Effects of hall current on heat transfer and magnetohydrodynamic mhd boundary layer flow induced by a continuous surface in a parallel free stream of a secondorder viscoelastic fluid are studied for uniform suctioninjection by taking viscous dissipation into account. For example, water flows more easily than syrup because it has a lower viscosity. Part ii numerical analysis with extended markerandcell method. The helix, a macroscopic scale model for the bacterial flagellar filament, is rigid and rotated at a constant rate while simultaneously translated along its axis. Pdf free and confined brownian motion in viscoelastic stokes. Unsteady mhd free convection flow of a viscoelastic fluid past 63 porous plate with heat generation and chemical reaction was studied by reddy et al. Some typical everyday examples of viscoelastic materials would be. Wei, jinjia, li, fengchen, yu, bo, and kawaguchi, yasuo. Several examples demonstrate that our hybrid method can sufficiently preserve fluid volumes and robustly and plausibly generate a variety of viscoelastic behaviors, such as. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Multiple solutions of heat and mass transfer of mhd slip. Table 2 presents a comparison of 0 in pst case among the results of, and the present study in the absence of slip, magnetic field, energy dissipation, thermal radiation and internal heat source. Springer nature is making coronavirus research free. The phase diagram of the surfactant in pure water was established using a pervaporationbased.
It is shown that when there is a suction of the fluid, the solutions are possible only upto a critical value of the viscoelastic parameter. The partial differential equations governing the flow problem are transformed into ordinary differential equations through similarity variables. Aan analytical investigation of unsteady mhd free convection flow of a viscoelastic fluid past a vertical porous plate through a porous medium with time dependent oscillatory permeability and suction in presence of a uniform transverse magnetic field. It viscosifies as it stimulates in carbonate formations, diverting the remaining acid treatment fluid into zones of lower injectivity for. When a wave travels in a poroelastic medium saturated with a viscoelastic fluid, a relative motion between the fluid and the solid skeleton is generated through viscous drag. Fluid dynamics of viscoelastic liquids springerlink. Some examples of these phenomena are discussed in this section1. Fluid mechanics of viscoelasticity, volume 6 1st edition. Proceedings of the asme 2004 international mechanical engineering congress and exposition. Extensional deformation, stress relaxation and necking failure of viscoelastic filaments1 minwu yaoa, gareth h.
The fluid occupies the half space y 0 and at infinity it is assumed that fluid is flowing with the constant freestream velocity u. Study on mechanism of viscoelastic polymer transient flow. Advances on viscoelastic fluid flow simulation bentham. A method for animating viscoelastic fluids citeseerx. Mhd flow of a viscoelastic fluid past a stretching sheet. Simulation of free surface viscoelastic fluid flow using the viscoelasticinterfoam solver. Simulation of free surface viscoelastic fluid flow using. Numerical simulation of viscoelastic freesurface flows using a.
Eulerian methods for animating incompressible fluids with free surfaces by including additional elastic terms in the basic. Typical approaches to free surface simulations are the marker and. The fluids are highly viscous to replicate the low reynolds number environment of microorganisms. Vda viscoelastic diverting acid carbonate ves schlumberger.
This chemical flooding method can increase oil production, and it can improve the macrodisplacement efficiency and microsweep efficiencies. A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on the steady flow of nonnewtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. Swirling flow of a viscoelastic fluid with free surfacepart i. Viscoelastic definition of viscoelastic by the free. With the newly proposed algorithm, solving a large system of the constitutive equations will not be much more complex than the solution of one linearized equation. Modulation of viscoelastic fluid response to external body. Radiation absorption and chemical reaction effects on mhd flow of heat generating casson fluid past oscillating vertical porous plate was considered by reddy et al. Optimize carbonate stimulation with a polymer free fluid. Experimental analysis of vortex motion by piv article pdf available in journal of fluids engineering 1281 january 2006 with. Polymers the basic materials of the rubber and plastic industries and important to the textile, petroleum, automobile, paper, and pharmaceutical industries as well exhibit viscoelasticity to a pronounced degree. The considered nonnewtonian fluid follows a viscoelastic model. May 31, 2017 viscoelastic uids do not behave like newtonian uids and have to be explained in a di erent way than classical ones. Pdf simulation of free surface viscoelastic fluid flow. The effects of the other parameters are described at length.
The governing equations of laminar, incompressible and isothermal ow of viscoelastic uids are the. Sapphire vf guarfree viscoelastic fracturing fluid is engineered to provide maximum well performance in shale reservoirs. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. Vda viscoelastic diverting acid, a selfdiverting, polymerfree acidizing fluid, can be used alone or with other treating acids to maximize zonal coverage in carbonate reservoirs. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the maxwell viscolastic. However, its application is limited to low throughput regime since the particles can defocus as flow rate increases. Consider the unsteady incompressible flow of secondgrade fluid over an infinite plate at y 0. However, in reality, in young and healthy subjects, the vitreous humour has complex rheological properties, and so here we model it as a viscoelastic fluid. Extensional deformation, stress relaxation and necking. Journal of nannewtonian fluid mechanics, 51 1994 309340 elsevier science b. The problem is modulated mathematically by a system of nonlinear differential equations. Pdf a model viscoelastic fluid hang nguyen academia.
Viscoelastic flow university of california, berkeley. They address issues relating to elasticstress based boundary conditions at rigidbody and freesurfaces. Viscoelastic fluid an overview sciencedirect topics. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Boundary element methods for particles and microswimmers. The viscoelastic fluid is induced by wormlikc micelles formed by selfassembled surfactants.
An extension of this tool, used for analysis of freesurface viscoelastic fluid flows using the vof methodology, is also presented. Sapphire vf guarfree viscoelastic hydraulic fracturing fluid. A new model for shallow viscoelastic fluids halenpc. This paper studies the velocity response of viscoelastic fluid to an applied external body force in a twodimensional fullydeveloped poiseuille flow model as shown in fig.
Unsteady boundarylayer flow over jerked plate moving in a. Pdf we linearize the stokesoldroyd b model for small peturbations. A leastsquares particle model with other techniques for 2d viscoelastic fluidfree surface flow. Sizebased separation of particles and cells utilizing.
Forcefree swimming of a model helical flagellum in. Pdf unsteady mhd free convection flow of a viscoelastic. Dubey department of applied mathematics, vivekananda college of. This book is about two special topics in rheological fluid mechanics. Issues in viscoelastic fluid mechanics physics courses.
Author links open overlay panel tao jiang a b jinlian ren a jinyun yuan b wen zhou c dengshan wang d. Swirling flow of a viscoelastic fluid with free surface. This relaxation time is an important parameter because it defines a boundary between a solidlike response like tearing or cracking and a fluid like response like flow. Purchase fluid mechanics of viscoelasticity, volume 6 1st edition. In this study, we establish physical models that include the deadend and complex models based on the porenetwork pattern etched into. An unsteady, free convective heat and mass transfer problem of awaltersb viscoelastic fluid nondarcy flow over a vertical cone with the influence of thermal radiation, thermophoresis and higher. Oil recovery, including conventional and viscous oil, can be improved significantly by flooding with polymer solutions. It provides better proppant transport and fracture cleanup compared with conventional linear gel or slickwater formulations while improving operational efficiency.
Flow behavior and instabilities in viscoelastic fluids. Influence of couple stresses and thermophoresis on free. Part i experimental analysis of vortex motion by piv. Viscoelastic behavior reflects the combined viscous and elastic responses, under mechanical stress, of materials which are intermediate between liquids and solids in character. It creates energy dissipation and wave attenuation even for a lowfrequency wave. Indeed, it has been extended for viscoelastic fluid flow simulations 2,19 20 212223, including flow problems involving free surface and twophase flows, by using the volume of fluid. Optimize carbonate stimulation with a polymerfree fluid. A basic property of a viscoelastic fluid in which it exerts force on itself.
Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Viscosity is a measure of a fluids resistance to flow. Mckinleyb, benoit debbautc a ohio aerospace institute, 22800 cedar point road, brook park, oh 44142, usa b dept. Effects of hall current on mhd boundary layer secondorder. Pdf swirling flow of a viscoelastic fluid with free. Applications involving viscoelastic fluid jets are quite broad, and include such areas as microdispensing of bioactive fluids through high throughput injection devices, creation of cell attachment sites, scaffolds for tissue engineering, coatings and drug delivery systems for controlled drug release, and viscoelastic blood flow flow past valves. The viscoelastic fluid flow constitutive equation consists of nonlinear terms, which are. Mhd free convection heat and mass transfer flow of.
Flow behavior of viscoelastic fluids accessscience from. Viscoelastic fluids, maxwell model, oldroyd model, saint venant model, shallow water. Using an engineered carrier medium with constant and low viscosity and strong elasticity, the sample flow. Velocities increase with rising permeability darcian parameter for both second and third grade viscoelastic free convection regimes and decrease with rising forchheimer parameter. A solver for timedependent viscoelastic fluid flows pdf. A leastsquares particle model with other techniques for. Double diffusive convection in a horizontal layer of maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient soret effects and concentration gradient dufour effects is investigated.
An adaptive solver for viscoelastic incompressible twophase. Huzyak and koelling 6 experimentally investigate the differences between newtonian fluid and nonnewtonian fluid driven by long bubble condition and pointed out in the text that the relationship between ca and m is irrelevant with pipe diameter in terms of newtonian fluid, but that will be affected by pipe diameter in terms of viscoelastic fluid. An exact analytical solution exists for the problem. In this paper, a twolevel finite element method for oseen viscoelastic fluid flow obeying an oldroydb type constitutive law is presented. Unsteady mhd free convection flow of a viscoelastic fluid. The difference between elastic materials and viscoelastic. Viscoelasticityinduced particle migration has recently received increasing attention due to its ability to obtain highquality focusing over a wide range of flow rates. In this paper, a corrected particle method based on the smoothed particle hydrodynamics sph method with highorder taylor expansion csphht for solving the viscoelastic flow is proposed and investigated. Deformed molecules are driven by thermal motions to return to their undeformed states, giving the bulk fluid elastic recovery.
Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as. Mhd free convection heat and mass transfer flow of viscoelastic fluid embedded in a porous medium of variable permeability with radiation effect and heat source in slip flow regime satya sagar saxena and g. We precisely measure the forcefree swimming speed of a rotating helix in viscous and viscoelastic fluids. Viscoelastic properties of polymers, 3rd edition wiley. We model blood as a shearthinning viscoelastic fluid with the b f ft 3 relaxation time characterizing the evolution of natural configurations pi p, pi, associated k. Viscoelastic fluid article about viscoelastic fluid by. High viscosity materials might include honey, syrups, or gels generally things that resist flow. The validity and merits of the csphht method are first tested by solving the nonlinear high order kuramotosivishinsky equation and simulating the drop stretching, respectively. Viscoelastic flow simulation in openfoam presentation of. Vda viscoelastic diverting acid, a selfdiverting, polymer free acidizing fluid, can be used alone or with other treating acids to maximize zonal coverage in carbonate reservoirs. It is seen that these three sets of heat transfer results agree very well for different values of prandtl number. A solver for timedependent 309 viscoelastic fluid flows fredrik. The laminar flow of a viscoelastic fluid past a stretching sheet in the presence of a magnetic field, when the fluid is extracted from the sheet at a uniform rate, is considered.695 1344 579 170 1277 1081 31 1053 523 1508 153 976 1409 562 1449 259 1083 1046 34 265 899 716 987 741 1160 275 592 641 990 189 585 1039 566 711 184 168 1476 530 948 886 294 385 1336 1272 46