# Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes

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## Abstract

**:**

## 1. Introduction

## 2. Thermoeconomic Optimization of a Curzon-Ahlborn Engine Model at Different Regimes of Performance

**Figure 2.**Profit functions for $\beta =0$ and $\beta =5$ versus η with $R=1$ and $\mathsf{\tau}=0.5$.

**Figure 3.**The steady-state efficiencies working under maximum power output (${\overline{\eta}}_{MP}$), maximum-efficient power (${\overline{\eta}}_{EP}$) and maximum ecological function (${\overline{\eta}}_{E}$) conditions.

## 3. Local Stability Analysis

**Figure 4.**Plot of relaxation times under maximum power conditions versus τ for (

**a**) several values of the endorreversibility parameter and a value of the fractional fuel cost and (

**b**) for several values of the fractional fuel cost f in the endoreversible case (R = 1).

**Figure 5.**Plot of relaxation times under maximum efficient power versus τ for (

**a**) several values of the endorreversibility parameter and a value of the fractional fuel cost and (

**b**) for several values of the fractional fuel cost f in the endoreversible case (R = 1).

**Figure 6.**Plot of relaxation times under maximum ecological function conditions versus τ for (

**a**) several values of the endorreversibility parameter and a value of the fractional fuel cost and (

**b**) for several values of the fractional fuel cost f in the endoreversible case (R = 1).

**Figure 7.**Relaxation times in the endoreversible case ($R=1$) versus fractional fuel cost for several values of τ for (

**a**) Maximum efficient power conditions and (

**b**) Maximum ecological function.

**Figure 8.**Ratio of the relaxation times versus τ for a value of the fractional fuel cost and several values of the parameter R (cases (

**a**), (

**c**) and (

**e**)), and for the endoreversible case $R=1$, for different values of the fractional fuel cost, (cases (

**b**), (

**d**) and (

**f**)).

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix

#### A. Linearization and Stability Analysis

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**MDPI and ACS Style**

Barranco-Jiménez, M.A.; Sánchez-Salas, N.; Reyes-Ramírez, I.
Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes. *Entropy* **2015**, *17*, 8019-8030.
https://doi.org/10.3390/e17127860

**AMA Style**

Barranco-Jiménez MA, Sánchez-Salas N, Reyes-Ramírez I.
Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes. *Entropy*. 2015; 17(12):8019-8030.
https://doi.org/10.3390/e17127860

**Chicago/Turabian Style**

Barranco-Jiménez, Marco A., Norma Sánchez-Salas, and Israel Reyes-Ramírez.
2015. "Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes" *Entropy* 17, no. 12: 8019-8030.
https://doi.org/10.3390/e17127860