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Nonequilibrium — filtration equations

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Abstract

Within the framework of the linear thermodynamics of irreversible processes, a general form is obtained for the equations of isothermal nonequilibrium filtration of an incompressible Liquid through a nondeforming porous matrix.

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Abbreviations

Q(e) :

external heat flux

Q′:

uncompensated heat

U:

interval energy

S:

entropy

T:

temperature

dA(i) :

elementary work of the internal surface forces

ηα :

internal degrees of freedom

B α :

thermodynamic parameters conjugate to ηα

φ:

dissipative function

σij :

stress tensor in the liquid

vi :

liquid-particle velocity

V0 :

volume of the porous medium

V:

liquid volumes

S0 :

surface of volume V0

Se :

“liquid part” of S0

S1 :

liquid contact surface with the porous matrix inside V0

P:

mean (over Se) liquid pressure

qi :

filtration velocity

s:

Laplace-transform parameters

t:

time

Literature cited

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  6. M. G. Alishaev and A. Kh. Mirzadzhanzade, “Taking account of lag phenomena in filtration theory,” Izv. Vyssh. Uchebn. Zaved., Nef.Gaz, No. 6, 71–74 (1975).

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Authors and Affiliations

  1. V. I. Ul'yanov-Lenin Kazan' State University, USSR

    A. V. Kosterin

Authors
  1. A. V. Kosterin
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Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 77–80, July, 1980.

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Kosterin, A.V. Nonequilibrium — filtration equations. Journal of Engineering Physics 39, 769–771 (1980). https://doi.org/10.1007/BF00821832

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  • DOI: https://doi.org/10.1007/BF00821832

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