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

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&#8211
• Boltzmann law
• Curzon&#8211
• Alhborn engine
• maximum power output
• ecological function
• maximum power density