Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channel

The unsteady flow of viscoelastic fluid with the fractional derivative Maxwell model (FDMM) in a channel is studied in this note. The exact solutions are obtained for an arbitrary pressure gradient by means of the finite Fourier cosine transform and the Laplace transform. Two special cases of pressure gradient are discussed. Some results given by the classical models with integer-order are included in this note.     

A finite-volume ELLAM for non-linear flux convection-diffusion problems

In this paper, a modified finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) extended for convection-diffusion problems with a non-linear flux function is introduced. Tracking schemes are discussed using viscous Burgers’ equation. It is shown that in order to have smooth results, only the new time level values should be used in tracking process. Then, the proposed method is employed to study immiscible incompressible two-phase flows in porous media. Various one- and two-dimensional test cases involving internal sources and sinks are solved and accuracy of solution and performance of the method are investigated by comparing the results obtained using FVELLAM with those of fine grid solutions. Finally, it is concluded that although proposed FVELLAM produces satisfactory results even on coarse grids and allows fairly large time-steps, its major advantage is in solving convection-dominated problems in heterogeneous media.     

Accurate solutions for viscoelastic boundary layer flow and heat transfer over stretching sheet

In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method （HAM） for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer＇s function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer.     

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic(MHD) boundary layer flow of an incompressible upper-convected Maxwell(UCM) fluid over a porous stretching surface.Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations.The nonlinear problem is solved by using the successive Taylor series linearization method(STSLM).The computations for velocity components are carried out for the emerging parameters.The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.     

MHD flow and mass transfer of chemically reactive upper convected Maxwell fluid past porous surface

The magnetohydrodynamic (MHD) flow and mass transfer of an electrically conducting upper convected Maxwell (UCM) fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the Keller-box method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.     

On the equivalence of simplest non-linear rheological equations for viscoelastic polymer media

Some equivalence conditions are formulated for non-linear models of polymer melts and solutions that are analogous to known conditions for three-constant linear rheological equations. The resulting model is analysed in simple shear and elongational flows. The kinematics of finite elastoviscous strains is considered in an appendix.     

A study on non-steady flow of upper-convected maxwell fluid in tube

The transient response of an upper-convected Maxwell fluid flow in a circular tube is analysed by variational approach of Kantorovich and the method of finite difference. The solution of the variational method is in agreement with the numerical results by the difference schemes. The results show that the method of Kantorovich is suitable for the study of non-steady flow of non-Newtonian fluids and the effect of elasticity of the fluid has an influence on the non-steady flow. project supported by National Natural Science Foundation of China     

A note on start-up and large amplitude oscillatory shear flow of multimode viscoelastic fluids

Start up of plane Couette flow and large amplitude oscillatory shear flow of single and multimode Maxwell fluids as well as Oldroyd-B fluids have been analyzed by analytical or semi-analytical procedures. The result of our analysis indicates that if a single or a multimode Maxwell fluid has a relaxation time comparable or smaller than the rate of change of force imparted on the fluid, then the fluid response is not singular as Elasticity Number (E ). However, if this is not the case, as E , perturbations of single and multimode Maxwell fluids give rise to highly oscillatory velocity and stress fields. Hence, their behavior is singular in this limit. Moreover, we have observed that transients in velocity and stresses that are caused by propagation of shear waves in Maxwell fluids are damped much more quickly in the presence of faster and faster relaxing modes. In addition, we have shown that the Oldroyd-B model gives rise to results quantitatively similar to multimode Maxwell fluids at times larger than the fastest relaxation time of the multimode Maxwell fluid. This suggests that the effect of fast relaxing modes is equivalent to viscous effects at times larger than the fastest relaxation time of the fluid. Moreover, the analysis of shear wave propagation in multimode Maxwell fluids clearly show that the dynamics of wave propagation are governed by an effective relaxation and viscosity spectra. Finally, no quasi-periodic or chaotic flows were observed as a result of interaction of shear waves in large amplitude oscillatory shear flows for any combination of frequency and amplitudes.     

Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet

The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered. Upper‐convected Maxwell (UCM) fluid is treated as a rheological model. The resulting nonlinear differential system is solved by homotopy analysis method (HAM). The influence of melting parameter (M), Prandtl number (Pr), Deborah number (β) and stretching ratio (A = a/c) on the velocity and temperature profiles is thoroughly examined. It is noticed that fields are effected appreciably with the variation of parameters. Furthermore, it is seen that the local Nusselt number is a decreasing function of melting parameter. Copyright © 2011 John Wiley & Sons, Ltd.     

Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet

The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third-grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temperature gradient while reduces the temperature profile.     

Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel

This study investigates the electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids through a microchannel under the Navier slip boundary condition. The flow is driven by the pressure gradient and electromagnetic force where the electric field is applied horizontally, and the magnetic field is vertically (upward or downward). When the electric field direction is consistent with the pressure gradient direction, the changes of the steady flow rate and velocity with the Hartmann number Ha are irrelevant to the direction of the magnetic field (upward or downward). The steady flow rate decreases monotonically to zero with the increase in Ha. In contrast, when the direction of the electric field differs from the pressure gradient direction, the flow behavior depends on the direction of the magnetic field, i.e., symmetry breaking occurs. Specifically, when the magnetic field is vertically upward, the steady flow rate increases first and then decreases with Ha. When the magnetic field is reversed, the steady flow rate first reduces to zero as Ha increases from zero. As Ha continues to increase, the steady flow rate (velocity) increases in the opposite direction and then decreases, and finally drops to zero for larger Ha. The increase in the fractional calculus parameter α or Deborah number De makes it take longer for the flow rate (velocity) to reach the steady state. In addition, the increase in the strength of the magnetic field or electric field, or in the pressure gradient tends to accelerate the slip velocity at the walls. On the other hand, the increase in the thickness of the electric double-layer tends to reduce it.

     

A three-dimensional photographic method for measurement of phase distribution in dilute bubble flow

A three-dimensional photographic method has been developed to measure phase distributions in bubbly flow in a pipe. In this method a mirror was used to reflect a side view of the flow into the front-view direction, and then flow images in both views were taken simultaneously by one camera. After three-dimensional position and size of each bubble in the flow field were determined by matching the two bubble images in the side and front views, the phase distributions were obtained for the bubbly flow. Received: 25 April 2000 / Accepted: 21 June 2001 Published online: 29 November 2001     

A new exact solution for the flow of a Maxwell fluid past an infinite plate

A new exact solution corresponding to the flow of a Maxwell fluid over a suddenly moved flat plate is determined. This solution is in all accordance with a previous one and for λ→0 it goes to the well-known solution for Navier-Stokes fluids.     

Numerical simulation for laminar flow and heat transfer of gas in rectanglar micropassages with constant wall heat flux

Theoretical investigations were performed on the developed laminar flow and convective heat transfer characteristics for incompressible gases flow through rectanglar micropassages with constant wall heat flux. Mathematical models were proposed for considering the change in viscosity and thermal conductivity of gas in the wall-adjacent region from the kinetic theory. The dimensionless velocity distribution and corresponding pressure drop, the dimensionless temperature distribution and corresponding heat transfer characteristics were both simulated numerically, and the results were compared to other report simulations [10–12] with brief discussions.     

A numerical study of bingham turbulent flow in sudden-expansion straight circular pipe

I.IntroductionBinghamfluidisonebranchofnon-Newtonianfluid,suchascrudeparaffinoil,highsediment--ladenwaterflow,highconcentrationmudandthelikewhicharetransportedinpipelinesinmanyindustries,soit'sofgreatsignificancetostudytheflowmechanismsofBinghamfluid.Tsaietal.II]studiedthelinkagebetweenBinghamfluidandpluggedflow.Wangetal.I2]measuredtheturbulencestructureofBinghammud.Mengetal.[3]researchedthekineticenergycorrectionfactorofBinghamfluidinacircularpipe.However,thestudyofBinghamfluidsofarisn't…     

The double von Mises transformation in the study of two-phase fluid flow over curved boundaries: Theory and analysis

Three kinds of grid system based on C-type grid are examined in order to reveal their relative flow characteristics of the turbomachinery cascade, especially near the trailing edge and wake. Here, a semi-conservative interpolation technique to treat the discontinuous boundary condition along the periodic boundary is proposed and is applied on the patched-type grid structure. Computational results are presented to see the influence of trailing-edge grid structure on the Navier-Stokes solutions for the high-turning transonic turbine cascade.     

Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study

This paper presents a numerical study for the unsteady flow of a magnetohydrodynamic (MHD) Sisko fluid in annular pipe. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field. Based on the constitutive relationship of a Sisko fluid, the non‐linear equation governing the flow is first modelled and then numerically solved. The effects of the various parameters especially the power index n, the material parameter of the non‐Newtonian fluid b and the magnetic parameter B on the flow characteristics are explored numerically and presented through several graphs. Moreover, the shear‐thinning and shear‐thickening characteristics of the non‐Newtonian Sisko fluid are investigated and a comparison is also made with the Newtonian fluid. Copyright © 2009 John Wiley & Sons, Ltd.     

A study on numerical methods for transient rotating flow induced by starting blades

Based on the finite volume method, three methods for rotational region treatment were presented and validated by simulating two-dimensional accelerating rotational flows. Separate transient incompressible flows induced by cross-shaped blades during starting process were simulated using the dynamic mesh, sliding mesh and dynamic reference frame methods. The computing performance and stability of the three methods were evaluated by comparing numerical results, and the transient characteristics of the accelerating rotational flow were analysed numerically. Results showed that the starting process affected the flow structure and transient characteristics of the accelerating rotational flows. The sliding mesh method showed higher computational efficiency and accuracy compared with other methods, and could easily be extended to solve three-dimensional transient flows in hydraulic machineries under transient operations, such as start-up and shutdown.     

A numerical study of bifurcation in laminar flow in curved ducts

The bifurcation phenomenon whereby multiple-vortex secondary flow occurs in place of the normal two-vortex flow in laminar flow in curved ducts has previously been studied numerically by several researchers. However, the various results have been conflicting on many points. The present paper describes a set of numerical experiments conducted to study the effect of numerical accuracy on the solution. The results show that the transition from two- to four-vortex structure depends strongly on the differencing scheme and to a lesser extent on the grid size. The study also shows that as the Reynolds number of the flow increases, a two-vortex structure is re-established via a path which involves strongly asymmetric secondary flow patterns. These results are in agreement, at least qualitatively, with recent experimental theoretical and numerical results.     

A hybrid method for computing the flow of viscoelastic fluids

A hybrid method for computing the flow of viscoelastic and second-order fluids is presented. It combines the features of the finite difference technique and the shooting method. The method is accurate because it uses central differences. Its convergence is at least superlinear. The method is applied to obtain the solutions to three problems of flow of Walters' B' fluid: (a) flow near a stagnation point, (b) flow over a stretching sheet and (c) flow near a rotating disk. Numerical results reveal some new characteristics of flows which are not easy to demonstrate using the perturbation technique.