Abstract
The system of transfer equations in a two-phase medium reduces to a single effective equation which can be analyzed without significant difficulties (in comparison with the given system), with the accuracy of the problem formulation being practically preserved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- Θ, t, x, u:
-
dimensionless temperature (pressure), time, coordinate, velocity
- Θ :
-
the value of x = 0
- a, ɛ, ν:
-
dimensionless parameters in (1)
- d:
-
parameter in (8)
- ξ:
-
self-similarity variable
- q:
-
debit (heat flux)
- χ:
-
piezoconductivity
- m°:
-
porosity at the initial pressure p°
- βp, βm :
-
compressibility factors of liquid and block pores
- σ:
-
critical pressure
- α:
-
dimensionless depression
- p:
-
parameter of the Laplace transform
- b(p):
-
function in (8)
- β(p), in (11), r0 :
-
dimensionless radius of a bore
- K:
-
operator in (5)
- L, L1 :
-
operators in (6)
- F(Θ 1):
-
function in (7)
- G(x, t):
-
function in (20)
- ▽:
-
gradient
- Δ:
-
the Laplace operator
- 1, 2:
-
refer to fissures and blocks
- a superscript bar:
-
the Laplace transform
Literature cited
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).
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).
Yu. A. Buevich and E. B. Perminov, Inzh.-Fiz. Zh.,38, No. 1, 29–37 (1980).
N. N. Smirnova, Physical Hydrodynamics and Heat Exchange [in Russian], Novosibirsk (1978), pp. 61–68.
A. Ban et al., The Effect of Rock Properties on Motion of Liquids [in Russian], Moscow (1962).
V. N. Nikolaevskii, K. S. Basniev, A. T. Gorbunov, and G. A. Zotov, Mechanics of Saturated Porous Media [in Russian], Moscow (1970).
P. M. Ogibalov and A. Kh. Mirzadzhanzade, Mechanics of Physical Processes [in Russian], Moscow (1976).
I. A. Vazhnova, “An investigation of the effect of mass exchange on filtrating processes,” Candidate's Thesis, Technical Sciences, Baku (1986).
E. P. Serov and V. P. Korol'kov, Dynamics of Processes in Heat and Mass Exchange Apparatus [in Russian], Moscow (1967).
N. V. Antonishin, M. A. Geller, and A. L. Parnas, Inzh.-Fiz. Zh.,26, No. 3, 503–508 (1974).
V. A. Ditkin and A. P. Prudnikov, Handbook on Operational Calculus [in Russian], Moscow (1965).
G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik, A Theory of Nonstationary Filtration of Liquid and Gas [in Russian] (1972).
T. D. Golf-Rakht, Foundations of Oil Field Geology and Fissured Collectors [in Russian], Moscow (1986).
Sh. K. Gimatudinov (ed.), Reference Design Handbook on Development and Operation of Oil Fields. Petroleum Production [in Russian], Moscow (1983).
Sh. K. Gimatudinov, Physics of Oil and Gas Bed [in Russian], Moscow (1971).
M. A. Lavrent'ev and B. V. Shabat, Methods of Theory of Functions of a Complex Variable [in Russian], Moscow (1965).
Yu. A. Buevich and V. S. Nustrov, Inzh.-Fiz. Zh.,48, No. 6, 943–950 (1985).
Author information
Authors and Affiliations
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 779–786, May, 1988.
Rights and permissions
About this article
Cite this article
Nustrov, V.S., Saifullaev, B.N. A method of an equivalent equation in the theory of heat and mass transfer. Journal of Engineering Physics 54, 527–533 (1988). https://doi.org/10.1007/BF00872572
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00872572