The flow due to these singularities is useful for understanding and studying microscale flows. They belong to a class of fluids with a nonsymmetric stress tensor. The fluid viscosity and thermal conductivity are assumed to be vary as inverse linear functions of temperature. The governing equations of motion, microrotation and energy are simplified with the help of suitable similarity transformations. Slip effects on heat and mass transfer in mhd micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction. Engineering systems and materials do experience heating or cooling of some kind during operation. Gangadhar 15 conclude that the local skin friction coefficient increases and local nusselt.
The system of odes is reduced to initial value problems ivps by employing the shooting method before. Unsteady unidirectional micropolar fluid flow sciencedirect. Recently effect of using micropolar fluid, nanofluid, etc. Our fluid flow experts would like to talk with you to learn about your specific products and the challenges you would like help with. Homogeneousheterogeneous reactions in micropolar fluid.
The solutions for the flow of micropolar fluid through an. The flow dynamics of nonnewtonian fluids can be described by nonlinear relationships between the shear stress and shear rate. In fluid dynamics, a secondary flow is a relatively minor flow superimposed on the primary flow, where the primary flow usually matches very closely the flow pattern predicted using simple. Who knows we just might be able to help you with your hardest problems. In the present article, the heat transfer rate and the fluid flow of a micropolar fluid along with temperature. It is shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. In this article, we reconsidered the problem of aurangzaib et al.
Oscillatory dissipative conjugate heat and mass transfer. Micropolar nanofluid is the extension of buongiornos model by considering the angular momentum effect on the fluid flow model. The original probelm refers to the following from book of theory and applications of micropolar fluids by grzegorz lukaszewicz. The flow and heat transfer of a micropolar fluid past a nonlinearly stretching plate is studied numerically, by taking into account the viscous dissipation effect. The influence of partial slip, thermal radiation, chemical reaction and temperaturedependent fluid properties on heat and mass transfer in hydromagnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and nonuniform heat sourcesink is studied. The problems of the flow of a viscous fluid past a micropolar fluid sphere and the flow of a micropolar fluid past a viscous fluid drop are discussed. 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. Computational micropolar fluid dynamicshagenpoiseuille flow. The general equations are these of conservation of momentum, mass, as well as one more equation of conservation of angular momentum. A significant amount of research on micropolar fluid flow and. The unsteady, twodimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. It considers the flow of a micropolar fluid between two parallel plates.
Autodesk is one of the worlds most innovative companies, working to solve some of the worlds most complex design solutions. Traditional newtonian fluids cannot precisely describe the characteristic of fluid with suspended particles. Pdf in this research, micropolar fluid flow of a porous plate due to linear. A mathematical study of nonnewtonian micropolar fluid in. Stagnation point flow of mhd micropolar fluid in the.
Analysis of the flow characteristics of the micropolar fluid has been done graphically by varying the reynolds number and the hartmann number. It has been observed from the figure 7 that an increase in micropolar parameter k results in slowing down of micromotion of fluid. In this research, micropolar fluid flow of a porous plate due to linear stretching is analyzed. A mathematical study of nonnewtonian micropolar fluid in arterial blood flow through composite stenosis r. Mhd micropolar fluid flow over a stretching permeable sheet in the presence of thermal radiation and thermal slip flow. The model developed by chaudhary and merkin fluid dyn. Also, kelson and desseaux 10 studied the flow of micropolar fluids on. The model of micropolar fluids introduced in 65 by c. A comprehensive overview of modern micropolar fluid mechanics and applications is provided. This paper considers the unsteady unidirectional flow of a micropolar fluid, produced by the sudden application of an arbitrary time dependent pressure gradient, between two parallel plates. The governing equations are transformed into a coupled nonlinear twopoints boundary value problem by a suitable similarity transformation. 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. It is assumed that the plate is stretched nonlinearly from the slot where it is issued. Heat transfer in a micropolar fluid over a stretching sheet with.
Recently, elaziz 14 studied the mixed convection flow of a micropolar fluid from an unsteady stretching surface with viscous dissipation. This paper is concerned with the effect of slip velocity on the steady twodimensional flow of a micropolar fluid near a stagnation point at a stretching plate in the presence of a uniform transverse magnetic field and thermal radiation with the bottom surface of. Engineering fluid flows and heat transfer analysis. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented or spherical particles. New fundamental solutions for micropolar fluids have been obtained in explicit form by considering stokes and oseen flows due to. The sheet coincides with the plane y0 and flow is confined in the region y 0. Ali and hayat 4 discussed the peristaltic flow of a micropolar fluid in an asymmetric channel. The micropolar fluid flow theory enables accurate computation of flows in a scale.
Perturbation solutions for a micropolar fluid flow in a semiinfinite. The micropolar theory of the eringen 1 has a unique feature of modelling a wide variety of problems of fluid flow as it is trying to apply to the porous bearing with single and double layer. The governing system of partial differential equations is transformed into ordinary differential equations, which are then solved numerically. Department of mathematics, kalyani government engineering college, kalyani, nadia, west bengal, india. As an application, the drag coefficients for a solid sphere or a circular cylinder that translates in a lowreynoldsnumber micropolar flow are determined and compared with those corresponding to newtonian flow. System of six nonlinear coupled differential equations has been solved analytically with the help of strong analytical tool known as homotopy analysis method.
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. The relevant partial differential equations have been reduced to ordinary differential equations. Numerical solution of mhd flow of micropolar fluid with. In this paper, we have presented the axisymmetric stagnation flow of a micropolar fluid in a moving cylinder. The expressions for the stream functions, velocities, spins and the drag are obtained in each case and are compared with the classical viscous fluid past a viscous fluid sphere results. Conclusion this workinvestigates the flow of an incompressible micropolar fluid between eccentrically placed disks. Micropolar fluid flow with temperaturedependent transport. Motivated by emerging applications in this area, the present article studies timedependent free convective flow of a chemically reacting micropolar fluid from a vertical plate oscillating in its own plane adjacent to a porous medium. Dual solutions and stability analysis of micropolar. Gamal and rahman 6 studied the effect of mhd on thin film of a micropolar fluid and they investigated that the rotation of microelement at the boundary increase the velocity when compared with the case. Mixed convective flow of micropolar nanofluid across a horizontal. 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. This work was supported by the research program international research common laboratory in cooperation.
Mhd peristaltic transport of a micropolar fluid in an. Hydromagnetic hiemenz slip flow of convective micropolar. Rathish kumar and peeyush chandra department of mathematics and statistics. It is found that the viscosity ratios and the parameters. This article looks at the steady flow of micropolar fluid over a stretching surface with heat transfer in the presence of newtonian heating. A number of powerful numerical methods including finite element methods, homotopy analysis methods, network simulation and differential transform methods are then applied to specific steady flow scenarios. Micropolar fluids formulated by eringen include certain microscopic effects arising from the local structure and micromotions of the fluid elements and provide a mathematical model for the nonnewtonian fluid flow behaviour such as. Axisymmetric stagnation flow of a micropolar fluid in a. The dimensionless fluid equations are solved by using homotopy analysis method ham and validated with runge. The special issue on engineering fluid flows and heat transfer analysis of the journal diffusion foundations presents.
Micropolar fluid flow and heat transfer over a nonlinearly. Effects of variable viscosity and thermal conductivity on. The governing equations of boundary layer micropolar nanofluid flow 8,9,10,11 subject to boundary conditions 12 are solved by shooting method with help of maple software. An exact solution representing the different flow characteristic of micropolar fluid has been derived by solving the ordinary differential equations. A mathematical model has been developed to examine the magneto hydrodynamic micropolar nanofluid flow with buoyancy effects. The transverse magnetic field is assumed as a function of the distance from the origin. The reduced ordinary differential equation system has been numerically solved by rungekuttafehlberg fourthfifth order method. Mathematical analysis of magnetohydrodynamic mhd flow of. Micropolar theory is a higherorder theory for fluid.
The paper investigates the numerical solution of problem of magnetohydrodynamic mhd micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate. In this paper, asymptotic solutions are constructed for the flow of a micropolar fluid through an expanding or contracting porous pipe. Finally, part iii is devoted to selected applications of micropolar fluids lubrication theory, porous media, exact solutions for poiseuille and couette flows, comparison of solutions of the navierstokes and micropolar fluid models, a numerical algorithm, etc. Mhd mixed convection micropolar fluid flow through a. In this paper, we explore dual solutions of mhd flow, heat and mass transfer of micropolar nanofluid over a linear vertical shrinking surface with buoyancy effects, which was not considered in the previous works. Stability analysis and dual solutions of micropolar.
Micropolar fluid flow modelling using the boundary element. A comprehensive investigation of mass and heat transfer in magnetohydrodynamics mhd flow of an electrically conducting nonnewtonian micropolar fluid because of curved stretching sheet is presented. Exact solution of micropolar fluid for poiseuille flow. Mhd flow of micropolar fluids over a shrinking sheet with. Let us consider the steady two dimensional mhd free convection and mass transfer micropolar fluid flow past a semiinfinite vertical porous plate y 0. Micropolar fluid behaviors on steady mhd free convection.
In this study, we consider both strong concentrations n 0 and weak concentrations n 12. Study of the couple stress convective micropolar fluid flow in a. Without loss of generality, the point force is placed at the origin, and the freestream velocity u. Pdf theory and simulation of micropolar fluid dynamics. Heat transfer in a micropolar fluid over a stretching. Paper presented at the 8th international conference on heat transfer, fluid mechanics and thermodynamics, mauritius, 11 july, 2011. Eringen is worth studying as a very well balanced one. Raza j, rohni am, omar z, awais m, heat and mass transfer analysis of mhd nanofluid flow in a rotating channel with slip effects, j mol liq 219. Each material point is a finite size particle, which contains 6. Pdf investigation of micropolar fluid flow and heat transfer in a two. Modelling and theoretical analysis of heat transfer problems will enhance the functional success of the materials and enable new product development in engineering. Slip effects on heat and mass transfer in mhd micropolar. The results of the momentum, angular velocity, temperature and concentration profiles are demonstrated graphically for different values of various physical parameters such. Micropolar fluid flow modelling using the boundary element method.
Mhd stagnation point flow of a micropolar fluid over a. Mhd flow of the micropolar fluid between eccentrically. Unsteady forced bioconvection slip flow of a micropolar. Using similarity transformations the governing partial differential equations of motion are reduced to. The governing equations have been transformed into nonlinear ordinary differential equations by applying the. The xaxis is taken along the heated plate in the upward direction and the yaxis normal to it. Triple solutions and stability analysis of micropolar. Buoyancy effects on the radiative magneto micropolar. This is the first example of computational micropolar fluid dynamics cmfd. Vafai4 1 department of mathematics and statistics, iiui, islamabad, pakistan 2 nust college of electrical and mechanical engineering, islamabad, pakistan. Figure 7 represents the variation of micromotion of fluid with micropolar parameter. Heat transfer issues in micropolar fluids flow have been analyzed by perdikis. Second order slip flow of a mhd micropolar fluid over an.
Research article analytical and numerical study of. Micropolar fluids consist of rigid, randomly oriented or spherical particles with their own spins and microrotations, suspended in a viscous medium. Pdf analytical and numerical study of micropolar fluid flow in a. High temperature nonnewtonian materials processing provides a stimulating area for process engineering simulation. 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. The micropolar fluid flow over a shrinking sheet with mass suction is steady, two dimensional and incompressible. The fluid flow is treated with strong magnetic field. Then, the behavior of an incompressible viscous fluid flow in a liddriven square cavity is investigated. Stokes and oseen flows of a micropolar fluid due to a point force consider a point force in an unbounded, quiescent, incompressible micropolar fluid. The micropolar fluid model describes the flow of fluids where the flow behaviour of microstructures affects entire flow. Theory and simulation of micropolar fluid dynamics j chen, c. Fluidis electrically conducting and a uniform magnetic field of.
Study of heat and mass transfer in mhd flow of micropolar. The governing fluid flow equations of this problem are transformed into nonlinear boundary value problems bvps of ordinary differential equations odes by applying similarity. Comparison between results of flexpde software and analytical. Without loss of generality, the point force is placed at the origin, and the freestream velocity u f is taken to be u f,0,0. Mhd micropolar fluid flow over a stretching permeable sheet in the. Application of differential transformation method in micropolar fluid. The system of governing equations has been transformed into the system of nonlinear ordinary differential equations odes by using exponential similarity transformation. Journal of nanomaterials, nanoengineering and nanosystems 2015 230. The noslip and the nospin boundary conditions are used. 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 present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. This model is derived from the navierstokes model and takes into account rotation of particles molecules independently of the fluid flow and its local vorticity field.
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