Igor Pažanin

Comparison between Darcy and Brinkman laws in a fracture

Different laws are used for modeling flows in porous media. In this paper, we focus on Brinkman and Darcy law. We derive them from microscopic equations by upscaling, compare them and estimate the error made by their application. Our results justify the use of Brinkman law.

On reactive solute transport through a curved pipe

Abstract The transport of a reactive solute by diffusion and convection in a thin (or long) curved pipe is considered. Using asymptotic analysis with respect to the pipe’s thickness, the effective model for solute concentration is formally derived. A simple approximation is computed, showing explicitly the effects of the pipe’s geometry in nature and magnitude.

Non-isothermal fluid flow through a thin pipe with cooling

The stationary flow of a Boussinesquian fluid with temperature-dependent viscosity through a thin straight pipe is considered. The fluid in the pipe is cooled by the exterior medium. The asymptotic approximation of the solution is built and rigorously justified by proving the error estimate in terms of domain thickness. The boundary layers for the temperature at the ends of the pipe are studied.

Effective Flow of Micropolar Fluid through a Thin or Long Pipe

The aim of this paper is to present the result about asymptotic approximation of the micropolar fluid flow through a thin (or long) straight pipe with variable cross section. We assume that the flow is governed by the prescribed pressure drop between pipes ends. Such model has relevance to some important industrial and engineering applications. The asymptotic behavior of the flow is investigated via rigorous asymptotic analysis with respect to the small parameter, being the ratio between pipes thickness and its length. In the case of circular pipe, we obtain the explicit formulae for the approximation showing explicitly the effects of microstructure on the flow. We prove the corresponding error estimate justifying the obtained asymptotic model.

Modeling of solute dispersion in a circular pipe filled with micropolar fluid

Abstract In this paper we study the transport of a reactive solute through a thin (or long) cylindrical pipe filled with micropolar fluid. We suppose that the solute particles undergo a first-order chemical reaction at the lateral boundary of the pipe. The effective model for solute concentration is derived by means of a formal asymptotic analysis with respect to the pipe’s thickness. The asymptotic approximation is built, showing explicitly the effects of fluid microstructure and chemical reaction on the solute dispersion.

Analysis of the thin film flow in a rough domain filled with micropolar fluid

Inspired by the lubrication framework, in this paper a micropolar fluid flow through a rough thin domain is studied. The domains thickness is considered as the small parameter e , while the roughness is defined by a periodical function with period of order e 2 . Starting from three-dimensional micropolar equations and using asymptotic analysis with respect to e , we formally derive the macroscopic model clearly detecting the effects of the specific rugosity profile and fluid microstructure. We provide the rigorous justification of our formally obtained asymptotic model by deriving the effective system by means of the two-scale convergence.

Flow of a Micropolar Fluid Through a Channel with Small Boundary Perturbation

Abstract The aim of this paper is to investigate the effects of small boundary perturbations on the flow of an incompressible micropolar fluid. The fluid domain is described as follows: we start from a simple rectangular domain and then perturb part of its boundary by the product of a small parameter ϵ and some smooth function h. Using formal asymptotic analysis with respect to ϵ, we derive the effective model in the form of the explicit formulae for the velocity, pressure and microrotation. The asymptotic solution clearly acknowledges the effects of the boundary perturbation and the micropolar nature of the fluid. The obtained results are illustrated by some numerical examples confirming that the considered perturbation has a nonlocal impact on the solution.

On the micropolar flow in a circular pipe: the effects of the viscosity coefficients

This paper considers the stationary flow of incompressible micropolar fluid through a thin cylindrical pipe governed by the pressure drop between pipes ends. Its goal is to investigate the influence of the viscosity coefficients on the effective flow. Depending on the magnitude of viscosity coefficients with respect to the pipes thickness, it derives different asymptotic models and discusses their properties.

On the Solvability of a Problem of Stationary Fluid Flow in a Helical Pipe

We consider a flow of incompressible Newtonian fluid through a pipe with helical shape. We suppose that the flow is governed by the prescribed pressure drop between pipes ends. Such model has relevance to some important engineering applications. Under small data assumption, we prove the existence and uniqueness of the weak solution to the corresponding Navier-Stokes system with pressure boundary condition. The proof is based on the contraction method.

On the Darcy–Brinkman Flow Through a Channel with Slightly Perturbed Boundary

The goal of this paper is to study the effects of a slightly perturbed boundary on the Darcy–Brinkman flow through a porous channel. We start from a rectangular domain and then perturb the upper part of its boundary by the product of the small parameter