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Toward a theory of transport in heterogeneous media

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Abstract

A unified equation is obtained for description of nonsteady state heat and mass transport in two-phase heterogeneous media in the low- and high-frequency approximations. Heating of a granular bed by a solid wall is considered as an example.

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Abbreviations

a :

particle size

c1,c2, d1, d2 :

specific heat capacities and densities of materials forming continuous and dispersed phases

L:

linear scale of mean fields

ℓ:

linear scale of interparticle space

m:

coefficient appearing in Eqs. (2) and (7)

n:

numerical particle concentration

p:

Laplace transform variable

Q:

thermal flux from wall to granular layer

q:

thermal flux to particle

r:

radial coordinate

T:

temperature within particle

T1, T2 :

mean temperatures of continuous and dispersed phases

To :

wall temperature

t:

time

u:

mean velocity of continuous phase in spaces between particles

w:

effective velocity introduced into Eq. (8)

x:

coordinate normal to wall

β:

interphase heat-exchange coefficient

γ2, σ2 :

effective thermal conductivity coefficients defined in Eq. (8) and (13)

δ − ω'a, ɛ:

porosity (volume fraction of continuous phase in heterogeneous medium)

χ,χ′:

thermal diffusivity coefficients of particle and continuous phase materials

λ, λ* :

thermal conductivity coefficients of particles and medium as a whole

τ, θ:

time scales introduced in Eqs. (8) and (13)

ω:

frequency

ω′ − √ω/2χ:

asterisk superscript denotes Laplace transform

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Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 770–779, May, 1988.

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Buevich, Y.A. Toward a theory of transport in heterogeneous media. Journal of Engineering Physics 54, 518–526 (1988). https://doi.org/10.1007/BF00872571

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Keywords

  • Statistical Physic
  • Mass Transport
  • Solid Wall
  • Heterogeneous Medium
  • State Heat