Diffusion equations based on generalized continuum mechanics

Takehide Yokozuka, Takumi Funasako, Hidenori Shimada, Kazuyuki Shizawa, Kunihiro Takahashi

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)84-96
Number of pages13
JournalHeat Transfer - Asian Research
Volume26
Issue number2
Publication statusPublished - 1997

Fingerprint

continuum mechanics
Continuum mechanics
Entropy
entropy
Fourier law
propagation
Thermal effects
mass transfer
numerical analysis
temperature effects
Numerical analysis
Differential equations
differential equations
Mass transfer
gradients

Keywords

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

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

Cite this

Yokozuka, T., Funasako, T., Shimada, H., Shizawa, K., & Takahashi, K. (1997). Diffusion equations based on generalized continuum mechanics. 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.

In: Heat Transfer - Asian Research, Vol. 26, No. 2, 1997, p. 84-96.

Research output: Contribution to journalArticle

Yokozuka, T, Funasako, T, Shimada, H, Shizawa, K & Takahashi, K 1997, 'Diffusion equations based on generalized continuum mechanics', Heat Transfer - Asian Research, vol. 26, no. 2, pp. 84-96.
Yokozuka T, Funasako T, Shimada H, Shizawa K, Takahashi K. Diffusion equations based on generalized continuum mechanics. Heat Transfer - Asian Research. 1997;26(2):84-96.
Yokozuka, Takehide ; Funasako, Takumi ; Shimada, Hidenori ; Shizawa, Kazuyuki ; Takahashi, Kunihiro. / Diffusion equations based on generalized continuum mechanics. In: Heat Transfer - Asian Research. 1997 ; Vol. 26, No. 2. pp. 84-96.
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