Journal of Mathematical Sciences

, Volume 238, Issue 2, pp 116–128 | Cite as

Modeling of the Flows of Admixtures in a Random Layered Strip with Probable Arrangement of Inclusions Near the Boundaries of the Body

  • O. Yu. Chernukha
  • A. E. Chuchvara

We study the random flow of admixtures in a two-phase stochastically inhomogeneous strip with the most probable arrangement of inclusions in the vicinity of the surfaces of the body. A mathematical model is formulated for the function of diffusion flow with nonzero constant initial concentration. A random diffusion flow is represented in the form of a Neumann series. The procedure of averaging of the random mass flow over the ensemble of phase configurations with arcsine distribution function is performed. The influence of the characteristics of the medium on the distribution of mass flow is analyzed. It is shown that if the diffusion coefficient of admixtures in the inclusion is higher than for the matrix, then the increase in the characteristic thickness of the layers causes a decrease in the value of the diffusion flow, whereas the mass flow in the entire body increases with the volume fraction of the inclusions.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • O. Yu. Chernukha
    • 1
  • A. E. Chuchvara
    • 2
  1. 1.Center of Mathematical Simulations, Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine
  2. 2.“L’vivs’ka Politekhnika” National UniversityLvivUkraine

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