# Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats

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## Abstract

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## 1. Introduction

## 2. Thermal Properties of CA Engine with Internal Irreversibilities

#### 2.1. Maximum Power Output (MP)

#### 2.2. Maximum Ecological Criterion (ME)

## 3. Steady-State Properties and Stability Analysis of the CA Engine

#### Dynamic Equations and Local Stability Analysis

## 4. Relaxation Times for NI and NIA Adiabats: A Comparative Analysis

## 5. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Diagram of Curzon and Ahlborn engine where both internal and external irreversibilities are considered; and (

**b**) the corresponding T-S diagram of the cycle.

**Figure 2.**(

**a**) Plot of maximum power output vs. $\tau $; and (

**b**) plot of efficiency at maximum power output vs. $\tau $. Solid lines correspond to instant adiabatic branches (IA), and dashed lines correspond to non-instantaneous adiabatic branches (NIA). Blue lines show $R=0.9$ and green lines show $R=0.6$.

**Figure 3.**(

**a**) Plot of the power at maximum ecological function vs. $\tau $; and (

**b**) plot of efficiency at maximum ecological function vs. $\tau $. Solid lines correspond to instantaneous adiabatic branches, and dashed lines to non-instantaneous adiabatic branches. Blue lines show $R=0.9$ and green lines show $R=0.6$.

**Figure 4.**Diagram of a Curzon–Ahlborn engine with internal irreversibilities (R), performing Carnot-like cycles between heat reservoirs ${T}_{H}$ and ${T}_{C}$. Exchange of heat (${J}_{1}$ and ${J}_{2}$) through thermal conductors is shown, for simplicity, with the same conductance value $\alpha $.

**Figure 5.**Plot of relaxation times ${t}_{1}$ and ${t}_{2}$, in units of $C/\alpha $, vs. $\tau $ for $R=0.9$ and $R=0.6$, under the ecological regime with NIA branches.

**Figure 7.**Plots of relaxation times ${t}_{1}$ and ${t}_{2}$, in units of $C/\alpha $, vs. $\tau $ for $R=0.9$. Solid lines correspond to IA and dashed lines to NIA adiabatic branches. (

**a**) Maximum power output regime; and (

**b**) maximum ecological function.

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**MDPI and ACS Style**

Paéz-Hernández, R.T.; Sánchez-Salas, N.; Chimal-Eguía, J.C.; Ladino-Luna, D.
Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats. *Entropy* **2017**, *19*, 632.
https://doi.org/10.3390/e19110632

**AMA Style**

Paéz-Hernández RT, Sánchez-Salas N, Chimal-Eguía JC, Ladino-Luna D.
Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats. *Entropy*. 2017; 19(11):632.
https://doi.org/10.3390/e19110632

**Chicago/Turabian Style**

Paéz-Hernández, Ricardo T., Norma Sánchez-Salas, Juan C. Chimal-Eguía, and Delfino Ladino-Luna.
2017. "Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats" *Entropy* 19, no. 11: 632.
https://doi.org/10.3390/e19110632