The problem of micropolar fluids past through a porous media has many applications, such as, porous rocks, foams and foamed solids, aerogels, alloys, polymer blends and. A mathematical study of nonnewtonian micropolar fluid in. Hassanien and gorla 6 numerically studied the effects of suction and blowing on the flow and heat transfer of a micropolar fluid over a nonisothermal stretching surface. The model of micropolar fluids introduced in 65 by c. Pdf a study of the convergence of weak solutions of the nonstationary micropolar fluids, in bounded domains of.
The relevant partial differential equations have been reduced to ordinary differential equations. They belong to a class of fluids with a nonsymmetric stress tensor. By using similarity transformation method, the equations of motion are reduced to a set of ordinary nonlinear coupled differential equations. The problem of micropolar fluids past through a porous media has many applications, such as, porous rocks, foams and foamed solids, aerogels, alloys, polymer blends and micro emulsions. The governing equations are transformed into a coupled nonlinear twopoints boundary value problem by a suitable similarity transformation. As pointed out by rawat and bhargava 11, the study of heat and mass transfer in micropolar fluids is of importance in the fields of chemical engineering, aerospace engineering and also industrial manufacturing effects processes. Micropolar fluids consist of rigid, randomly oriented or spherical particles with their own spins and microrotations, suspended in a viscous medium.
The presence of a small amount of additives in the fluid significantly lower down the skin friction near a. Homogeneousheterogeneous reactions in micropolar fluid flow. First, it is a wellfounded and significant generalization of the classical navierstokes. In last few decades, the research interest in micropolar fluid theory has significantly increased due to its enormous applications in many industrial processes. Mhd flow of the micropolar fluid between eccentrically. In contrast to the classical navierstokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. Unsteady free convection and mass transfer flow of micropolar. Turbulent micropolar sph fluids with foam dan koschier.
New fundamental solutions for micropolar fluids have. Pdf the micropolar fluid model for blood flow through a. A mathematical study of nonnewtonian micropolar fluid in arterial blood flow through composite stenosis r. Theory and simulation of micropolar fluid dynamics j chen, c. The governing equations of motion, microrotation and energy are simplified with the help of suitable similarity transformations. A boundary layer approach in the modelling flows in. However, as a result of diverse fluid characteristics in nature, all the non newtonian fluids cannot be captured by a single constitutive model, hence, different models of nonnewtonian fluids have been formulated such as casson fluid, jeffery fl uid, maxwell fluid, ostwald dewaele power law fluid and micropolar fluids chen et al. Pdf theory and simulation of micropolar fluid dynamics. The problem of micropolar fluid n the presence of transverse magnetic field finds application in nuclear engineering and other fields. First, it is a wellfounded and significant generalization of the classical navierstokes model, covering, both in theory and applications, many more phenomena than the classical one. Mhd, micropolar fluid flow, thermal radiation, nanofluid, shrinking sheet. The governing equations of motion, microrotation and energy are simplified with the.
Muthu, et al 17 have analyzed the peristaltic motion of micropolar fluid in. Rees and pop 6 studied the free convection boundary layer flow of micropolar fluid from a vertical flat plate. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the wellestablished navier. The relevant partial differential equations have been reduced to. Thus the concept of micropolar fluid which was first proposed by eringen 1966 has taken into account the microstructure of the fluid and the physical characteristics of the fluid itself, i. The steady mhd mixed convection flow towards a vertical stretching surface immersed in an incompressible micropolar fluid was investigated by ishak et al. Introduction micropolar fluids are well known as the fluids with microstructure. The effect of rotation on generalized micropolar thermoelasticity for a halfspace under five theories has been discussed by. Vafai4 1 department of mathematics and statistics, iiui, islamabad, pakistan 2 nust college of electrical and mechanical engineering, islamabad, pakistan. The micropolar fluid model is a generalization of the classical navierstokes equations, which are typically used in computer graphics to simulate fluids. These pdf merging software offer various features, like. Guram and anwar 10 considered the steady, laminar and incompressible flow of a micropolar fluid due to a rotating disk with suction and injection.
Peristaltic transport of micropolar fluid in a tubes under. The problem of micropolar fluid flow in a channel subject to a chemical reaction is presented. Moreover, it is elegant and not too complicated, in other words, man ageable to both mathematicians who study its theory and physicists and engineers who apply it. Nanofluid and micropolar fluid flow over a shrinking sheet. Mhd flow of micropolar fluids over a shrinking sheet with. Physically, it represents a fluid consisting of randomly oriented. Dynamic performance characteristics of misaligned hybrid. All these pdf joiners are completely free and can be downloaded to windows pc. Stokes and oseen flows of a micropolar fluid due to a point force consider a point force in an unbounded, quiescent, incompressible micropolar fluid. Momentum equations for micropolar fluid physics stack exchange. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar. The governing equations involve the fluid and micropolar velocities respectively, temperature and concentration fields. The micropolar fluid behavior on steady mhd free convection and mass transfer flow past a semiinfinite vertical porous plate with constant heat and mass fluxes, the diffusion thermo, thermal diffusion. The effect of rotation on generalized micropolar thermoelasticity for a halfspace under five theories has been discussed by othman and singh 16.
The present problem is concerned with the flow of micropolareringen fluid sandwiched between two newtonian fluid layers through the horizontal. The above equations can be rewritten for an incompressible steady micropolar fluid in the presence of mhd neglecting the body forces and couple terms through the space between two noncoaxial disks and takes the form as follows. Scaling transformation for free convection flow of a. The reduced ordinary differential equation system has been numerically solved by rungekuttafehlberg fourthfifth order method. New fundamental solutions for micropolar fluids have been obtained in explicit form by considering stokes and oseen flows due to a point force and a point couple. Steady flow of a micropolar fluid between two rotating disks of infinite radius rotating at differentsame speeds has been investigated. Unsteady free convection and mass transfer flow of. Micropolar fluids consist of rigid, randomly oriented or spherical particles with their own. The above equations can be rewritten for an incompressible steady micropolar fluid in the presence of mhd neglecting the body forces and couple terms through the space between two. Introduction micropolar fluids are well known as the fluids with. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the wellestablished navierstokes model of classical fluids that we shall call ordinary fluids. The effect of small and large peclet numbers on the temperature and concentration profiles is determined while.
Let there be periodic injection or suction at the lower and upper plates and the nonuniform temperature and concentration at the plates are varying periodically with. In this paper, we have presented the axisymmetric stagnation flow of a micropolar fluid in a moving cylinder. This paper deals with the unsteady free convection and mass transfer flow of micropolar fluid embedded in a porous media. Flow of a micropolar fluid in channel with heat and mass transfer. The derived model exactly matches the nonsteady linearized micropolar fluid flow model small gyrations and velocity distributions, giving analytical interpretation of typical micropolar empirical coefficients in terms of a knudsen number and a time characteristic constant. Effects of homogeneous and heterogeneous chemical reactions. Rathish kumar and peeyush chandra department of mathematics and statistics. Theory and simulation of micropolar fluid dynamics article pdf available in proceedings of the institution of mechanical engineers part n journal of nanoengineering and nanosystems 22412. The similarity approach is adopted and selfsimilar ordinary differential equations are obtained and then those are solved numerically using very efficient shooting method. Over decades, micropolar fluids have been the focus of research of many researchers working in the field of fluid mechanics owing to its practical applications in.
Mhd stagnationpoint flow over a stretchingshrinking. The presence of a small amount of additives in the fluid significantly lower down the skin friction near a rigid body and also the frictional drag is reduced by polymer concentration 1. Effects of thermal radiation on magnetohydrodynamic mhd. The importance of boundary layer flow of micropolar fluid and heat transfer over an exponentially permeable shrinking sheet is analysed. Sep 01, 2016 in this paper, we have presented the axisymmetric stagnation flow of a micropolar fluid in a moving cylinder. Optimal and numerical solutions for an mhd micropolar. These pdf mergers let you merge multiple pdf files easily. The micropolar fluid model is a generalization of the classical navier stokes equations, which are typically used in computer graphics to simulate fluids. Mhd stagnation point flow of a micropolar fluid over a. Corresponding results for twodimensional flows are also presented.
Micropolar fluids theory and applications grzegorz. This article looks at the steady flow of micropolar fluid over a stretching surface with heat transfer in the presence of newtonian heating. Slip effects on heat and mass transfer in mhd micropolar. Slip effects on heat and mass transfer in mhd micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction. Influence of magnetic field on the flow of micropolar fluid. This paper presents an incompressible twodimensional heat and mass transfer of an electrically conducting micropolar fluid flow in a porous medium between two parallel plates with chemical. The lower and upper disks rotate with angular velocities.
Heat transfer from moving surfaces in a micropolar fluid with. This paper presents an incompressible twodimensional heat and mass transfer of an electrically conducting micropolar fluid flow in a porous medium between two parallel plates with chemical reaction, hall and ion slip effects. Micropolar fluid flow in a vertical channel using hpm. Heat transfer in a micropolar fluid over a stretching sheet. Natural convection in a micropolar fluid with thermal dispersion and internal heat generation investigate tby elhakiem 2004. Flow and heat transfer of two micropolar fluids 25 or coarse grain structure fall in this category. The theory of micropolar fluids introduced by eringen 1 is one of the best theories of fluids to describe the. The unsteady, twodimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. Finite element analysis of heat and mass transfer of a mhd. A micropolar fluid is the fluid with internal structures in.
The solutions for the flow of micropolar fluid through an. As pointed out by rawat and bhargava 11, the study of heat and mass transfer in micropolar fluids is of importance in the fields of chemical. Heat and mass transfer analysis on the flow of non newtonian. Micropolar fluid behaviors on steady mhd free convection and. The rotatory flow of the fluid has special applications in various engineering fields such as mechanical, petroleum and chemical.
Kucabapietal department of fluid mechanics and aerodynamics, rzeszow university of technology 8 powstancow warszawy st. Eringen is worth studying as a very well balanced one. Paper presented at the 8th international conference on heat transfer, fluid mechanics and thermodynamics, mauritius, 11 july, 2011. A micropolar material model for turbulent sph fluids. Microchannels flow modelling with the micropolar fluid.
The governing equations involve the fluid and micropolar velocities respectively. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented or spherical particles suspended in a viscous medium, where the deformation of fluid particles is ignored. Later, the problem of stagnationpoint flow in a micropolar fluid was extended in numerous ways to include. Axisymmetric stagnation flow of a micropolar fluid in a. Pdf download for theory and simulation of micropolar fluid. Micropolar fluid flow and heat transfer over an exponentially. To the best of authors knowledge, the flow of micropolar fluid over a stretching sheet with heat transfer in the presence of newtonian heating has not been addressed so far. The effects of material parameters on the velocities, temperature and concentration are discussed. The rotatory flow of the fluid has special applications in various. In last few decades, the research interest in micropolar fluid theory has significantly increased due to its. The similarity approach is adopted and selfsimilar ordinary.
The effects of a homogeneousheterogeneous reaction on steady micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium are numerically investigated in this. In addition to the geophysical fluid dynamic which helps in explaning the. Heat and mass transfer in mhd micropolar fluid flow over a. The micropolar fluid model for blood flow through a tapered artery with a stenosis article pdf available in acta mechanica sinica 246. Singh 7 has studied the free convection flow of a micropolar fluid past an infinite vertical plate using the finite difference method. Heat and mass transfer analysis on the flow of non. The micropolar fluid behavior on steady mhd free convection and mass transfer flow past a semiinfinite vertical porous plate with constant heat and mass fluxes, the diffusion thermo, thermal diffusion, viscous dissipation and joule heating have been studied under the action of a transverse magnetic field. The derived model exactly matches the nonsteady linearized micropolar fluid flow model small gyrations and velocity distributions, giving. Micropolar fluid is a nonnewtonian fluid that belongs to a class of fluids with nonsymmetrical stress tensor and is referred to as polar fluid. Physically, it represents a fluid consisting of randomly oriented particles suspended in a for the rotation of fluid particles by means of an independent. Magnetohydrodynamic micropolar fluid flow in presence of. Hassanien and gorla 6 numerically studied the effects of suction and blowing on the flow and heat transfer of a micropolar.
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