# Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model

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## Abstract

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**PACS**05.70. Ln, 44.40.+a89., 65.Gh

## 1. Introduction

## 2. Theoretical Model

**Figure 2.**Variation of the thermoeconomic objective function ${\overline{F}}_{mp}$ respect to $\theta =\frac{{T}_{X}}{{T}_{H}}$, for (a) different values of the parameter R with ${A}_{R}=1$, and for (b) several values of ${A}_{R}$ with $R=1$.

**Figure 3.**Variation of the thermoeconomic objective function ${\overline{F}}_{E}$ respect to $\theta =\frac{{T}_{X}}{{T}_{H}}$, for (a) different values of the parameter R with ${A}_{R}=1$, and for (b) several values of ${A}_{R}$ with $R=0.8$.

**Figure 4.**Comparison of both the thermoeconomic objective functions, ${\overline{F}}_{mp}$ and ${\overline{F}}_{E}$, respect to $\theta =\frac{{T}_{X}}{{T}_{H}}$, for (a) different values of the parameter R and for (b) several values of ${A}_{R}$.

## 3. Numerical Results and Discussion

**Figure 5.**Variations of the dimensionless thermoeconomic objective function ${\overline{F}}_{mp}$, with respect to thermal efficiency for various R (a), β (b), ${A}_{R}$ (c) and f (d) values, respectively. ($\xi =0.02$).

**Figure 6.**Variations of the dimensionless thermoeconomic objective function ${\overline{F}}_{E}$, with respect to thermal efficiency for various R (a), β (b), ${A}_{R}$ (c) and f (d) values, respectively. ($\xi =0.02$).

**Figure 7.**Variation of the two maximum thermoeconomic objective functions with respect to ${A}_{R}$ for: (a) two values of R with $\tau =4$, and (b) for several values of τ with $R=0.8$. In both cases, $\beta =1$, $f=0.7$ and $\xi =0.02$.

**Figure 8.**Optimal thermal efficiencies vs. ${A}_{R}$ for the two regimes. (a) For three values of R with $\tau =4$ and (b) For three values of τ with $R=0.8$. In both cases, $\beta =1$, $f=0.7$ and $\xi =0.02$ (these optimal thermal efficiencies were obtained by substituting ${\theta}^{*}$ in Equation (18)).

**Figure 9.**Optimal thermal efficiencies vs. ξ at maximum ecological regime, for four values of R with $\tau =2.46$, ${A}_{R}=1$ and $\beta =4.1373$ for comparison with the values reported by Wu [30].

## 4. Conclusions

## Acknowledgements

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**MDPI and ACS Style**

Barranco-Jimenez, M.A.; Sanchez-Salas, N.; Angulo-Brown, F.
Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model. *Entropy* **2011**, *13*, 171-183.
https://doi.org/10.3390/e13010171

**AMA Style**

Barranco-Jimenez MA, Sanchez-Salas N, Angulo-Brown F.
Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model. *Entropy*. 2011; 13(1):171-183.
https://doi.org/10.3390/e13010171

**Chicago/Turabian Style**

Barranco-Jimenez, Marco A., Norma Sanchez-Salas, and Fernando Angulo-Brown.
2011. "Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model" *Entropy* 13, no. 1: 171-183.
https://doi.org/10.3390/e13010171