# A Simple Thermodynamic Model of the Internal Convective Zone of the Earth

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## Abstract

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## 1. Introduction

## 2. Finite-Time Thermodynamics and the Gordon-Zarmi Convective Model

#### Atmospheric Convection

## 3. GZ Model Applied to the Convective Zone of the Earth

#### 3.1. Maximum Power Regime

#### 3.2. Ecological Function Regime

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Scheme of a simplified solar-driven heat engine (taken from Reference [7]).

**Figure 4.**Schematic diagram of the energy fluxes present in the first internal convective cell. ${T}_{1}$ = 4500 ${}^{\xb0}$C is taken as the temperature of the first isothermal layer (${T}_{2}$ = 1500 ${}^{\xb0}$C is taken as the cold reservoir temperature, and ${T}_{1w}$ and ${T}_{2w}$ are the internal temperatures for this endoreversible model of convective cells.

**Figure 5.**Diagram of the first and second convective layers of the Earth’s mantle for the case of maximum Power. The temperature intervals ${T}_{1}-{T}_{1w}$, ${T}_{2w}-{T}_{1w}^{\prime}$ and ${T}_{2w}^{\prime}-{T}_{2}$ approximately correspond to the D-layer, the Repetti transition zone and the 410 km - discontinuity, respectively.

**Figure 6.**Diagram of the first and second convective layers of the Earth’s mantle for the case of maximum ecological function. The temperature intervals ${T}_{1}-{T}_{1w}$, ${T}_{2w}-{T}_{1w}^{\prime}$ and ${T}_{2w}^{\prime}-{T}_{2}$ are also not very far from those corresponding to the discontinuities mentioned in Figure 5.

**Table 1.**Numerical results for the two convective layers between the outer core and the lower limit of the crust of the Earth at maximum power conditions.

n | ${\mathit{T}}_{1\mathit{w}}$ (${}^{\xb0}$C) | ${\mathit{T}}_{2\mathit{w}}$ (${}^{\xb0}$C) | ${\mathit{T}}_{1\mathit{w}}^{\prime}$ (${}^{\xb0}$C) | ${\mathit{T}}_{2\mathit{w}}^{\prime}$ (${}^{\xb0}$C) |
---|---|---|---|---|

(1st It) | (1st It) | (2nd It) | (2nd It) | |

1 | 3249.04 | 2049.04 | 1901.1 | 1626.58 |

1.2 | 3524.01 | 2145.41 | 1957.67 | 1663.95 |

1.25 | 3517.36 | 2166.97 | 1969.85 | 1672.98 |

1.5 | 3483.91 | 2261.83 | 2021.24 | 1715.69 |

**Table 2.**Numerical results for the two convective layers between the outer core and the lower limit of the crust of the Earth at maximum ecological function conditions.

n | ${\mathit{T}}_{1\mathit{w}}$ (${}^{\xb0}$C) | ${\mathit{T}}_{2\mathit{w}}$ (${}^{\xb0}$C) | ${\mathit{T}}_{1\mathit{w}}^{\prime}$ (${}^{\xb0}$C) | ${\mathit{T}}_{2\mathit{w}}^{\prime}$ (${}^{\xb0}$C) |
---|---|---|---|---|

(1st It) | (1st It) | (2nd It) | (2nd It) | |

1 | 3256.23 | 2427.05 | 2025.06 | 1871.51 |

1.2 | 3709.21 | 1965.91 | 1871.34 | 1582.23 |

1.25 | 3705.38 | 1981.63 | 1882.12 | 1586.81 |

1.5 | 3685.58 | 2051.01 | 1933.14 | 1602.4 |

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**MDPI and ACS Style**

Arango-Reyes, K.; Barranco-Jiménez, M.A.; Ares de Parga-Álvarez, G.; Angulo-Brown, F.
A Simple Thermodynamic Model of the Internal Convective Zone of the Earth. *Entropy* **2018**, *20*, 985.
https://doi.org/10.3390/e20120985

**AMA Style**

Arango-Reyes K, Barranco-Jiménez MA, Ares de Parga-Álvarez G, Angulo-Brown F.
A Simple Thermodynamic Model of the Internal Convective Zone of the Earth. *Entropy*. 2018; 20(12):985.
https://doi.org/10.3390/e20120985

**Chicago/Turabian Style**

Arango-Reyes, Karen, Marco Antonio Barranco-Jiménez, Gonzalo Ares de Parga-Álvarez, and Fernando Angulo-Brown.
2018. "A Simple Thermodynamic Model of the Internal Convective Zone of the Earth" *Entropy* 20, no. 12: 985.
https://doi.org/10.3390/e20120985