### Abstract

In the previous paper, noninstantaneities of thermodynamic quantities were introduced in the laws of thermodynamics, to express nonequilibrium processes for continua. Then it was discussed that the time rate of temperature must be newly added to the set of state variables for materials under nonequilibrium processes. In the present paper, the thermodynamic relationships for the above materials are derived and expressed by a newly defined thermodynamic potential and by a dissipation function. Moreover, the constitutive equations are obtained on the basis of the previous results to satisfy the above relationships. The system of basic equations for the continua considering noninstantaneities of thermodynamic quantities is shown, by substituting the constitutive equations into balance laws derived in the previous paper. As a result, it is clarified that the effect of new thermal stress is introduced in the equation of motion and that the velocity of propagation of temperature is finite in the equation of heat conduction according to this theory.

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

Pages (from-to) | 2885-2892 |

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 | 568 |

Publication status | Published - 1993 Dec |

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*(568), 2885-2892.

**Basic equations for continua considering noninstantaneities.** / 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. 568, pp. 2885-2892.

}

TY - JOUR

T1 - Basic equations for continua considering noninstantaneities

AU - Kobayashi, Seiichi

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1993/12

Y1 - 1993/12

N2 - In the previous paper, noninstantaneities of thermodynamic quantities were introduced in the laws of thermodynamics, to express nonequilibrium processes for continua. Then it was discussed that the time rate of temperature must be newly added to the set of state variables for materials under nonequilibrium processes. In the present paper, the thermodynamic relationships for the above materials are derived and expressed by a newly defined thermodynamic potential and by a dissipation function. Moreover, the constitutive equations are obtained on the basis of the previous results to satisfy the above relationships. The system of basic equations for the continua considering noninstantaneities of thermodynamic quantities is shown, by substituting the constitutive equations into balance laws derived in the previous paper. As a result, it is clarified that the effect of new thermal stress is introduced in the equation of motion and that the velocity of propagation of temperature is finite in the equation of heat conduction according to this theory.

AB - In the previous paper, noninstantaneities of thermodynamic quantities were introduced in the laws of thermodynamics, to express nonequilibrium processes for continua. Then it was discussed that the time rate of temperature must be newly added to the set of state variables for materials under nonequilibrium processes. In the present paper, the thermodynamic relationships for the above materials are derived and expressed by a newly defined thermodynamic potential and by a dissipation function. Moreover, the constitutive equations are obtained on the basis of the previous results to satisfy the above relationships. The system of basic equations for the continua considering noninstantaneities of thermodynamic quantities is shown, by substituting the constitutive equations into balance laws derived in the previous paper. As a result, it is clarified that the effect of new thermal stress is introduced in the equation of motion and that the velocity of propagation of temperature is finite in the equation of heat conduction according to this theory.

UR - http://www.scopus.com/inward/record.url?scp=0027831985&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027831985&partnerID=8YFLogxK

M3 - Article

VL - 59

SP - 2885

EP - 2892

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 - 568

ER -