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This paper presents a finite-time thermodynamic optimization based on three different optimization criteria: Maximum Power Output (MP), Maximum Efficient Power (MEP), and Maximum Power Density (MPD), for a simplified Curzon-Ahlborn engine that was first proposed by Agrawal. The results obtained for the MP are compared with those obtained using MEP and MPD criteria. The results show that when a Newton heat transfer law is used, the efficiency values of the engine working inthe MP regime are lowerthan the efficiency values ( &tau, ) obtained withthe MEP and MPD regimesfor all values of the parameter &tau, = T 2 / T 1 , where T 1 and T 2 are the hot and cold temperatures of the engine reservoirs ( T 2 &lt, T 1 ) , respectively. However, when a Dulong-Petit heat transfer law is used, the efficiency values of the engine working at MEP are larger than those obtained withthe MP and the MPD regimesfor all values of &tau, Notably, when 0 &lt, &tau, &lt, 0.68 , the efficiency values for the MP regime are larger than those obtained withthe MPD regime. Also, when 0.68 &lt, 1 , the efficiency values for the aforementioned regimes are similar. Importantly, the parameter &tau, plays a crucial role in the engine performance, providing guidance during the design of real power plants.

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.