### Abstract

In the previous paper, the thermodynamic behavior of materials for nonequilibrium processes was discussed in continuum mechanics. The spatial nonequilibrium of thermodynamic quantities have been treated as their nonlocalities there. Then balance laws for the above materials under nonequilibrium processes have been derived introducing the nonlocalities of thermodynamic quantities. In the present paper, the constitutive equations for the above materials are constructed on the basis of the previous results to satisfy the thermodynamic relations which are expressed by the newly defined thermodynamic potential and by the dissipative function. Moreover, the basic equation system is shown, substituting the above constitutive equations into balance laws. Furthermore, the relationships among the moduli defined in the constitutive equations, are indicated. As a result, it is clarified that the heat conduction depends on not only the temperature gradient but also microscopic gradient and microscopic curvature of temperature under nonequilibrium processes.

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

Pages (from-to) | 868-875 |

Number of pages | 8 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 59 |

Issue number | 559 |

Publication status | Published - 1993 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*59*(559), 868-875.

**Basic equations for continua considering microscopic curvature of temperature.** / Kobayashi, Seiichi; Shizawa, Kazuyuki; Takahashi, Kunihiro.

Research output: Contribution to journal › Article

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 59, no. 559, pp. 868-875.

}

TY - JOUR

T1 - Basic equations for continua considering microscopic curvature of temperature

AU - Kobayashi, Seiichi

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1993/3

Y1 - 1993/3

N2 - In the previous paper, the thermodynamic behavior of materials for nonequilibrium processes was discussed in continuum mechanics. The spatial nonequilibrium of thermodynamic quantities have been treated as their nonlocalities there. Then balance laws for the above materials under nonequilibrium processes have been derived introducing the nonlocalities of thermodynamic quantities. In the present paper, the constitutive equations for the above materials are constructed on the basis of the previous results to satisfy the thermodynamic relations which are expressed by the newly defined thermodynamic potential and by the dissipative function. Moreover, the basic equation system is shown, substituting the above constitutive equations into balance laws. Furthermore, the relationships among the moduli defined in the constitutive equations, are indicated. As a result, it is clarified that the heat conduction depends on not only the temperature gradient but also microscopic gradient and microscopic curvature of temperature under nonequilibrium processes.

AB - In the previous paper, the thermodynamic behavior of materials for nonequilibrium processes was discussed in continuum mechanics. The spatial nonequilibrium of thermodynamic quantities have been treated as their nonlocalities there. Then balance laws for the above materials under nonequilibrium processes have been derived introducing the nonlocalities of thermodynamic quantities. In the present paper, the constitutive equations for the above materials are constructed on the basis of the previous results to satisfy the thermodynamic relations which are expressed by the newly defined thermodynamic potential and by the dissipative function. Moreover, the basic equation system is shown, substituting the above constitutive equations into balance laws. Furthermore, the relationships among the moduli defined in the constitutive equations, are indicated. As a result, it is clarified that the heat conduction depends on not only the temperature gradient but also microscopic gradient and microscopic curvature of temperature under nonequilibrium processes.

UR - http://www.scopus.com/inward/record.url?scp=0027555082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027555082&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0027555082

VL - 59

SP - 868

EP - 875

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 - 559

ER -