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Entropy 2012, 14(12), 2611-2625; doi:10.3390/e14122611
Article

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

1
, 2,*  and 3
1 Centro de Investigación en Computación del IPN., Av. Juan de Dios Bátiz s/n U.P. Zacatenco CP 07738, DF, Mexico 2 Departamento de Física, Escuela Superior de Física y Matemáticas del IPN, Edif. 9 U.P. Zacatenco, CP 07738, DF, Mexico 3 Departamento de Formación Básica, Escuela Superior de Cómputo del IPN, Av. Miguel Bernard s/n Esq. Juan de Dios Bátiz, U.P. Zacatenco, DF 07738, Mexico
* Author to whom correspondence should be addressed.
Received: 16 October 2012 / Revised: 5 December 2012 / Accepted: 5 December 2012 / Published: 17 December 2012
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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.
Keywords: variational approach; Stefan–Boltzmann law; Curzon–Alhborn engine; maximum power output; ecological function; maximum power density variational approach; Stefan–Boltzmann law; Curzon–Alhborn engine; maximum power output; ecological function; maximum power density
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Chimal-Eguía, J.C.; Sánchez-Salas, N.; Barranco-Jiménez, M.A. A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria. Entropy 2012, 14, 2611-2625.

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