Kucabapietal department of fluid mechanics and aerodynamics, rzeszow university of technology 8 powstancow warszawy st. Slip effects on heat and mass transfer in mhd micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction. 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. 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 problem of micropolar fluid flow in a channel subject to a chemical reaction is presented. 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.
A micropolar fluid is the fluid with internal structures in. Physically, it represents a fluid consisting of randomly oriented. 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. The micropolar fluid model is a generalization of the classical navierstokes equations, which are typically used in computer graphics to simulate fluids. Rees and pop 6 studied the free convection boundary layer flow of micropolar fluid from a vertical flat plate.
The governing equations involve the fluid and micropolar velocities respectively. The theory of micropolar fluids introduced by eringen 1 is one of the best theories of fluids to describe the. Micropolar fluid behaviors on steady mhd free convection and. Heat and mass transfer analysis on the flow of non newtonian. 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. 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. Stokes and oseen flows of a micropolar fluid due to a point force consider a point force in an unbounded, quiescent, incompressible micropolar fluid. Micropolar fluids consist of rigid, randomly oriented or spherical particles with their own. Effects of homogeneous and heterogeneous chemical reactions. Vafai4 1 department of mathematics and statistics, iiui, islamabad, pakistan 2 nust college of electrical and mechanical engineering, islamabad, pakistan. In last few decades, the research interest in micropolar fluid theory has significantly increased due to its enormous applications in many industrial processes. The solutions for the flow of micropolar fluid through an. Natural convection in a micropolar fluid with thermal dispersion and internal heat generation investigate tby elhakiem 2004.
The rotatory flow of the fluid has special applications in various. The importance of boundary layer flow of micropolar fluid and heat transfer over an exponentially permeable shrinking sheet is analysed. Pdf download for theory and simulation of micropolar fluid. 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. In this paper, we have presented the axisymmetric stagnation flow of a micropolar fluid in a moving cylinder. Influence of magnetic field on the flow of micropolar fluid. Optimal and numerical solutions for an mhd micropolar.
The effects of material parameters on the velocities, temperature and concentration are discussed. A boundary layer approach in the modelling flows in. The micropolar fluid model is a generalization of the classical navier stokes equations, which are typically used in computer graphics to simulate fluids. 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. Pdf the micropolar fluid model for blood flow through a. Mhd flow of micropolar fluids over a shrinking sheet with. Heat and mass transfer analysis on the flow of non.
In last few decades, the research interest in micropolar fluid theory has significantly increased due to its. This paper deals with the unsteady free convection and mass transfer flow of micropolar fluid embedded in a porous media. Momentum equations for micropolar fluid physics stack exchange. Heat transfer in a micropolar fluid over a stretching sheet. 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. The governing equations of motion, microrotation and energy are simplified with the help of suitable similarity transformations. These pdf merging software offer various features, like.
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 effect of small and large peclet numbers on the temperature and concentration profiles is determined while. The similarity approach is adopted and selfsimilar ordinary differential equations are obtained and then those are solved numerically using very efficient shooting method. The problem of micropolar fluid n the presence of transverse magnetic field finds application in nuclear engineering and other fields. This article looks at the steady flow of micropolar fluid over a stretching surface with heat transfer in the presence of newtonian heating. The governing equations are transformed into a coupled nonlinear twopoints boundary value problem by a suitable similarity transformation. Steady flow of a micropolar fluid between two rotating disks of infinite radius rotating at differentsame speeds has been investigated. The similarity approach is adopted and selfsimilar ordinary. The effect of rotation on generalized micropolar thermoelasticity for a halfspace under five theories has been discussed by. Singh 7 has studied the free convection flow of a micropolar fluid past an infinite vertical plate using the finite difference method. By using similarity transformation method, the equations of motion are reduced to a set of ordinary nonlinear coupled differential equations. The governing equations involve the fluid and micropolar velocities respectively, temperature and concentration fields. 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.
A micropolar material model for turbulent sph fluids. The effect of rotation on generalized micropolar thermoelasticity for a halfspace under five theories has been discussed by othman and singh 16. 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. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar. Homogeneousheterogeneous reactions in micropolar fluid flow.
Finite element analysis of heat and mass transfer of a mhd. Scaling transformation for free convection flow of a. Introduction micropolar fluids are well known as the fluids with. All these pdf joiners are completely free and can be downloaded to windows pc. 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. The rotatory flow of the fluid has special applications in various engineering fields such as mechanical, petroleum and chemical.
Heat and mass transfer in mhd micropolar fluid flow over a. Nanofluid and micropolar fluid flow over a shrinking sheet. Micropolar fluid flow in a vertical channel using hpm. Pdf theory and simulation of micropolar fluid dynamics. 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. Pdf a study of the convergence of weak solutions of the nonstationary micropolar fluids, in bounded domains of. Slip effects on heat and mass transfer in mhd micropolar.
Axisymmetric stagnation flow of a micropolar fluid in a. These pdf mergers let you merge multiple pdf files easily. Mhd, micropolar fluid flow, thermal radiation, nanofluid, shrinking sheet. Turbulent micropolar sph fluids with foam dan koschier. Hassanien and gorla 6 numerically studied the effects of suction and blowing on the flow and heat transfer of a micropolar. Mhd flow of the micropolar fluid between eccentrically. Effects of thermal radiation on magnetohydrodynamic mhd. In contrast to the classical navierstokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. Heat transfer from moving surfaces in a micropolar fluid with. 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.
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. Theory and simulation of micropolar fluid dynamics j chen, c. Microchannels flow modelling with the micropolar fluid. The steady mhd mixed convection flow towards a vertical stretching surface immersed in an incompressible micropolar fluid was investigated by ishak et al. They belong to a class of fluids with a nonsymmetric stress tensor. 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. Flow of a micropolar fluid in channel with heat and mass transfer. The lower and upper disks rotate with angular velocities. 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. Guram and anwar 10 considered the steady, laminar and incompressible flow of a micropolar fluid due to a rotating disk with suction and injection. Introduction micropolar fluids are well known as the fluids with microstructure. First, it is a wellfounded and significant generalization of the classical navierstokes.
Eringen is worth studying as a very well balanced one. Micropolar fluids theory and applications grzegorz. Mhd stagnation point flow of a micropolar fluid over a. Flow and heat transfer of two micropolar fluids 25 or coarse grain structure fall in this category. Pdf micropolar fluids with vanishing viscosity researchgate. Magnetohydrodynamic micropolar fluid flow in presence of. The reduced ordinary differential equation system has been numerically solved by rungekuttafehlberg fourthfifth order method.
The relevant partial differential equations have been reduced to. In addition to the geophysical fluid dynamic which helps in explaning the. Micropolar fluids consist of rigid, randomly oriented or spherical particles with their own spins and microrotations, suspended in a viscous medium. 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. Muthu, et al 17 have analyzed the peristaltic motion of 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 presence of a small amount of additives in the fluid significantly lower down the skin friction near a. 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 relevant partial differential equations have been reduced to ordinary differential equations.
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. Micropolar fluid is a nonnewtonian fluid that belongs to a class of fluids with nonsymmetrical stress tensor and is referred to as polar fluid. Unsteady free convection and mass transfer flow of micropolar. The derived model exactly matches the nonsteady linearized micropolar fluid flow model small gyrations and velocity distributions, giving. Micropolar fluid flow and heat transfer over an exponentially. 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. Unsteady free convection and mass transfer flow of. New fundamental solutions for micropolar fluids have.
The governing equations of motion, microrotation and energy are simplified with the. Physically, it represents a fluid consisting of randomly oriented particles suspended in a for the rotation of fluid particles by means of an independent. 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. Paper presented at the 8th international conference on heat transfer, fluid mechanics and thermodynamics, mauritius, 11 july, 2011. The unsteady, twodimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. Falknerskan solution for gravitydriven film flow of a. The model of micropolar fluids introduced in 65 by c. Peristaltic transport of micropolar fluid in a tubes under. Rathish kumar and peeyush chandra department of mathematics and statistics. Dynamic performance characteristics of misaligned hybrid. 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 present problem is concerned with the flow of micropolareringen fluid sandwiched between two newtonian fluid layers through the horizontal. A mathematical study of nonnewtonian micropolar fluid in arterial blood flow through composite stenosis r. Mhd stagnationpoint flow over a stretchingshrinking.
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