Admixture diffusion in a strip with randomly disposed interlayer under nonideal mass contact conditions. (Ukrainian. English summary) Zbl 1088.76561

Summary: An initial-boundary value problem of admixture diffusion is considered in a two-phase random nonhomogeneous strip under nonideal conditions of mass contact on interphases. A constant value of admixture concentration is given on one strip surface. It equals to zero on the another surface. The contact problem is reduced to the diffusion equation for the whole body by the theory of generalized functions. The constructed initial-boundary value problem is reduced to an integro-differential equation. By the method of successive iterations, a solution to this equation is constructed in terms of absolutely and uniformly convergent series. Convergence of the Neuman series is proved, and an estimate for remainder of infinite series is proposed. The obtained approximated solution was averaged over the ensemble of phase configurations with uniform distribution function. It was shown that distinction in physical characteristics of phases leads to essential changes of the averaged concentration field.


76R50 Diffusion
76M35 Stochastic analysis applied to problems in fluid mechanics