### Abstract

Thermopolar theory explains nonequilibrium processes, introducing the nonlocalities of thermodynamic quantities in continuum mechanics. In a previous report considering this concept, thermodynamic laws and the balance law for fluctuations of thermodynamic quantities were formulated, and the constitutive equations for thermopolar materials were constructed. In this paper, the basic equations governing thermopolar materials with microscopic gradient of temperature are discussed on the basis of previous results. Moreover, these basic equations are applied to thermopolar materials, and relations among the moduli, which were defined when the constitutive equations were constructed, are derived. As the result of these investigations, it is clarified that the heat conduction of thermopolar materials with microscopic gradient of temperature is governed not only by the equation of heat conduction but also by the equation for the balance of the microscopic gradient of temperature.

Original language | English |
---|---|

Pages (from-to) | 725-730 |

Number of pages | 6 |

Journal | Transactions of the Japan Society of Mechanical Engineers Series A |

Volume | 58 |

Issue number | 549 |

DOIs | |

Publication status | Published - 1992 |

Externally published | Yes |

### Fingerprint

### Keywords

- Constitutive Equation
- Continuum Mechanics
- Material Design
- Microscopic Gradient of Temperature
- Nonequilibrium
- Thermal Stress
- Thermodynamics
- Thermoelasticity
- Thermopolar Material

### ASJC Scopus subject areas

- Materials Science(all)
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Transactions of the Japan Society of Mechanical Engineers Series A*,

*58*(549), 725-730. https://doi.org/10.1299/kikaia.58.725

**Basic Equations for Thermopolar Materials with Microscopic Gradient of Temperature.** / Kobayashi, Seiichi; Shizawa, Kazuyuki; Takahashi, Kunihiro.

Research output: Contribution to journal › Article

*Transactions of the Japan Society of Mechanical Engineers Series A*, vol. 58, no. 549, pp. 725-730. https://doi.org/10.1299/kikaia.58.725

}

TY - JOUR

T1 - Basic Equations for Thermopolar Materials with Microscopic Gradient of Temperature

AU - Kobayashi, Seiichi

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1992

Y1 - 1992

N2 - Thermopolar theory explains nonequilibrium processes, introducing the nonlocalities of thermodynamic quantities in continuum mechanics. In a previous report considering this concept, thermodynamic laws and the balance law for fluctuations of thermodynamic quantities were formulated, and the constitutive equations for thermopolar materials were constructed. In this paper, the basic equations governing thermopolar materials with microscopic gradient of temperature are discussed on the basis of previous results. Moreover, these basic equations are applied to thermopolar materials, and relations among the moduli, which were defined when the constitutive equations were constructed, are derived. As the result of these investigations, it is clarified that the heat conduction of thermopolar materials with microscopic gradient of temperature is governed not only by the equation of heat conduction but also by the equation for the balance of the microscopic gradient of temperature.

AB - Thermopolar theory explains nonequilibrium processes, introducing the nonlocalities of thermodynamic quantities in continuum mechanics. In a previous report considering this concept, thermodynamic laws and the balance law for fluctuations of thermodynamic quantities were formulated, and the constitutive equations for thermopolar materials were constructed. In this paper, the basic equations governing thermopolar materials with microscopic gradient of temperature are discussed on the basis of previous results. Moreover, these basic equations are applied to thermopolar materials, and relations among the moduli, which were defined when the constitutive equations were constructed, are derived. As the result of these investigations, it is clarified that the heat conduction of thermopolar materials with microscopic gradient of temperature is governed not only by the equation of heat conduction but also by the equation for the balance of the microscopic gradient of temperature.

KW - Constitutive Equation

KW - Continuum Mechanics

KW - Material Design

KW - Microscopic Gradient of Temperature

KW - Nonequilibrium

KW - Thermal Stress

KW - Thermodynamics

KW - Thermoelasticity

KW - Thermopolar Material

UR - http://www.scopus.com/inward/record.url?scp=84998389320&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84998389320&partnerID=8YFLogxK

U2 - 10.1299/kikaia.58.725

DO - 10.1299/kikaia.58.725

M3 - Article

AN - SCOPUS:84998389320

VL - 58

SP - 725

EP - 730

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 549

ER -