Abstract
This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT). Using an endoreversible Curzon–Ahlborn (CA) heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan–Boltzmann law) was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the Müser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the Müser engine performance were obtained.
Highlights
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
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
Later Ares de Parga et al [23,24] used the variational approach to study a CA engine under both maximum power and maximum ecological function conditions [25]. They analyzed the performance of the CA engine with a nonlinear heat transfer law, obtaining results consistent with those previously obtained by means of other procedures
Summary
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. Later Ares de Parga et al [23,24] used the variational approach to study a CA engine under both maximum power and maximum ecological function conditions [25]. They analyzed the performance of the CA engine with a nonlinear heat transfer law (the Dulong and Petit law [24]), obtaining results consistent with those previously obtained by means of other procedures. A variational approach was used to study a CA engine for three different criteria: maximum power output, ecological function and maximum power density, where a heat transfer law different from previous studies was used.
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