efficiency at the maximum of the ecological function is the semisum of the Carnot and the maximum power efficiencies for any heat transfer law. This result is obtained by using the quasiparabolic behavior of power versus efficiency. From this property, we obtain a corollary over a general quantitative relation between the power (and also the entropy production) of both maximum power and maximum ecological regimes. We also discuss a criterion to find the best ecological function.

Thermoeconomic Optimization of an Irreversible Novikov Plant Model under Different Regimes of Performance

“…Now, we define two additional objective functions, one in terms of the so-called modified ecological function (E ≡ W− ∈ T L σ, with σ the rate of total entropy production of the Novikov model and ∈ a parameter which depends on the heat transfer law used in the Novikov model [19,20]). This function is a slight modification of the former ecological function [19], which preserves the original physical meaning of that function; that is, it represents a good trade-off between high power output and low dissipation.…”

“…Here, De Vos refers to the power production rate W of the Novikov plant model. Later, Barranco-Jiménez and Angulo-Brown [17,18] extended the De Vos thermoeconomic approach, but using the so-called ecological function [19,20], and they also showed that the economical efficiency under this regime of performance lies between the CA efficiency and the Carnot efficiency. In 2009, Barranco-Jiménez [21] studied the thermoeconomics of a nonendoreversible Novikov engine.…”

A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria

“…Alternatively, Yan [31] proposed that it might be more convenient to use E = P − T 0 σ, if the cold reservoir temperature T L is not equal to the environmental temperature T 0 , from the exergy analysis point of view. Ecological function shows two important properties [6,23,25]. Firstly, if a CA engine works in this regime, the thermal efficiency is shown as…”

“…Secondly, in this regime the CA engine produces around 80% of maximum power, while entropy production is reduced down to around 30% of the entropy produced in the maximum power regime. It has been shown that Equation (21), called the semi-sum property, is independent of the heat transfer law used in the process and is termed as a universal property for the endoreversible systems [6,23].…”

“…Several authors [1][2][3][4][5][6][7][8][9] have pointed out that endoreversible thermal cycle models working in maximum power conditions have an efficiency that strongly depends on the heat transfer law used to describe the heat fluxes between the working fluid and its surroundings. In fact, one of the most impressive results of the Curzon-Alhborn (CA) paper [10] was that the authors found very reasonable numerical results for the efficiency of certain power plants by means of a very simple formula for a Carnot-like finite time heat engine in a maximum power output regime but where a linear heat transfer law was used.…”