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Добірка наукової літератури з теми "Micropolar fluids equations"

Автор: Grafiati

Опубліковано: 21 грудня 2024

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Статті в журналах з теми "Micropolar fluids equations"

Stamenkovic, Zivojin, Milos Kocic, Jasmina Bogdanovic-Jovanovic, and Jelena Petrovic. "Nano and micropolar MHD fluid flow and heat transfer in inclined channel." Thermal Science, no. 00 (2023): 170. http://dx.doi.org/10.2298/tsci230515170k.

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Magnetohydrodynamic (MHD) fluid flows attract a lot of attention in the extrusion of polymers, in the theory of nanofluids, as well as in the consideration of biological fluids. The considered problem in the paper is the flow and heat transfer of nano and micropolar fluid in inclined channel. Fluid flow is steady, while nano and micropolar fluids are incompressible, immiscible, and electrically conductive. The upper and lower channel plates are electrically insulated and maintained at constant and different temperatures. External applied magnetic field is perpendicular to the fluid flow and considered problem is in induction-less approximation. The equations of the considered problem are reduced to ordinary differential equations, which are analytically solved in closed form. The influence of characteristics parameters of nano and micropolar fluids on velocity, micro-rotation and temperature fields are graphically shown and discussed. The general conclusions given through the analysis of graphs can be used for better understanding of the flow and heat transfer of nano and micropolar fluid, which have a great practical application. Fluids with nanoparticles innovated the modern era, due to their comprehensive applications in nanotechnology and manufacturing processes, while the theory of micropolar fluids explains the flow of biological fluids and various types of liquid metals and crystals.

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Kocić, Miloš, Živojin Stamenković, Jelena Petrović, and Jasmina Bogdanović-Jovanović. "Control of MHD Flow and Heat Transfer of a Micropolar Fluid through Porous Media in a Horizontal Channel." Fluids 8, no. 3 (March 8, 2023): 93. http://dx.doi.org/10.3390/fluids8030093.

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The problem considered in this paper is a steady micropolar fluid flow in porous media between two plates. This model can be used to describe the flow of some types of fluids with microstructures, such as human and animal blood, muddy water, colloidal fluids, lubricants and chemical suspensions. Fluid flow is a consequence of the constant pressure gradient along the flow, while two parallel plates are fixed and have different constant temperatures during the fluid flow. Perpendicular to the flow, an external magnetic field is applied. General equations of the problem are reduced to ordinary differential equations and solved in the closed form. Solutions for velocity, microrotation and temperature are used to explain the influence of the external magnetic field (Hartmann number), the characteristics of the micropolar fluid (coupling and spin gradient viscosity parameter) and the characteristics of the porous medium (porous parameter) using graphs. The results obtained in the paper show that the increase in the additional viscosity of micropolar fluids emphasizes the microrotation vector. Moreover, the analysis of the effect of the porosity parameter shows how the permeability of a porous medium can influence the fluid flow and heat transfer of a micropolar fluid. Finally, it is shown that the influence of the external magnetic field reduces the characteristics of micropolar fluids and tends to reduce the velocity field and make it uniform along the cross-section of the channel.

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Yang, Hujun, Xiaoling Han, and Caidi Zhao. "Homogenization of Trajectory Statistical Solutions for the 3D Incompressible Micropolar Fluids with Rapidly Oscillating Terms." Mathematics 10, no. 14 (July 15, 2022): 2469. http://dx.doi.org/10.3390/math10142469.

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This article studies the 3D incompressible micropolar fluids with rapidly oscillating terms. The authors prove that the trajectory statistical solutions of the oscillating fluids converge to that of the homogenized fluids provided that the oscillating external force and angular momentum possess some weak homogenization. The results obtained indicate that the trajectory statistical information of the 3D incompressible micropolar fluids has a certain homogenization effect with respect to spatial variables. In addition, our approach is also valid for a broad class of evolutionary equations displaying the property of global existence of weak solutions without a known result of global uniqueness, including some model hydrodynamic equations, MHD equations and non-Newtonian fluids equations.

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Rahman, M. M., and T. Sultana. "Radiative Heat Transfer Flow of Micropolar Fluid with Variable Heat Flux in a Porous Medium." Nonlinear Analysis: Modelling and Control 13, no. 1 (January 25, 2008): 71–87. http://dx.doi.org/10.15388/na.2008.13.1.14590.

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A two-dimensional steady convective flow of a micropolar fluid past a vertical porous flat plate in the presence of radiation with variable heat flux has been analyzed numerically. Using Darcy-Forchheimer model the corresponding momentum, microrotation and energy equations have been solved numerically. The local similarity solutions for the flow, microrotation and heat transfer characteristics are illustrated graphically for various material parameters. The effects of the pertinent parameters on the local skin friction coefficient, plate couple stress and the heat transfer are also calculated. It was shown that large Darcy parameter leads to decrease the velocity while it increases the angular velocity as well as temperature of the micropolar fluids. The rate of heat transfer in weakly concentrated micropolar fluids is higher than strongly concentrated micropolar fluids.

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Chen, James, James D. Lee, and Chunlei Liang. "Constitutive equations of Micropolar electromagnetic fluids." Journal of Non-Newtonian Fluid Mechanics 166, no. 14-15 (August 2011): 867–74. http://dx.doi.org/10.1016/j.jnnfm.2011.05.004.

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IDO, Yasushi. "Basic Equations of Micropolar Magnetic Fluids." Transactions of the Japan Society of Mechanical Engineers Series B 70, no. 696 (2004): 2065–70. http://dx.doi.org/10.1299/kikaib.70.2065.

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Duarte-Leiva, Cristian, Sebastián Lorca, and Exequiel Mallea-Zepeda. "A 3D Non-Stationary Micropolar Fluids Equations with Navier Slip Boundary Conditions." Symmetry 13, no. 8 (July 26, 2021): 1348. http://dx.doi.org/10.3390/sym13081348.

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Анотація:

Micropolar fluids are fluids with microstructure and belong to a class of fluids with asymmetric stress tensor that called Polar fluids, and include, as a special case, the well-established Navier–Stokes model. In this work we study a 3D micropolar fluids model with Navier boundary conditions without friction for the velocity field and homogeneous Dirichlet boundary conditions for the angular velocity. Using the Galerkin method, we prove the existence of weak solutions and establish a Prodi–Serrin regularity type result which allow us to obtain global-in-time strong solutions at finite time.

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Kocić, Miloš, Živojin Stamenković, Jelena Petrović, and Jasmina Bogdanović-Jovanović. "MHD micropolar fluid flow in porous media." Advances in Mechanical Engineering 15, no. 6 (June 2023): 168781322311784. http://dx.doi.org/10.1177/16878132231178436.

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Анотація:

The analysis of mass and heat transfer in magnetohydrodynamic (MHD) flows has significant applications in heat exchangers, cooling nuclear reactors, designing energy systems and casting and injection processes of different types of fluids. On the other hand, extraction of crude oil, the flow of human or animal blood, as well as other polymer fluids or liquid crystals are just some examples of micropolar fluid flows. Due to the broad application spectrum of the theory of micropolar fluid flows, and the significance the impact the external magnetic field has on the flow of these fluids, this paper considers the stationary flow of a micropolar fluid between two plates under the influence of an external magnetic field which is perpendicular to the direction of the flow. Stationary plates are maintained at constant and different temperatures, while the whole problem is considered in the non-inductive approximation. The equation system used to define the physical problem under consideration is reduced to the system of differential equations that have been solved analytically and the solutions of which are of general nature. In addition to the solutions for velocity, microrotation and temperature, the paper gives solutions for shear stress at plates, the Nusselt number and flow rate. The provided solutions have been applied in order to reach some general conclusions about the influence of the magnetic field and physical characteristics of a micropolar fluid and the characteristics of porous media on the nature of micropolar fluid flows in porous media by means of chart analysis. General conclusions, obtained in the result analysis in this paper, give us the opportunity to understand the flows of micropolar fluids and highlight their significance.

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Hassanien, I. A. "Mixed Convection in Micropolar Boundary-Layer Flow Over a Horizontal Semi-Infinite Plate." Journal of Fluids Engineering 118, no. 4 (December 1, 1996): 833–38. http://dx.doi.org/10.1115/1.2835517.

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Анотація:

A boundary layer analysis is presented to study the effects of buoyancy-induced streamwise pressure gradients on laminar forced convection heat transfer to micropolar fluids from a horizontal semi-infinite flat plate. The transformed boundary-layer equations have been solved numerically. The effects of the buoyancy force, material parameters, and viscous dissipative heat on the friction factor, total heat transfer, displacement thickness, and wall couple stress, as well as the details of the velocity, microrotation, and temperature fields are discussed. A comparison has been made with the corresponding results for Newtonian fluids. Micropolar fluids display drag reduction and reduced heat transfer rate as compared with Newtonian fluids. Also the micropolar properties of the fluid are found to play an important role in controlling flow separation. Furthermore, it is observed that, for high values of the buoyancy and material parameters, the flow and thermal fields are significantly affected by the presence of viscous dissipation heat.

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Srinivas, J., J. V. Ramana Murthy, and Ali J. Chamkha. "Analysis of entropy generation in an inclined channel flow containing two immiscible micropolar fluids using HAM." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1027–49. http://dx.doi.org/10.1108/hff-09-2015-0354.

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Анотація:

Purpose – The purpose of this paper is to examine the flow, heat transfer and entropy generation characteristics for an inclined channel of two immiscible micropolar fluids. Design/methodology/approach – The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. The flow is assumed to be governed by Eringen’s micropolar fluid flow equation. The resulting governing equations are then solved using the homotopy analysis method. Findings – The following findings are concluded: first, the entropy generation rate is more near the plates in both the zones as compared to that of the interface. This indicates that the friction due to surface on the fluids increases entropy generation rate. Second, the entropy generation rate is more near the plate in Zone I than that of Zone II. This may be due to the fact that the fluid in Zone I is more viscous. This indicates the more the viscosity of the fluid is, the more the entropy generation. Third, Bejan number is the maximum at the interface of the fluids. This indicates that the amount of exergy (available energy) is maximum and irreversibility is minimized at the interface between the fluids. Fourth, as micropolarity increases, entropy generation rate near the plates decreases and irreversibility decreases. This indicates an important industrial application for micropolar fluids to use them as a good lubricant. Originality/value – The problem is original as no work has been reported on entropy generation in an inclined channel with two immiscible micropolar fluids.

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Більше джерел

Дисертації з теми "Micropolar fluids equations"

Gumgum, Sevin. "The Dual Reciprocity Boundary Element Method Solution Of Fluid Flow Problems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611605/index.pdf.

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In this thesis, the two-dimensional, transient, laminar flow of viscous and incompressible fluids is solved by using the dual reciprocity boundary element method (DRBEM). Natural convection and mixed convection flows are also solved with the addition of energy equation. Solutions of natural convection flow of nanofluids and micropolar fluids in enclosures are obtained for highly large values of Rayleigh number. The fundamental solution of Laplace equation is used for obtaining boundary element method (BEM) matrices whereas all the other terms in the differential equations governing the flows are considered as nonhomogeneity. This is the main advantage of DRBEM to tackle the nonlinearities in the equations with considerably small computational cost. All the convective terms are evaluated by using the DRBEM coordinate matrix which is already computed in the formulation of nonlinear terms. The resulting systems of initial value problems with respect to time are solved with forward and central differences using relaxation parameters, and the fourth-order Runge-Kutta method. The numerical stability analysis is developed for the flow problems considered with respect to the choice of the time step, relaxation parameters and problem constants. The stability analysis is made through an eigenvalue decomposition of the final coefficient matrix in the DRBEM discretized system. It is found that the implicit central difference time integration scheme with relaxation parameter value close to one, and quite large time steps gives numerically stable solutions for all flow problems solved in the thesis. One-and-two-sided lid-driven cavity flow, natural and mixed convection flows in cavities, natural convection flow of nanofluids and micropolar fluids in enclosures are solved with several geometric configurations. The solutions are visualized in terms of streamlines, vorticity, microrotation, pressure contours, isotherms and flow vectors to simulate the flow behaviour.

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Llerena, Montenegro Henry David. "Sur l'interdépendance des variables dans l'étude de quelques équations de la mécanique des fluides." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM048.

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Анотація:

Cette thèse est consacrée à l'étude de la relation entre les variables dans les équations des fluides micro-polaires. Ce système, basé sur les équations de Navier-Stokes, consiste en un couplage de deux variables: le champ de vitesse vec{u} et le champ de micro-rotation vec{w}. Notre objectif est de mieux comprendre comment l'information concernant une variable influence le comportement de l'autre. À cette fin, nous avons divisé cette thèse en quatre chapitres, où nous étudierons les propriétés de régularité locale des solutions faibles de type Leray, puis nous nous concentrerons sur la régularité et l'unicité des solutions faibles dans le cas stationnaire. Le premier chapitre présente une rapide déduction physique des équations micro-polaires, suivie de la construction des solutions faibles de type Leray. Dans le chapitre 2, nous commençons par prouver un gain d'intégrabilité pour les deux variables vec{u} et vec{w} lorsque la vitesse appartient à certains espaces de Morrey. Ce résultat souligne un effet de domination de la vitesse. Nous montrons ensuite que cet effet peut également être observé dans le cadre de la théorie de Caffarelli-Kohn-Nirenberg, i.e., sous une hypothèse de petitesse supplémentaire uniquement sur le gradient de la vitesse, nous pouvons démontrer que la solution devient Hölder continue. Pour cela, nous introduisons la notion de solution partiellement adaptée, qui est fondamentale dans ce travail et représente l'une des principales nouveautés. Dans la dernière section de ce chapitre, nous obtenons des résultats similaires dans le contexte du critère de Serrin. Dans le chapitre 3, nous nous concentrons sur le comportement de la norme L^3 de la vitesse vec{u} autour des possibles points où la régularité peut être perdue. Plus précisément, nous établissons un critère d'explosion pour la norme L^3 de la vitesse et améliorons ce résultat en présentant un phénomène de concentration. Nous vérifions également que le cas limite L^infty_t L^3_x du critère de Serrin reste valable pour les équations des fluides micro-polaires. Enfin, le problème de l'existence et de l'unicité des équations stationnaires des fluides micro-polaires est abordé dans le chapitre 4. En effet, nous prouvons l'existence de solutions faibles (vec{u}, vec{w}) dans l'espace d'énergie naturel dot{H}^1(mathbb{R}^3) imes H^1(mathbb{R}^3). De plus, en utilisant la relation entre les variables, nous déduisons que ces solutions sont régulières. Il convient de noter que la solution triviale peut ne pas être unique, et pour surmonter cette difficulté, nous développons un théorème de type Liouville. Ainsi, nous démontrons qu'en imposant une décroissance plus forte à l'infini uniquement sur vec{u}, nous pouvons en déduire l'unicité de la solution triviale (vec{u},vec{w})=(0,0)
This thesis is devoted to the study of the relationship between the variables in the micropolar fluids equations. This system, which is based on the Navier-Stokes equations, consists in a coupling of two variables: the velocity field vec{u} and the microrotation field vec{w}. Our aim is to provide a better understanding of how information about one variable influences the behavior of the other. To this end, we have divided this thesis into four chapters, where we will study the local regularity properties of Leray-type weak solutions, and later we will focus on the regularity and uniqueness of weak solutions for the stationary case. The first chapter presents a brief physical derivation of the micropolar equations followed by the construction of the Leray-type weak solutions. In Chapter 2, we begin by proving a gain of integrability for both variables vec{u} and vec{w} whenever the velocity belongs to certain Morrey spaces. This result highlights an effect of domination by the velocity. We then show that this effect can also be observed within the framework of the Caffarelli-Kohn-Nirenberg theory, i.e., under an additional smallness hypothesis only on the gradient of the velocity, we can demonstrate that the solution becomes Hölder continuous. For this, we introduce the notion of a partial suitable solution, which is fundamental in this work and represents one of the main novelties. In the last section of this chapter, we derive similar results in the context of the Serrin criterion. In Chapter 3, we focus on the behavior of the L^3-norm of the velocity vec{u} near possible points where regularity may get lost. More precisely, we establish a blow-up criterion for the L^3 norm of the velocity and we improve this result by presenting a concentration phenomenon. We also verify that the limit point L^infty_t L^3_x of the Serrin criterion remains valid for the micropolar fluids equations. Finally, the problem of existence and uniqueness for the stationary micropolar fluids equations is addressed in Chapter 4. Indeed, we prove the existence of weak solutions (vec{u}, vec{w}) in the natural energy space dot{H}^1(mathbb{R}^3) imes H^1(mathbb{R}^3). Moreover, by using the relationship between the variables, we deduce that these solutions are regular. It is worth noting that the trivial solution may not be unique, and to overcome this difficulty, we develop a Liouville-type theorem. Hence, we demonstrate that by imposing stronger decay at infinity only on vec{u}, we can infer the uniqueness of the trivial solution (vec{u},vec{w})=(0,0)

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Mostefai, Mohamed Sadek. "Déduction rigoureuse de l'équation de Reynolds à partir d'un système modélisant l'écoulement à faible épaisseur d'un fluide micropolaire, et étude de deux problèmes à frontière libre : Hele-Shaw généralisé et Stephan à deux phases pour un fluide non newtonien." Saint-Etienne, 1997. http://www.theses.fr/1997STET4019.

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Dans le chapitre 1, on considère le modèle micropolaire de Navier-Stokes avec conditions de bords de type Dirichlet non homogènes en dimension deux. On donnera un résultat d'existence d'une solution faible en utilisant le théorème du point fixe de Leray-Schauder, puis on prouvera l'unicité de la solution faible du problème sous certaines hypothèses. On établiera une justification mathématique de l’équation de Reynolds généralisé à partir de ce modèle là. On étudiera ensuite la forme de l'équation de Reynolds suivant le choix de la viscosité et des données initiales. Dans le chapitre 2, nous considérons le modèle de Hele-Shaw généralisé dans une cellule laminaire, qui consiste à injecter du fluide, avec un débit non constant w 0, à travers un trou de frontière 1, situé sur l'une des deux surfaces ; et à tenir compte que l'une des surfaces a une géométrie quelconque et animée d'un mouvement relatif vertical. En introduisant un changement de variable de type Baiocchi, le problème initial se ramène à l'étude d'une inéquation variationnelle avec terme de Volterra. L'existence d'une solution pour cette dernière est donnée par le théorème du point fixe de Banach. Des résultats de régularité en espace pour la solution seront prouvés en introduisant un problème pénalisé et en utilisant la méthode de Rothe (semi-discrétisation en temps), puis on montrera que la dérivée par rapport à t de la solution de l'inéquation variationnelle est dans l#(0, t, h#2()), ce dernier résultat nous permet de revenir au problème initial. Dans le chapitre 3, on considère un problème de Stefan à deux phases avec convection. Le problème est gouverné par un système couple non linéaire, comprenant la loi de Darcy pour un fluide non newtonien et l'équation d'équilibre d'énergie avec second membre dans l#1. Pour prouver l'existence de solutions du problème faible on introduira une famille de solutions approchées (#, p#), > 0, définies sur le domaine entier , en insérant une fonction de pénalité convenable dans l'équation de pression. On considère ensuite séparement les problèmes en # et p#, respectivement, et en utilisant le principe de point fixe de Schauder, on montre l'existence de couples solutions (#, p#) du problème approché, pour tout > 0. En faisant tendre vers zéro, on montre que les solutions du problème approché convergent vers une limite (, p) qui est une solution faible du problème variationnel. On montre aussi que la fonction est continue d'où le domaine où > 0 est un ensemble ouvert, et l'interface des deux phases est définie a posteriori comme l'ensemble de niveau = 0. On établira, enfin, quelques relations entre les solutions faibles et classiques, dans le cas d’une courbe assez régulière

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BENHABOUCHA, Nadia. "Quelques problèmes mathématiques relatifs à la modélisation des conditions aux limites fluide-solide pour des écoulements de faible épaisseur." Phd thesis, Université Claude Bernard - Lyon I, 2003. http://tel.archives-ouvertes.fr/tel-00005482.

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Анотація:

Ce travail de thèse est consacré à l'étude asymptotique d'écoulements de faible épaisseur et à la modélisation des conditions aux limites à imposer à l'interface fluide-solide dans différentes situations. Le chapitre 1 est consacré à l'etude asymptotique d'un écoulement fluide constitué d'une couche poreuse mince adjacente à un milieu fluide mince. On met en évidence l'existence d'un rapport critique entre la taille de la microstructure du milieu poreux et les deux épaisseurs, rapport pour lequel une équation de Reynolds modifiée est obtenue. De plus il est montré qu'on peut toujours pour une géométrie réelle se placer dans ce cas critique. Enfin, on présente des simulations numériques qui mettent en évidence les différences entre le modèle présenté ici et deux autres modèles utilisés en mécanique. Dans le chapitre 2, on s'intéresse à l'étude d'un écoulement de faible épaisseur quand une des surfaces est rugueuse. Ceci peut etre relié à l'étude du chapitre précédent en considérant un milieu poreux qui ne comporterait qu'une seule couche. On utilise la technique de la double échelle en homogénéisation pour obtenir rigoureusement les résultats de convergences. En outre, la convergence des contraintes normales et tangentielles sur les surfaces lisses et rugueuses est étudiée. Dans le chapitre 3, on étudie un écoulement d'un fluide non newtonien de type micropolaire avec de nouvelles conditions à l'interface fluide solide couplant la vitesse et la microrotation par l'introduction d'une viscosité de surface. On démontre l'existence et l'unicité de la solution et des estimations a priori qui conduisent, via l'étude asymptotique, à une équation de Reynolds micropolaire généralisée. Une étude numérique montre l'influence des conditions aux limites sur la charge et le coefficient de frottement. Les résultats sont comparés avec ceux d'autres modèles retenant une condition d'adhérence à la paroi.

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Частини книг з теми "Micropolar fluids equations"

Simčić, Loredana, and Ivan Dražić. "Some Properties of a Generalized Solution for Shear Flow of a Compressible Viscous Micropolar Fluid Model." In Differential and Difference Equations with Applications, 455–65. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_35.

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Dražić, Ivan. "Homogeneous Boundary Problem for the Compressible Viscous and Heat-Conducting Micropolar Fluid Model with Cylindrical Symmetry." In Differential and Difference Equations with Applications, 79–92. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75647-9_7.

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Dražić, Ivan. "Non-homogeneous Boundary Problems for One-Dimensional Flow of the Compressible Viscous and Heat-Conducting Micropolar Fluid." In Differential and Difference Equations with Applications, 389–95. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_30.

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Mujaković, N., and N. Črnjarić–Žic. "Finite Difference Formulation for the Model of a Compressible Viscous and Heat-Conducting Micropolar Fluid with Spherical Symmetry." In Differential and Difference Equations with Applications, 293–301. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32857-7_27.

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Dražić, Ivan, and Nermina Mujaković. "Some Properties of a Generalized Solution for 3-D Flow of a Compressible Viscous Micropolar Fluid Model with Spherical Symmetry." In Differential and Difference Equations with Applications, 205–13. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32857-7_19.

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Merkin, John H., Ioan Pop, Yian Yian Lok, and Teodor Grosan. "Basic equations and mathematical methods." In Similarity Solutions for the Boundary Layer Flow and Heat Transfer of Viscous Fluids, Nanofluids, Porous Media, and Micropolar Fluids, 1–21. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-12-821188-5.00002-3.

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Conca, C., R. Gormaz, E. Ortega, and M. Rojas. "Existence and uniqueness of a strong solution for nonhomogeneous micropolar fluids." In Nonlinear Partial Differential Equations and their Applications - Collège de France Seminar Volume XIV, 213–41. Elsevier, 2002. http://dx.doi.org/10.1016/s0168-2024(02)80012-1.

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Sava, V. Al. "An initial boundary value problem for the equations of plane flow of a micropolar fluid in a time-dependent domain." In Integral methods in science and engineering, 160–64. Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780367812027-32.

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Тези доповідей конференцій з теми "Micropolar fluids equations"

Najafi, A., F. Daneshmand, and S. R. Mohebpour. "Analysis of Vibrating Micropolar Plate in Contact With a Fluid." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31036.

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Micropolar theory constitutes extension of the classical field theories. It is based on the idea that every particles of the material can make both micro rotation and volumetric micro elongation in addition to the bulk deformation. Since this theory includes the effects of micro structure which could affect the overall behaviour of the medium, it reflects the physical realities much better than the classical theory for the engineering materials. In the micropolar theory, the material points are considered to possess orientations. A material point carrying three rigid directors introduces one extra degree of freedom over the classical theory. This is because in micropolar continuum, a point is endowed with three rigid directors only. A material point is then equipped with the degrees of freedom for rigid rotations, in addition to the classical translational degrees of freedom. In fact, the micropolar covers the results of the classical continuum mechanics. The micropolar theory recently takes attentions in fluid mechanics and mathematicians and engineers are implementing this theory in various theoretical and practical applications. In this paper the fluid-structure analysis of a vibrating micropolar plate in contact with a fluid is considered. The fluid is contained in a cube which all faces except for one of the lateral faces are rigid. The only non-rigid lateral face is made of a flexible micropolar plate and therefore, interacts with the fluid. An analytical approach is utilized to investigate the vibration characteristics of the aforementioned fluid-structure problem. The fluid is non-viscous and incompressible. Duplicate Chebyshev series, multiplied by boundary functions are used as admissible functions and the frequency equations of the micropolar plate are obtained by the use of Chebyshev-Ritz method. Also the vibration analysis of the plates modeled by micropolar theory has been done. This analysis shows that some additional frequencies due to the micropolarity of the plate appears among the values of the frequencies obtained in the classical theory of elasticity, as expected. These new frequencies are called micro-rotational waves. We also observed that when the micropolar material constants vanish, these additional frequencies disappear and only the classical frequencies remain. Specially, we observed that these additional frequencies are more sensitive to the change of the micro elastic constants than the classical frequencies. The frequencies and mode shapes of the coupled fluid structure interaction problem are obtained in the present study based on the micropolar and classical modeling. The numerical results for the problem are compared with those obtained by the analytical method for their differences and to confirm the proposed method. The microrotatinal wave frequencies and mode shapes are also developed. The results show that the natural frequencies and mode shapes for the transverse vibrations of the problem are in good agreement with the classical one and our knowledge from the physical nature of the problem.

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Fatunmbi, E. O., and O. O. Akanbi. "Magnetohydrodynamic Flow and Heat Transfer Characteristics in Micropolar-Casson Fluid over a Stretching Surface with Temperature-dependent Material Properties." In 28th iSTEAMS Multidisciplinary Research Conference AIUWA The Gambia. Society for Multidisciplinary and Advanced Research Techniques - Creative Research Publishers, 2021. http://dx.doi.org/10.22624/aims/isteams-2021/v28n2p7.

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The current investigation communicates the flow and heat transfer characteristics of an electrically conducting micropolar-Casson fluid over a two-dimensional stretching surface with variable thermal conductivity and viscosity. Thermal radiation, viscous dissipation and heat source effects are also accounted for in the energy equation. The formulated equations of flow and heat transfer are converted from partial to ordinary differential equations using suitable similarity transformations while the dimensionless equations are solved by Runge-Kutta Fehlberg integration scheme. The effects of the physical parameters are publicized through graphs and validated by related published studies in the limiting situations. It is found from the investigation that there is accelerated flow due to the material micropolar term whereas the presence of Casson fluid and magnetic field terms decelerate the velocity. Besides, the surface temperature improves with a rise in the Casson fluid term, Eckert number and thermal conductivity parameter whereas the trend is reversed for micropolarity influence. Keywords: Micropolar-Casson fluid; Magnetohydrodynamic, Variable viscosity; Variable thermal conductivity;Viscous dissipation

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Mingyang Pan, Xiandong Zhu, Liancun Zheng, and Xinhui Si. "Multiple solutions of the micropolar fluid equation in a porous channel." In 2014 ISFMFE - 6th International Symposium on Fluid Machinery and Fluid Engineering. Institution of Engineering and Technology, 2014. http://dx.doi.org/10.1049/cp.2014.1228.

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Al-Sharifi, H. A. M. "Numerical solutions of equations Eyring-Powell micropolar fluid across stretching surface." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0114694.

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Hazbavi, Abbas, and Sajad Sharhani. "Micropolar Fluid Flow Between Two Inclined Parallel Plates." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-72528.

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In this study, the hydrodynamic characteristics are investigated for magneto-micropolar fluid flow through an inclined channel of parallel plates with constant pressure gradient. The lower plate is maintained at constant temperature and upper plate at a constant heat flux. The governing equations which are continuity, momentum and energy are are solved numerically by Explicit Runge-Kutta. The effect of characteristic parameters is discussed on velocity and microrotation in different diagrams. The nonlinear parameter affected the velocity microrotation diagrams. An increase in the value of Hartmann number slows down the movement of the fluid in the channel. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Also the effect of pressure gradient is investigated on velocity and microrotation in different diagrams.

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Ghasvari-Jahromi, H., Gh Atefi, A. Moosaie, and S. Hormozi. "Analytical Solution of Turbulent Problems Using Governing Equation of Cosserat Continuum Model." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15837.

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In present paper the theory of the micropolar fluid based on a Cosserat continuum model has been applied for analysis of Couette flow and turbulent flow through rough pipes. The obtained results for the velocity field have been compared with known results from experiments done by Reichardt at Max Plank institute for fluids in Gottingen [1,2] and analytical solution of the problem from Gradient theory by alizadeh[3] for couette problem and with known results from experiments done by Nikuradse (1932). the boundary condition used here was the no slip one and Trostel's slip boundary condition[4].a good agreement between experimental results and the results of the problem for Reynolds near 18000 has beeen found in the couette case also in this case A new dimensionless number introduced that indicates the theoretical relation between cosserat theory and slip theory and their interaction. The solution has been performed for a Reynolds number of 106 for pipes with different values of roughness and the validity analysis approved by the results of Nikuradse's experiments.

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