International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 12 Issue 11 ǁ November 2024 ǁ PP. 134-138 www.ijres.org 134 | Page The nature of the change in the lifting force acting on a porous cylinder U. Dalabaev University of World Economy and Diplomacy, Tashkent, Uzbekistan Corresponding Author udalabaev@mail.ru ABSTRACT The paper investigates the nature of the lifting force acting on a porous cylindrical particle. The porous cylinder is located perpendicular to the flow and is flown by a viscous liquid in a flat channel. The calculation of the lifting force acting on the cylinder is made for different values of the Reynolds number, porosity and their location in the flow. KEYWORDS Flow, Darci law, Rakhmatulin model, porous media, numerical method. -------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 13-11-2024 Date of acceptance: 26-11-2024 -------------------------------------------------------------------------------------------------------------------------------------- I. INTRODUCTION In many technological processes, viscous fluid flows are observed in areas with and without porous inclusions. In this regard, there is a need to study such phenomena [1-3]. The experimental results of Segre-Silberberg [4] on particle migration gave impetus to many researchers to search for an analytical expression for the lift force acting on a particle from the flow. An analytical expression for the lift force for a sphere in an unlimited linear flow was obtained in the work of Saffman [5]. There were attempts to expand Saffman's formula by many authors [6-12]. In [6,7], a correction to Saffman's lift force is given. In the work of Asmolov [8], the formula for the transverse force acting on a spherical particle in a laminar boundary layer was expanded using the method of matched asymptotic expansions. The magnitude of the force is expressed through a multiple integral. In [10], using Asmolov's corrections [8,11], the motion of a particle in the Couette layer was investigated. Work [11] is devoted to the effect of inertia and the presence of a boundary on the lift force. The effect of inertia on the lift force in a linear velocity field was investigated in [11] using the numerical Fourier method. In [13], the flow around a cylinder by an infinite two-dimensional flow was numerically investigated based on the non-stationary Navier-Stokes equation in the variables of the stream function and vortex. Important elements of such studies are the mathematical description of such phenomena. The complexity of such flows lies in the consideration of the flow in two subdomains: the free zone and the porous subdomain. In the free zone, the flow is modeled by the Stokes/Navier-Stokes equations, and in the porous subdomain there are various approaches to modeling the flow in the porous region [1-3]. There are two directions of modeling such flows in the literature. The first direction is characterized by modeling the flow with its own equations in each subdomain. The flow in the free zone is modeled using the Navier-Stokes/Stokes equation systems. There are many equations to describe the filtration flow through a saturated porous layer [1-3]. In particular, the classical Darcy equation [1] is widely used to describe the flow through a porous layer. The Brinkman filtration equation is similar in type to the Navier-Stokes equation. When using a two-region model, a choice of interregional boundary arises. The Beavers-Joseph or Saffman conditions are used as the interboundary condition [14]. The second direction is characterized by the use of a single differential equation for the entire region [15,16]. In this case, the use of the interphase boundary is eliminated. In this case, the use of the equation in the free zone turns into the Navier-Stokes equation. In this article, we use a single equation for the entire region, and the model is obtained on the basis of a two-velocity continuum, first described by H.A. Rakhmatulin [18]. The study of filtration motion based on a two- speed model was also carried out in works [19,20], in which the forces of interaction between the phases corresponded to Darcy's law, while observing the Kozeny-Carman relation. . II. MATHEMATICAL MODEL Let a porous cylinder be located in the region of a viscous flow (Fig. 1). To describe the flow inside and outside the porous cylinder, we proceed from the interpenetrating model of two-phase media. If in the two-velocity model for describing the flow of two-phase media we assume that 1) there is no motion of the discrete phase, 2) the deformation of the discrete phase can be neglected, 3) there is no heat and mass transfer between the phases,