Pdf couple stress fluid flow with variable properties. In continuum mechanics, the cauchy stress tensor, true stress tensor, or simply called the stress tensor is a second order tensor named after augustinlouis cauchy. Pulsatile flow of couple stress fluid through a porous medium with periodic body acceleration and magnetic field was presented by rathod et al. Couple stress fluid theory is a simple generalization of the classical theory of viscous newtonian fluids that allow the sustenance of couple stresses and body couples in the fluid medium. Couple stress is the culmination of an assumption that.
Nonisothermal analysis of a couple stress fluid in blade. This paper aims at presenting exact solutions for mhd flow of couple stress fluid with heat transfer. The basic theory and constitutive equations for couple stress fluid initially developed by stokes, is one amongst the polar fluid theories which consider couple stresses in addition to the classical cauchy stresses. A theoretical analysis of rolloverweb coating of couple. Consider the mixed convective laminar couple stress fluid flow with. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous newtonian fluid. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration.
There is a porous lining attached to the inside of an outer cylinder. In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steadystate of the present flow are developed. With the help of bessels functions, analytic expressions for axial velocity, flow rate, impedance, and wall shear stress have been obtained. A general expression is derived for the drag experienced by an axially symmetric body in the slow steady flow of stokes couple stress fluids. International communication in heat and mass transfer, vol. This article presents the mhd flow and heat transfer of a couple stress fluid over oscillatory stretching sheet embedded in a porous medium in the presence of heat sourcesink. The governing system is simplified using lubrication approximation theory lat.
Steady flow of a couple stress fluid in constricted tapered artery has been studied under the effects of transverse magnetic field, moving catheter, and slip velocity. Numerical study of mixed convective flow of a couple stress. Making use of stream function, the twodimensional flow equations are transformed into nonlinear compatibility equation, and then it is linearized by vorticity function. Couple stress is the culmination of an assumption that the force and moment distribution acting on. The study of couple stress fluid is very useful in understanding various physical problems because it possesses the mechanism to describe rheological complex fluids such as liquid crystals and human blood. In case of a polar fluid we must introduce a body torque per unit mass in addition to the body force and a couple stress in addition to the normal stress t n. These joints normal synovial fluid is clear or yellowish and is a viscous, nonnewtonian fluid. Consider the steady, incompressible, and offcentered stagnation point flow of a couple stress fluid over an infinite disk rotating with angular velocity the stagnation flow is at distance b along zaxis intruding on a rotating disk shown in figure 1. To the extent the present authors have surveyed the flow of immiscible incompressible couple stress fluids between two porous beds has not been studied so far. Peristaltic pumping of couple stress fluid through non. Theoretical solutions of a thermal runaway and irreversibility thermodynamic analysis of a couple stress hydromagnetic reactive fluid with navier slip conditions and variable properties are examined. The equations governing the flow of an incompressible couple stress fluid are given by 2, 9 q 0 4. Its effect is to create rotation without translation or, more generally, without any acceleration of the centre of mass. Entropy generation in a couple stress fluid flow through a vertical channel filled with saturated porous media article pdf available in entropy 1511.
This article describes a new model for obtaining closedform semianalytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a twodimensional rotating infinite channel. To achieve the set objective, we focus our attention on couple stress fluid that was. Couple stress fluid is a special case of nonnewtonian fluid which was developed by stokes 11. This theory introduces a size dependent effect in contrast to classical viscous theory. The unsteady flow problem is reduced to two coupled partial differential equations using dimensionless variables. In the theory of nonnewtonian fluids, the couple stress fluid introduced by stokes 1 has gained considerable attention and has been widely. Pdf transient couple stress fluid past a vertical cylinder. Canadian journal of physics canadian science publishing. Entropy generation analysis of the mhd flow of couple stress. Synchronous and asynchronous temperature modulation of. Abstract the peristaltic motion of a couple stress fluid of three dimensional analysis with parameter estimation through a two dimensional flexible channel under long wave length approximation and low reynolds number is studied. The concept of couple stresses arises due to the way in which the mechanical interactions in. The consideration of couple stress, in addition to the classical cauchy stress, has led to the recent development of theories of fluid micro continua.
A perturbation method of solution is obtained in terms of wall slope. This type of fluid encloses inflexible and randomoriented particles in a viscous medium. Normal synovial fluid is clear or yellowish and is a nonnewtonian, viscous fluid. Analytical solutions of couple stress fluid flows with slip boundary. Exact solutions for mhd flow of couple stress fluid with heat. These joints normal synovial fluid is clear or yellowish and is a viscous, non newtonian fluid. A time dependent slip flow of a couple stress fluid between. Couple stress fluid between concentric cylinders with slip. Flow and heat transfer of couple stress fluid in a porous channel with expanding and contracting walls. The methodology is implemented for linearizing the flow. The result is compared with that obtained for micropolar fluids and then applied to the particular case of flow past a sphere. The fluid flow is treated with strong magnetic field. Ariman 29 discussed the applications on couple stress fluids and compared with that. To improve the efficiency of curing and speed up the process, activation energy has been added to the process.
Transport of mhd couple stress fluid through peristalsis in a. The effect of various parameters on velocity for each problem is discussed. Study of the couple stress convective micropolar fluid flow. Couple stress fluid theory is a simple generalization of the classical theory of viscous newtonian fluids that allow the sustenance of couple stresses and body. The governing equations of the channel deformation. The governing differential equation developed under the approximation is solved to get exact expressions for velocity and pressure gradient. Natural convection flow of couple stress fluid in a vertical. Abstract in the present article, the exact solutions for fundamental flows namely couette, poiseuille and generalized couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions.
The effects of poststenotic dilatations on the flow of. Steady flow of couplestress fluid in constricted tapered. Thermodynamics analysis of radiative hydromagnetic. Pdf the present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple.
The governing partial differential equations pdes for an incompressible mhd flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. Peristaltic blood flow of couple stress fluid suspended with. The poiseuille flow of couple stress fluid with blood flow applications is studied by valanis et al. Pdf exact solutions for mhd flow of couple stress fluid. Peristaltic motion of a couple stress fluid of three. Exact solutions for mhd flow of couple stress fluid with heat transfer. The cylinder is subjected to torsional oscillations ei. Pdf analytical solutions of couple stress fluid flows with slip. The impact of developing dimensionless parameters on. Flow of a couple stress fluid generated by a circular.
It is of interest to note that these solutions can be used for different types of. Some earlier developments in couple stress fluid theory with some basic flows can be found in the book by stokes. Exact solutions for mhd flow of couple stress fluid with. Analytical solutions of couple stress fluid flows with slip. The expressions are obtained for temperature, coefficient of heat transfer and velocity.
On the exact solutions of couple stress fluids scipress ltd. The nonsymmetric stress and couple stress tensors aredefinedrespectivelyby1,2 ti,j. The computational analytical solution of a time periodic velocity for an electroosmotic flow in an oscillatory microchannel is assessed by solving analytically, the set of governing equations that obeys couple stress fluid model. An exact solution of the equation of motion is obtained by applying the laplace and finite hankel transforms. The flow is under the influence of a radial magnetic field. The influence of magnetic field, hall current, and couple stress are mainly focused in this work. Pulsatile flow of blood through a porous medium has been studied under the influence of periodic body acceleration by considering blood as a couple stress, incompressible, electrically conducting fluid in the presence of magnetic field. The equations governing the flow of a couple stress fluid are given by. In rigid body mechanics, force couples are free vectors, meaning their effects on a body are. Study of the couple stress convective micropolar fluid. Couple stress fluid, twodimensional flows, bxact solutions.
It is of interest to note that these solutions can be used for different types. Peristaltic blood flow of couple stress fluid suspended. Homotopy analysis method is employed to obtain the solution of these equations. The spin field due to microrotation of freely suspended particles sets up an antisymmetric stress, known as couplestress, and thus forms a couplestress fluid. Jan 22, 2019 the poiseuille flow of couple stress fluid with blood flow applications is studied by valanis et al. Transport of mhd couple stress fluid through peristalsis. Second law analysis of ion slip effect on mhd couple. The aim of this paper is to analyse the influence of ion slip on the entropy generation of mhd couple stress fluid. Pdf unsteady electrodynamic flow of a couple stress. The couple stress theory was first introduced by stokes 9 as a generalization of nonpolar navierstokes theory that allows couple stresses and body couples in fluid medium. Effect of peripheral layer on peristaltic transport of couple stress fluid was studied by maruthiprasad et al. Second law analysis of ion slip effect on mhd couple stress fluid. Pdf unsteady electrodynamic flow of a couple stress fluid.
Couple stress fluid flow in a rotating channel with peristalsis. The couettepoiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The channel rotates with a constant angular speed about the z axis and is filled with couple stress fluid. Thermodynamics analysis of radiative hydromagnetic couple. The tiny size gold particles drift in free space of catheters having flexible walls with couple stress fluid.
Exact solutions of the momentum equations of couple stress fluid are investigated. Walicki and walicka 1999 modeled synovial fluid as couplestress fluid in human joints because of the long chain of lauronic acid molecules found as additives in synovial fluid. In this paper, a nonisothermal analysis for the process of blade coating of an incompressible couple stress fluid is presented using both plane and exponential coaters. The couple stress fluids are proficient of describing different types of. In this paper we consider the flow of couple stress fluid generated by a circular cylinder subjected to longitudinal and torsional oscillations.
In mechanics, a couple refers to two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action a better term is force couple or pure moment. It is found that, for each of the problems, the solution in the limiting case. The continuity, momentum, energy, and concentration equations for an mhd incompressible couple stress fluid, in the absence of body couples, are 8, 16 in which represents the material derivative and is darcys resistance in the porous medium which are given by where is the velocity vector, is the density, is the pressure, is the viscosity, is material constant associated with couple stress. On couple stress effects on unsteady nanofluid flow over. Consider an incompressible, nonnewtonian couple stress fluid through a channel, the wall plates exchanges heat with the ambient in an axisymmetrical manner and hot fluid is injected and sucked off at the lower and upper walls respectively with the same velocity. Pdf pulsatile flow of couple stress fluid through a porous. Pdf entropy generation in a couple stress fluid flow.
The theory of couple stress fluids originated by stokes has many biomedical, industrial, and scientific applications and was used to model synthetic fluids, polymer thickened oils, liquid crystals, animal blood, and synovial fluid. Pdf this paper aims at presenting exact solutions for mhd flow of couple stress fluid with heat transfer. The symmetry of the stress tensor a polar fluid is one that is capable of transmitting stress couples and being subject to body torques, as in magnetic fluids. The unsteady threedimensional flow of couple stress fluid over a stretched surface is investigated. The concept of couple stresses arises due to the way in which the mechanical interactions in the fluid medium are modeled. Mhd flow and heat transfer of couple stress fluid over an. Analytical solutions of couple stress fluid flows with. The steady nonisothermal convective heat transfer in magnetohydrodynamic micropolar fluid flow over a nonlinear extending wall is examined.
According to the study by gould, the variation of viscosity with pressure is important especially in the highpressure squeeze films. Heat irreversibiility analysis for a couple stress fluid flow in an inclined channel with isothermal boundaries so adesanya, b souayeh, m rahimigorji, mn khan, og adeyemi journal of the taiwan institute of chemical engineers 101, 251258, 2019. Steady flow of a couplestress fluid in constricted tapered artery has been studied under the effects of transverse magnetic field, moving catheter, and slip velocity. Pdf pulsatile flow of couple stress fluid through a. An attempt has been made to study the entropy generation analysis of couple stress fluid flow in an annulus between two concentric rotating vertical cylinders.
An analysis has been provided for threedimensional magnetohydrodynamic flow of couple stress fluid with newtonian heating by ramzan, farooq, alsaedi, and hayat 20. The problem of a couplestress fluid heated from below in a porous. An attempt has been made to examine the effects of magnetohydrodynamic couple stress fluid in peristaltic flow with porous medium under the impact of slip, heat transfer and wall properties. Natural convection, joule heating effect, couple stress fluid, hall effect, ham. Numerical study of mixed convective flow of a couple. Entropy generation analysis of the mhd flow of couple. Flow of an incompressible couple stress fluid in the region. Flow of couple stress fluid between two parallel porous plates. Walicki and walicka 1999 modeled synovial fluid as couple stress fluid in human joints because of the long chain of lauronic acid molecules found as additives in synovial fluid. Offcentered stagnation point flow of a couple stress. Analysis has been performed in the presence of mass transfer and chemical reaction. Following the scheme described in the introduction, the possible effects of couple stresses will first be considered in isolation by assuming that the fluid has no microstructure at the kinematic level, so that the kinematics of motion is fully determined by the velocity field.
The tensor relates a unitlength direction vector n to the traction. A time dependent slip flow of a couple stress fluid. The important feature of these fluids is that stress tensor is not symmetric and their accurate flow behavior cannot be predicted by classical newtonian theory. On a couplestress fluid heated from below in hydromagnetics. Analytical solutions of some fully developed flows of couple. The main effects of couple stress fluid are to introduce a size dependent effect which is not present in classical viscous theories. The couple stress fluid is a special case of a nonnewtonian fluid which is intended to take into account the particle size effects. Flow of couple stress fluid between two parallel porous plates d. Consider a circular cylinder of radius a within an incompressible couple stress fluid. By couple stress fluid, we mean a fluid whose particles sizes are taken into account, a special case of nonnewtonian fluids. The theory of couple stress fluid was developed by stokes as a simple generalization of classical viscous theory that sustains couple stresses and body couples.
In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of torque. Khan, mahmood, and ara 20 found the approximate solution of the couple stress fluid between expanding and contracting walls. Chemically reactive species of timedependent natural convection couple stress fluid flow past an isothermal vertical flat plate. The problem of a couple stress fluid heated from below in a porous. Numerical simulation for the unsteady mhd flow and heat. Let u, v, and w be the velocity components along x, y and z directions, respectively.
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