They belong to a class of fluids with a nonsymmetric stress tensor. Corresponding results for twodimensional flows are also presented. The unsteady, twodimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. Electrohydrodynamic convection in a rotating dielectric. Heat and mass transfer in mhd micropolar fluid flow over a. Micropolar fluid flow over a stretching sheet wiley online library. Homogeneousheterogeneous reactions in micropolar fluid flow. In this paper, we deal with the study of the effect of magnetohydrodynamic on thin films of unsteady micropolar fluid through a porous medium. Micropolar fluid behaviors on steady mhd free convection. Also, the influences of temperature dependent viscosity, thermal radiation and nonuniform heat generationabsorption and chemical reaction of a general order are examined on. This manuscript addresses a numerical work describing the flow of a micropolar fluid in a porous medium under the influence of thermophoresis. The steady mhd mixed convection flow towards a vertical stretching surface immersed in an incompressible micropolar fluid was investigated by ishak et al. Navierstokes equation, does not account for the rotational effects of the fluid microconstituents. The similarity approach is adopted and selfsimilar ordinary differential equations are obtained and then those are solved numerically using very efficient shooting method.
Kucabapietal department of fluid mechanics and aerodynamics, rzeszow university of technology 8 powstancow warszawy st. Micropolar fluid is a nonnewtonian fluid that belongs to a class of fluids with nonsymmetrical stress tensor and is referred to as polar fluid. The micropolar nonnewtonian fluid is assumed to be steady, incompressible, and dilute. The micropolar fluid flow over a shrinking sheet with mass suction is steady, two dimensional and incompressible. The theory of micropolar fluids was first introduced by erinqrn. Fluidis electrically conducting and a uniform magnetic field of. Mhd flow of micropolar fluids over a shrinking sheet with.
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. Unsteady free convection and mass transfer flow of. Numerous applications of stagnation flows in engineering and scientific interest have attracted the attention of number of researchers 15. 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 sheet coincides with the plane y0 and flow is confined in the region y 0. Flow of a micropolar fluid bounded by a stretching sheet. Introduction micropolar fluids are a subset of the micromorphic fluid theory introduced in a pioneering paper by eringen1. Thermal convection of a rotating dielectric micropolar fluid layer under the action of an electric field and temperature gradient has been investigated. Global classical large solution to compressible viscous.
They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar. The effects of material parameters on the velocities, temperature and concentration are discussed. The relevant partial differential equations have been reduced to ordinary differential equations. However, as a result of diverse fluid characteristics in nature, all the nonnewtonian fluids cannot be captured by a single constitutive model, hence, different models of nonnewtonian fluids have been formulated such as casson fluid, jeffery fluid, maxwell fluid, ostwald dewaele power law fluid and micropolar fluids chen et al. Effects of chemical reaction on magnetomicropolar fluid flow. Pdf theory and simulation of micropolar fluid dynamics. A mathematical study of nonnewtonian micropolar fluid in arterial blood flow through composite stenosis r. Peristaltic transport of micropolar fluid in a tubes under. The governing equations are transformed into a coupled nonlinear twopoints boundary value problem by a suitable similarity transformation.
Pdf on the micropolar fluid flow through porous media. Hamdan3 1,3 department of mathematical sciences 2 department of engineering university of new brunswick p. The fluid motion is due to a constant pressure gradient, and an external uniform magnetic field. The fluid motion is due to a constant pressure gradient, and an external uniform magnetic field directed perpendicular to the flow direction is applied. Rathish kumar and peeyush chandra department of mathematics and statistics. 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. If the inline pdf is not rendering correctly, you can download the pdf file here. Flow of a micropolar fluid in channel with heat and mass. In this paper we consider the nonstationary 1d flow of a compressible viscous and heatconducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. Homotopy analysis of mhd free convective micropolar fluid. 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. Thia garajan considered a semi analytical investigation on mhd micropolar fluid and.
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. Numerical solution of the thermal instability in micropolar fluid layer between rigid boundaries. The governing nonsimilar boundary layer equations are analyzed using the i series. Stokes and oseen flows of a micropolar fluid due to a point force consider a point force in an unbounded, quiescent, incompressible micropolar fluid.
I to model fluids with micmructureslwhich cannot be ade quately described by the classical. Axisymmetric stagnation flow of a micropolar fluid in a. Pabula, ifce effect of additives on fluid friction u. A micropolar material model for turbulent sph fluids.
Magnetohydrodynamic convective flow and heat transfer of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generationabsorption with constant suction has been analyzed numerically. Steady magnetohydrodynamic flow of an incompressible micropolar fluid through a pipe of circular crosssection is studied by considering hall and ionic effects. 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. The importance of boundary layer flow of micropolar fluid and heat transfer over an exponentially permeable shrinking sheet is analysed.
The similarity approach is adopted and selfsimilar ordinary differential equations are obtained and then those are solved. Effect of magnetohydrodynamic on thin films of unsteady. The reduced ordinary differential equation system has been numerically solved by rungekuttafehlberg fourthfifth order method. Vafai4 1 department of mathematics and statistics, iiui, islamabad, pakistan 2 nust college of electrical and mechanical engineering, islamabad, pakistan. Momentum equations for micropolar fluid physics stack exchange. The present paper considers the flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using. At the present moment the theory of cosserats is in the full development. Thin film flow of micropolar fluid in a permeable medium mdpi. Mhd stagnation point flow of a micropolar fluid over a. The aim of this paper is to study the applicability of the theory of micropolar fluids to modelling and calculating flows in mi.
This procedure has gained popularity since the introduction of averaging theorems, cf. This article investigates the twodimensional creeping flow of a non newtonian micropolar fluid in a small width permeable channel. System of six nonlinear coupled differential equations has been solved analytically with the help of strong analytical tool known as homotopy analysis method. Hydrodynamical study of micropolar fluid in a porouswalled. 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. Mhd flow of the micropolar fluid between eccentrically. The governing continuity, momentum and angular momentum equations are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. 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. The cartesian coordinate system is xyz, and the corresponding velocity components are uv,0.
Pdf field equations governing the steady flow of an incompressible micropolar fluid through isotropic porous sediments are derived using intrinsic. Scaling transformation for free convection flow of a. 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 time. A mathematical study of nonnewtonian micropolar fluid in. Heat transfer in a micropolar fluid over a stretching. The effect of rotation on generalized micropolar thermoelasticity for a halfspace under five theories has been discussed by othman and singh 16.
Micropolar fluid behaviors on steady mhd free convection and. With appropriate transformations the boundary layer equations are transformed into nonlinear ordinary differential equations. Magnetohydrodynamic convective flow of a micropolar fluid. Effects of homogeneous and heterogeneous chemical reactions. This article looks at the steady flow of micropolar fluid over a stretching surface with heat transfer in the presence of newtonian heating. 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 effect of small and large peclet numbers on the. Fundamental solutions for micropolar fluids springerlink. On the micropolar fluid flow through porous media m. Mhd, micropolar fluid flow, thermal radiation, nanofluid, shrinking sheet.
Let us consider the steady two dimensional mhd free convection and mass transfer micropolar fluid flow past a semiinfinite vertical porous plate y 0. Pdf numerical study of mixed bioconvection associated. These thin films are considered for three different geometries. The problem of micropolar fluid flow in a channel subject to a chemical reaction is presented. Homogeneousheterogeneous reactions in micropolar fluid. Guram and anwar 10 considered the steady, laminar and incompressible flow of a micropolar fluid due to a rotating disk with suction and injection. 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. Increasing interest in polar fluid flow through and over porous surfaces is witnessed by the large number of recent studies which deal with deriving appropriate models of flow through porous structures, 11, analyzing flow in various porous settings, and modeling the boundary layer flow of a polar fluid over a porous surface or inside a porous. The xaxis is taken along the heated plate in the upward direction and the yaxis normal to it. Effects of chemical reaction on magnetomicropolar fluid. The model developed by chaudhary and merkin fluid dyn. Flow of a micropolar fluid bounded by a stretching sheet the pdf file you selected should load here if your web browser has a pdf reader plugin installed for example, a recent version of adobe acrobat reader if you would like more information about how to print, save, and work with pdfs, highwire press provides a helpful frequently asked questions about pdfs. Muthu, et al 17 have analyzed the peristaltic motion of micropolar fluid in. Slow motion of spherical droplet in a micropolar fluid flow perpendicular to a planar solid surface.
The model of micropolar fluids introduced in 65 by c. In contrast to the classical navierstokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. The governing equations involve the fluid and micropolar velocities respectively, temperature and concentration fields. Thermal instability in a micropolar fluid layer subjected to a magnetic field. We have applied the hodograph transformation method to convert the governing nonlinear. Umavathi studied mixed convection flow of a micropolar fluid 12 with concentration in a vertical channel in the presence of heat source or sink. Microchannels flow modelling with the micropolar fluid. Finite element analysis of heat and mass transfer of a mhd.
Nanofluid and micropolar fluid flow over a shrinking sheet. The micropolar fluid model is a generalization of the classical navier stokes equations, which are typically used in computer graphics to simulate fluids. Numerical study of viscoelastic micropolar heat transfer. Thermal radiation effects on magnetohydrodynamicmixed convection flow of a micropolar fluid past a continuously moving semiinfinite plate for high temperature differences. Micropolar fluid flow in a vertical channel using hpm. Heat transfer in a micropolar fluid over a stretching sheet. This article investigates the twodimensional creeping flow of a nonnewtonian micropolar fluid in a small width permeable channel. This study presents the problem of a steady, twodimensional, heat and mass transfer of an incompressible, electrically conducting micropolar fluid flow past a stretching surface with velocity and thermal slip conditions.
Here one should also mention the generalizing work by a. The formulation for micropolar fluid theory allows their implementation in boundary layer flows, of relevance to materials processing, and has resulted in considerable activity among researchers. In some situations flow is stagnated by a solid wall, while in others a free stagnation point or line exist interior to the fluid domain. 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. 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. New fundamental solutions for micropolar fluids are derived in explicit form for two and threedimensional steady unbounded stokes and oseen flows due to a point force and a point couple, including the twodimensional micropolar stokeslet, the two and threedimensional micropolar stokes couplet, the threedimensional micropolar oseenlet, and the threedimensional micropolar oseen couplet. The dispersion relation has been derived using normal mode analysis. A micropolar fluid is the fluid with internal structures in. Nowacki the linear theory of micropolar elasticity theory have also been derived by e. The xaxis is directed towards the continuous stretching sheet along the flow while the yaxis is normal to it. Pdf numerical study of mixed bioconvection associated with. The governing equations of motion, microrotation and energy are simplified with the help of suitable similarity transformations.
Micropolar fluids are those consisting of randomly oriented particles suspended in a viscous. 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 paper. In this paper, we have presented the axisymmetric stagnation flow of a micropolar fluid in a moving cylinder. Bitterson, an experimental investigation of the effect of additives injected into the boundary layer of an underwater. Micropolar fluid flow and heat transfer over an exponentially. This paper deals with the unsteady free convection and mass transfer flow of micropolar fluid embedded in a porous media. In last few decades, the research interest in micropolar fluid theory has significantly increased due to its enormous applications in many industrial processes. Eringen is worth studying as a very well balanced one. Physically, it represents a fluid consisting of randomly oriented particles suspended in a for the rotation of fluid particles by means of an independent. Optimal and numerical solutions for an mhd micropolar. The solutions for the flow of micropolar fluid through an. In this paper we have considered the flow of a steady, homogenous, incompressible, plane micropolar fluid through a porous medium. The the presence of the nanoparticles is assumed to not affect the direction and swimming velocity of. Micropolar fluids consist of rigid, randomly oriented or spherical particles with their own spins and microrotations, suspended in a viscous medium.226 1609 1162 59 566 517 449 83 888 86 295 151 42 1456 36 1028 247 144 1077 343 461 1245 1445 581 1142 610 1586 916 644 362 1683 62 1313 1668 71 1215 1629 1188 1534 541 1453 1273 50 218 1131 354