Abstract
The Laplace transform is used to obtain a unique equation for describing essentially nonsteady heat or mass transfer in a heterogeneous medium. The equation is used to analyze the heating of a half-space through a plane boundary.
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Abbreviations
- A:
-
parameter introduced in (11)
- a :
-
particle radius
- b:
-
coefficient accounting for irregularity of particle packing near the wall
- c:
-
heat capacity
- d:
-
density
- Fo:
-
dimensionless time (Fourier number)
- k, k′:
-
dimensionless parameters determined in (8) and (10)
- Nu:
-
Nusselt number
- n:
-
numerical concentration of particles
- p:
-
Laplace transform parameter
- Qw :
-
dimensional heat flux to the granular layer from the wall
- q:
-
heat flux to a particle
- R:
-
contact thermal resistance
- r:
-
radial coordinate in the system connected with the particle
- Ti :
-
mean temperatures of the phases
- Tw :
-
wall temperature
- t:
-
time
- u:
-
rate of convective transport
- x:
-
space coordinate
- α:
-
parameter in (3)
- ε:
-
porosity
- ki :
-
thermal diffusivity of the materials of the phases
- κ:
-
parameter in (15)
- gl:
-
thermal conductivity
- gl* :
-
effective thermal conductivity
- ξ:
-
dimensionless coordinate
- τ:
-
temperature inside particle
- 1 and 2:
-
pertain to the continuous and discrete phases, respectively; an asterisk above a quantity denotes its Laplace transform
Literature cited
N. V. Antonishin and V. V. Lushchikov, Transport Processes in Units with Disperse Systems [in Russian], Minsk (1986), pp. 3–25.
A. P. Baskakov, V. V. Berg, A. F. Ryzhkov, and N. F. Filippovskii, Heat and Mass Transfer Processes in a Fluidized Bed [in Russian], Moscow (1978).
Yu. A. Buevich, Inzh.-Fiz. Zh.,54, No. 5, 770–779 (1988).
A. P. Baskakov, Inzh.-Fiz. Zh.,12, No. 5, 599–604 (1967).
A. G. Gorelik, Inzh.-Fiz. Zh.,13, No. 6, 931–936 (1967).
N. V. Antonishin, N. V. Lyutich, and A. L. Parnas, Heat and Mass Transfer in Heat Treatment of Disperse Materials [in Russian], Minsk (1974), pp. 3–6.
J. S. M. Botterill and J. R. Williams, Trans. Inst. Chem. Eng.,41, No. 5, 217–230 (1963).
J. Gabor, Chem. Eng. Progr. Symp. Ser., Vol. 66, No. 105, 76–86 (1970).
J. Botterill, Heat Transfer in a Fluidized Bed [Russian translation], Moscow (1980).
G. Carslaw and D. Jaegar, Thermal Conductivity of Solids [Russian translation], Moscow (1964).
V. I. Krylov and N. S. Skoblya, Handbook of Numerical Laplace Transformation [in Russian], Minsk (1968).
I. I. Kal'tman and A. I. Tamarin, Inzh.-Fiz. Zh.,16, No. 4, 630–638 (1969).
G. F. Puchkov, Heat and Mass Transfer in Disperse Systems [in Russian], Minsk (1982), pp. 29–33.
S. P. Detkov, Prom. Teplotekh.,7, No. 2, 99–105 (1985).
Yu. A. Buevich, Yu. A. Korneev, and I. N. Shchelchkova, Inzh.-Fiz. Zh.,30, No. 6, 979–985 (1976).
B. S. Endler, Inzh.-Fiz. Zh.,37, No. 1, 110–117 (1979).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 779–787, May, 1989.
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Buevich, Y.A., Ustinov, V.A. & Khuzhaerov, B. Nonsteady transfer in disperse and heterogeneous media. Journal of Engineering Physics 56, 552–558 (1989). https://doi.org/10.1007/BF01297605
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DOI: https://doi.org/10.1007/BF01297605