# On Thermomechanics of a Nonlinear Heat Conducting Suspension

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## Abstract

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## 1. Introduction

## 2. The Governing Equations

## 3. The Constitutive Equations

#### 3.1. Stress Tensor

#### 3.2. Heat Flux Vector

## 4. Entropy Analysis

## 5. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

$\mathbf{D}$ | symmetric part of the velocity gradient |

$\mathbf{I}$ | identity tensor |

$\mathbf{L}$ | gradient of the velocity vector |

$\mathbf{T}$ | Cauchy stress tensor |

${a}_{i}$ | heat flux vector constitutive coefficients, i = 1 to 6 |

$\mathbf{b}$ | body force vector |

$div$ | divergence operator |

k | thermal conductivity |

$\mathbf{q}$ | heat flux vector |

r | radiant heating |

$\mathbf{u}$ | velocity vector |

$\mathbf{x}$ | spatial position |

${\beta}_{i}$ | material constitutive coefficients, i = 0 to 5 |

ε | specific internal energy |

θ | temperature |

ρ | bulk density |

${\rho}_{10}$ | reference density |

φ | volume fraction |

∇ | gradient symbol |

Δ | Laplacian operator |

⊗ | outer product |

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Massoudi, M.; Kirwan, A.D.
On Thermomechanics of a Nonlinear Heat Conducting Suspension. *Fluids* **2016**, *1*, 19.
https://doi.org/10.3390/fluids1020019

**AMA Style**

Massoudi M, Kirwan AD.
On Thermomechanics of a Nonlinear Heat Conducting Suspension. *Fluids*. 2016; 1(2):19.
https://doi.org/10.3390/fluids1020019

**Chicago/Turabian Style**

Massoudi, Mehrdad, and A. D. Kirwan.
2016. "On Thermomechanics of a Nonlinear Heat Conducting Suspension" *Fluids* 1, no. 2: 19.
https://doi.org/10.3390/fluids1020019