This article presents an integrated mathematical model of radial filtration in a cylindrical filter, in which the flow movement is carried out from the outer layer to the inner cavity. Free flow areas are described by Navier-Stokes equations for incompressible fluid, where the filtration process through the porous layer is formalized based on Darcy’s law, and the pressure distribution is determined by the Poisson equation. The transfer of dissolved substances is modeled using the advection-diffusion equation. The model includes a mechanism for the evolution of porosity over time (sealing or clogging), which allows tracking the conjugate dynamics of the "pressure-velocity-porosityconcentration" parameters. The analysis showed that considering the vertical orientation of the cylindrical filter is a significant factor influencing the reduction of energy costs and increasing the selectivity of the process.
| Mualliflar | Saidov, U., Juraev, I., Turakulov, J., Саидов, У., Жураев, И., Туракулов, Ж. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-09-20 |
| Son | 4 |
| Betlar | 47-55 |
| Til | Rus |
| DOI | 10.71310/pcam.4_68.2025.10 |
DOI: 10.71310/pcam.4_68.2025.10 · Maqolaning asl sahifasi
mathematical model, cylindrical filter, Navier–Stokes equations, Darcy’s law, Poisson equation, advection–diffusion, hydrodynamics, математическая модель, цилиндрический фильтр, уравнения Навье–Стокса, закон Дарси, уравнение Пуассона, адвекция–диффузия, гидродинамика
The article considers the problem of constructing self-similar solutions of a system of nonlinear differential equations modeling mutual diffusion processes in multicomponent media. An analysis of a mathematical model…
This work proposes an expanded 3D Euler model for calculating the spatiotemporal evolution of pollutant concentrations released into the atmosphere under changing meteorological conditions. The model, alongside the…
This paper addresses the problem of constructing optimal quadrature formulas for the numerical evaluation of Hadamard-type hypersingular integrals with hihg oscillation. Such integrals frequently arise in the analysis…
Many applied problems are described by the Dirichlet problem for the Poisson equa tions. This problem is used in the following practical situations: membrane or plate deflection, electric potential, gravitational and…
In this work, the problem of stabilizing the equilibrium state for a hyperbolic equation with negative nonlocal characteristic velocity and measurement error is investigated. The formulation of the mixed control problem…
This article presents a comprehensive mathematical modeling of thermo-electro magneto-elastic processes in anisotropic thin plates of complex shapes using the R function method (RFM). The model considers interrelated…
In the world, special attention is given to developing various optimal computational methods for the approximate calculation of definite integrals. This article focuses on constructing composite optimal quadrature…
Usually, the solution of a plane problem of the theory of elasticity in stresses is reduced to solving a biharmonic equation for the Airy stress function. In this paper, two (A and B) variants of plane boundary value…
The article studies the dynamics of derivatives up to the highest derivative of an ordinary differential equation of the fourth order with a small parameter at the highest derivative. The solution of the differential…
This study investigates the classification of rooftop shapes using convolutional neural networks (CNNs), with a particular focus on regional adaptation through transfer learning. Initial training of the AlexNet…