Transverse diffusion and heat conduction in a granular layer
The process of non-steady-state transverse diffusion of a passive additive in a granular layer described by a cellular model is investigated. The general results obtained in  are applied to an analysis of concrete transport processes of matter and heat in a granular layer. The following four cell models are treated: (1) ideal mixing cells without stagnation zones; (2) ideal mixing cells with stagnation zones; (3) ideal mixing cells with diffusive stagnation zones; (4) ideal mixing cells with diffusive stagnation zones having a finite exchange rate between the free volume and the stagnation zone. The conditions of applicability for each of the above models are found. The time to establish a normal distribution in the transverse diffusion process is determined for all the models. This quantity is then connected with the physical characteristics of transport processes of matter in a layer of nonporous and porous particles, the transport of heat in a granular layer, and the transport of matter in a layer of particles which adsorb an additive.
KeywordsMathematical Modeling Normal Distribution Mechanical Engineer Exchange Rate Heat Conduction
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- 1.L. M. Pis'men, S. I. Kuchanov, and V. G. Levich, “Transverse diffusion in a granular layer,” Dokl. AN SSSR, vol. 174, no. 3, 1967.Google Scholar
- 2.H. Kramers and G. Abberda, “Frequency response analysis of continuous flow systems,” Chem. Engng Sci., vol. 2, p. 173, 1953.Google Scholar
- 3.V. G. Levich, V. S. Markin, and Yu. A. Chizmadzhev, “Hydrodynamical mixing in a model of a porous medium with stagnation zones,”Dokl. AN SSSR, vol. 166, no. 6, 1966.Google Scholar
- 4.H. Gottschlich, “Axial dispersion in packed beds,” Amer. Inst. Chem. Engng. J., vol. 9, p. 88, 1963.Google Scholar
- 5.R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice-Hall, Englewood Cliffs, N.J., 1965.Google Scholar
- 6.V. G. Levich, L. M. Pis'men, and S. I. Kuchanov, “Hydrodynamic mixing in a granular layer. The physical model of stagnation zones,” Dokl. AN SSSR, vol. 168, no. 2, 1966.Google Scholar
- 7.V. G. Levich, Yu. I. Kharkats, andL. M. Pis'men, “The effect of external diffusion stagnation on a process in a porous catalyst,” Dokl. AN SSSR, vol. 171, no. 2, 1966.Google Scholar
- 8.S. Masamune and J. M. Smith, “Thermal conductivity of beds of spherical particles,” Industr. Engng. Chem. Fund., vol. 2, p. 136, 1963.Google Scholar