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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- a :
- c1,c2, d1, d2 :
specific heat capacities and densities of materials forming continuous and dispersed phases
linear scale of mean fields
linear scale of interparticle space
coefficient appearing in Eqs. (2) and (7)
numerical particle concentration
Laplace transform variable
thermal flux from wall to granular layer
thermal flux to particle
temperature within particle
- T1, T2 :
mean temperatures of continuous and dispersed phases
- To :
mean velocity of continuous phase in spaces between particles
effective velocity introduced into Eq. (8)
coordinate normal to wall
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)
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′ − √ω/2χ:
asterisk superscript denotes Laplace transform
A. N. Tikhonov, Zh. Éksp. Teor. Fiz.,7, No. 1, 138–168 (1937).
L. I. Rubinshtein, Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz.,12, No. 1, 27–45 (1948).
N. V. Antonishin, L. E. Simchenko, and G. A. Surkov, Inzh.-Fiz. Zh.,11, No. 4, 537–541 (1966).
Yu. A. Buevich and Yu. A. Korneev, Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 79–87 (1974).
Yu. A. Buevich, Yu. A. Korneev, and I. N. Shchelkova, Inzh.-Fiz. Zh.,30, No. 6, 979–985 (1976).
Yu. A. Buevich and Yu. A. Korneev, Inzh.-Fiz. Zh.,31, No. 1, 21–28 (1976).
G. I. Barenblatt, Yu. P. Zheltov, and I. N. Kochina, Prikl. Mat. Mekh.,24, No. 5, 852–864 (1960).
Yu. A. Buevich, Inzh.-Fiz. Zh.,46, No. 4, 593–600 (1984).
D. Tondeur, Genie Chim.,103, No. 21, 2799–2812 (1970).
I. A. Vazhnova, “Study of the effect of mass transport on filtration processes,” Author's Abstract of Candidate's Dissertation, Baku (1986).
M. E. Curtin and A. C. Pipkin, Arch. Rat. Mech. Anal.,31, No. 1, 113–126 (1968).
N. V. Antonishin, M. A. Geller, and A. L. Parnas, Inzh.-Fiz. Zh.,26, No. 3, 503–508 (1974).
A. V. Lykov, Inzh.-Fiz. Zh.,26, No. 5, 781–790 (1974).
J. Verhas, Period. Polytech. Mech. Eng.,21, No. 3, 271–277 (1977).
V. L. Kolpashchikov and A. I. Shnip, Inzh.-Fiz. Zh.,34, No. 2, 352–360 (1978).
G. P. Yasnikov and V. S. Belousov, Inzh.-Fiz. Zh.,34, No. 6, 1085–1089 (1978).
Yu. A. Buevich and E. B. Perminov, Inzh.-Fiz. Zh.,38, No. 1, 29–37 (1980).
V. S. Nustrov and B. N. Saifullaev, Inzh.-Fiz. Zh.,54, No. 5, 779–786 (1988).
A. Yu. Zubarev, Inzh.-Fiz. Zh.,50, No. 2, 272–278 (1986).
Yu. A. Buevich, A. Yu. Zubarev, and S. L. Komarinskii, Inzh.-Fiz. Zh.,53, No. 2, 211–217 (1987).
N. V. Antonishin, M. A. Geller, V. V. Lushchikov, and T. V. Soroko, Heat-Mass Transport-VI, Vol. VI, Part 1 [in Russian], Minsk (1960), pp. 3–8.
N. V. Antonishin, Heat-Mass Transport-VI. Problem Reports, Part 2 [in Russian], Minsk (1981), pp. 39–53.
N. V. Antonishin and V. V. Lushchikov, Transport Problems in Equipment with Dispersed Systems [in Russian], Minsk (1986), pp. 3–25.
G. L. Ivantsov and B. Ya. Lyubov, Dokl. Akad. Nauk SSSR,136, No. 2, 293–296 (1952).
N. N. Smirnova, “Study of the heat-mass transport process during filtration in mineral extraction,” Author's Abstract of Candidate's Dissertation, Novosibirsk (1978).
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford Univ. Press (1959).
L. D. Landau and E. M. Lifshits, Hydrodynamics [in Russian], Moscow (1986).
A. V. Lykov and B. M. Berkovskii, Convection and Thermal Waves [in Russian], Moscow (1974).
A. P. Baskakov, Inzh.-Fiz. Zh.,6, No. 11, 20–25 (1963).
Yu. A. Buevich and B. E. Perminov, Inzh.-Fiz. Zh.,48, No. 1, 35–44 (1985).
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
- Statistical Physic
- Mass Transport
- Solid Wall
- Heterogeneous Medium
- State Heat