### Abstract

We propose that an increasing value in entropy inequality is not a local value of entropy but an average value in a mesodomain. From this standpoint, new balance equations are obtained by applying the concept of generalized continuum mechanics to mass transfer. In the present paper, it is clarified that the influence of a mesoscopic gradient of mass concentration should be included in Pick's first law and Fourier's law. Even if thermal effects on diffusion are neglected, the diffusion equations obtained here are simultaneous differential equations with two undetermined values, which include the conventional diffusion equation as a special case. The conventional diffusion equation describing infinite velocity of propagation associated with diffusion entails a contradiction. The velocity of propagation defined here is shown in the results of a numerical analysis for an extreme initial state. Consequently, it is indicated that the present theory gives an acceptable solution to the above problem in the conven-tional theory.

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

Pages (from-to) | 84-96 |

Number of pages | 13 |

Journal | Heat Transfer - Asian Research |

Volume | 26 |

Issue number | 2 |

Publication status | Published - 1997 |

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### Keywords

- Constitutive equation
- Diffusion
- Entropy
- Material design
- Micromechanics
- Nonequilibrium
- Nonlocality
- Polar materials
- Thermodynamics

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

*Heat Transfer - Asian Research*,

*26*(2), 84-96.

**Diffusion equations based on generalized continuum mechanics.** / Yokozuka, Takehide; Funasako, Takumi; Shimada, Hidenori; Shizawa, Kazuyuki; Takahashi, Kunihiro.

Research output: Contribution to journal › Article

*Heat Transfer - Asian Research*, vol. 26, no. 2, pp. 84-96.

}

TY - JOUR

T1 - Diffusion equations based on generalized continuum mechanics

AU - Yokozuka, Takehide

AU - Funasako, Takumi

AU - Shimada, Hidenori

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1997

Y1 - 1997

N2 - We propose that an increasing value in entropy inequality is not a local value of entropy but an average value in a mesodomain. From this standpoint, new balance equations are obtained by applying the concept of generalized continuum mechanics to mass transfer. In the present paper, it is clarified that the influence of a mesoscopic gradient of mass concentration should be included in Pick's first law and Fourier's law. Even if thermal effects on diffusion are neglected, the diffusion equations obtained here are simultaneous differential equations with two undetermined values, which include the conventional diffusion equation as a special case. The conventional diffusion equation describing infinite velocity of propagation associated with diffusion entails a contradiction. The velocity of propagation defined here is shown in the results of a numerical analysis for an extreme initial state. Consequently, it is indicated that the present theory gives an acceptable solution to the above problem in the conven-tional theory.

AB - We propose that an increasing value in entropy inequality is not a local value of entropy but an average value in a mesodomain. From this standpoint, new balance equations are obtained by applying the concept of generalized continuum mechanics to mass transfer. In the present paper, it is clarified that the influence of a mesoscopic gradient of mass concentration should be included in Pick's first law and Fourier's law. Even if thermal effects on diffusion are neglected, the diffusion equations obtained here are simultaneous differential equations with two undetermined values, which include the conventional diffusion equation as a special case. The conventional diffusion equation describing infinite velocity of propagation associated with diffusion entails a contradiction. The velocity of propagation defined here is shown in the results of a numerical analysis for an extreme initial state. Consequently, it is indicated that the present theory gives an acceptable solution to the above problem in the conven-tional theory.

KW - Constitutive equation

KW - Diffusion

KW - Entropy

KW - Material design

KW - Micromechanics

KW - Nonequilibrium

KW - Nonlocality

KW - Polar materials

KW - Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=0031380982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031380982&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 84

EP - 96

JO - Heat Transfer - Asian Research

JF - Heat Transfer - Asian Research

SN - 1099-2871

IS - 2

ER -