Effects Of Weissenberg Number Research Articles

Numerical study of an individual bubble rise in a shear-thinning viscoelastic liquid based on a combination of the Carreau and FENE-CR models

The rise behavior of a single bubble in shear-thinning viscoelastic liquids was investigated using a volume of fluid method based on a combination of the Carreau and FENE-CR models. The effects of Weissenberg number (Wi), polymer stretching parameter (L), Eötvös number (Eo) and rheological index (n) on bubble shape and typical characteristics of flow fields were investigated in detail. The results show that bubble tail becomes pointed under the influence of elastic stress, and the bubble becomes longer along the longitudinal direction with a decrease in Wi. When the magnitude of n is relatively large, the bubble appears as an ellipsoidal shape with a cusp; however, when the magnitude of n is relatively small, bubble shape is closer to a disc, and the tip of bubble tail disappears. Wi affects the magnitude of elastic tensile stress, and affects the action rang of the large tensile stress. With an increase in Wi, the action rang of elastic tensile stress develops from both sides of the bubble towards regions below bubble tail. The appearance of negative wake is not directly related to bubble shape, but to the relaxation of elastic stres.

Delineation of heat transfer and flow analysis of Carreau nanofluid in microchannel using Buongiorno model

This paper reports the hydromagnetic mixed convective flow of Carreau nanofluid in the vertical microchannel with slip and convective mechanisms at the boundaries. The main objective of this work is to analyze the conduct of Carreau nanofluid under Buongiorno model as the nano-dimensions of the particle consequently encounters random motion. The novel impression is to retain the outcomes of the flow in regard of Brownian dispersion and thermophoresis. Parameters such as buoyancy ratio, Brownian motion and thermophoresis along with the effect of Weissenberg number are discussed on distribution of flow, temperature and concentration by using graphical demonstration. Surface drag coefficients, transport rates of mass and heat are portrayed by numeric esteems. Boundary layer approximations are made use to tackle nonlinear ordinary differential equations and solved by Runge–Kutta–Fehlberg 4-5th-order method. Results so obtained elaborate that velocity depletes with increased values of buoyancy ratio and viscosity ratio parameter along with power law index. Also, distinct behavior is noticed in the profile of velocity for varying Weissenberg number by boosting and diminishing depending on the power law index. On the other hand, temperature rises by augmentation of thermophoresis and Brownian motion parameter. Elevation in Brownian motion parameter accelerate the concentration panel of the fluid. Skin friction and Nusselt number are in direct proportion with buoyancy ratio parameter and Brownian motion parameter, respectively.

Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity.

This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation of the Carreau fluid. The shooting method is utilized to obtain graphical and numeric outcomes. Additionally, initial guesses are generated with the help of Newton's method. The effect of Weissenberg number, Magnetization, stretching ratio, Prandtl number, suction/blowing parameter, and Lewis number is obtained on velocity, temperature and species continuity profile and analyzed. Shear stress rates and Nusselt number outcomes under body forces influences are present in tabulated data and discussed. It is observed that in absence of magnetization force, B = 0 and strong mass suction 5≤S≤7.5 effect high rates of Nusselt number is obtained. It is concluded that under the influence of power law index and non-linearity parameter maximum heat transfer and reduced shear stress rates are obtained.

Pulsatile Oldroyd-B blood flow dynamics in a stenosed artery

The viscoelastic nature of blood flow through 25% size of stenosis is investigated numerically using Comsol-Multiphysics 5.4. The flow geometry of the stenosed artery is modeled by asymmetric 2D channel with a rigid wall. Blood is characterized as a mixture of Newtonian and viscoelastic fluid. The coupled nonlinear Navier–Stokes equation and the Oldroyd-B models equations are solved numerically in General PDE solver. The governing equations are discretized using the finite element method for the two-dimensional flow to estimate the velocity and pressure distribution. The effect of the velocity field, pressure distribution, and wall shear stress is reported for the Newtonian model and the viscoelastic Oldroyd-B model. The deviation of fluid behavior from the Newtonian fluids is compared to the practical blood behavior. The effects of Weissenberg number (Wi) over velocity field and wall shear stress have tested for moderate Reynolds numbers. The Oldroyd-B model showed quite reliable blood behavior when compared to existing literature values.

Inclined hydromagnetic impact on tangent hyperbolic fluid flow over a vertical stretched sheet

The current research aims to examine the impact of a tangent hyperbolic fluid flow confined by a stretching sheet with the existence of variable thermal conductivity, mixed convection, and magneto hydrodynamics. A mathematical model is developed in the form of partial differential equations (PDEs) and then converted into ordinary differential equations by using self-felicitous transformations. The technique of BVP4C (MATLAB package) has been used to simplify these ordinary differential equations. The numerical solution of skin friction, mixed convection, Nusselt number, and velocity and temperature profiles for different values of the involved parameters is indicated through tables and graphs. It can be noticed that the velocity profile decreases when the Hartmann number increases. The effect of Weissenberg number, inclined angle, and power law index for velocity profiles is also identical to the Hartmann number. The temperature profile decays due to an increment in the Prandtl number. Skin friction and the Nusselt number have also been explained. The physical reasoning for growth or decay of these parameters has been discussed in detail.

Forced Convection Heat Transfer of a Giesekus Fluid in Circular Micro-Channels Subjected to a Constant Wall Temperature

Abstract In this paper, an exact analytical solution for forced convective heat transfer of nonlinear viscoelastic fluid in isothermal circular micro-channel is presented. The nonlinear Giesekus constitutive equation is used to model the Giesekus fluid heat transfer in micro-channel with constant wall temperature, which is the main innovative aspect of the current study. This constitutive equation is a powerful tool and able to model the fractional viscometric functions, extensional viscosity, and elastic property. The solution of temperature profile and Nusselt number is obtained based on the Frobenius method. The effects of Weissenberg number, mobility factor, slip coefficient, and Navier index on temperature distribution, velocity profile, and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause the increases in slip velocity and maximum dimensionless temperature at the wall and the micro-channel center, respectively. Moreover, the Nusselt number has an upward trend with increases in slip coefficient and Navier index parameters. The results are indicated that the flow and temperature fields have a complex relation with mobility factor which controls the level of the nonlinearity of the Giesekus model. Additionally, three correlations for Nusselt number of Giesekus flow in micro-channel are presented.

An exact analysis on heat convection of nonlinear viscoelastic flows in isothermal microtubes under slip boundary condition

In this paper, forced convective heat transfer of Phan–Thien–Tanner fluid in isothermal microtubes is studied analytically. The nonlinear Navier slip law is used to model the slip boundary condition at microtubes wall. The second-order eigenvalue form of related ODE is solved using the Frobenius method and the temperature distribution obtained in the form of power series. The Nusselt number is also calculated using the modal analysis technique. The effects of Weissenberg number, slip coefficient, and Navier index on velocity profile, temperature distribution and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause to increases in slip velocity and maximum dimensionless temperature at the wall and the microtube center, respectively. Moreover, the Nusselt number is enhanced by increasing the slip coefficient and Navier index parameters.

Vortex behavior of particle suspension flow in a wedge for the second-order fluid

Effect of Weissenberg number, Reynolds number, Stokes number and wedge angle on the vortex behavior of particle suspension flow is investigated numerically in a wedge for the second-order viscoelastic fluid. The results show that there exist symmetrical vortices near the walls close to apex for different wedge angles, and the vortex length is inversely proportional to the wedge angle. Increase of the Reynolds number not only increases the vortex length but also their dependence on the Weissenberg number. The vortex length increases with the increase of Weissenberg number and finally reaches an asymptotic value. The vortex gradually developed as the Stokes number is decreased, and the vortex length has a maximum for the single phase flow. The presence of particles will suppress the development of vortex, and the suppression degree is directly proportional to the Stokes number. The Reynolds number has a larger impact on the vortex length than the wedge angle in the parameter region studied here.

Effect of Elasticity Parameter on Viscoelastic Fluid in Pipe Flow Using Extended Pom-Pom Model

In this study prediction of the steady-state flow of branched polymer melts in pipe geometry with finite volume method is presented. Our analysis in this study revealed that; for normal-stress τθθ , the XPP model can predict this tensor unlike the other viscoelastic models such as PTT or Gieskus which can not predict τθθ for viscoelastic fluid in two dimensional pipe flows. The fluid is modelled using a modification of the Pom-Pom model known as the single eXtended Pom-Pom (XPP) where viscoelastic fluid is typically a commercial low-density polyethylene. In finite volume method, the operator-integration is used to discretize the governing equations in space or control volume. An iterative solution algorithm that decouples the computation of momentum from that of stress is used to solve the discrete equations. Numerical results are presented, including the profiles of all relevant stresses, the axial velocity, stretch and the viscosity across the gap, demonstrating the performance of the model predictions. The influence of elasticity parameter on flow behaviour is studied, which demonstrates in particular, the dependence of velocity and stresses distribution as a function of Weissenberg number is analyzed. Also, the effect of Weissenberg number on pressure gradient has been considered. Finally, verification of the present model was made by comparing to the Generalized Newtonian Fluid (GNF) model.

Forced convection heat transfer of Giesekus viscoelastic fluid in pipes and channels

A theoretical solution is presented for the convective heat transfer of Giesekus viscoelastic fluid in pipes and channels, under fully developed thermal and hydrodynamic flow conditions, for an imposed constant heat flux at the wall. The fluid properties are taken as constant and axial conduction is negligible. The effect of Weissenberg number (We), mobility parameter (α) and Brinkman number (Br) on the temperature profile and Nusselt number are investigated. The results emphasize the significant effect of viscous dissipation and fluid elasticity on the Nusselt number in all circumstances. For wall cooling and the Brinkman number exceeds a critical value (Br 1), the heat generated by viscous dissipation overcomes the heat removed at the wall and fluid heats up longitudinally. Fluid elasticity shifts this critical Brinkman number to higher values.

Flow of Giesekus viscoelastic fluid in a concentric annulus with inner cylinder rotation

An approximate analytical solution is derived for the steady state, purely tangential flow of a viscoelastic fluid obeying the Giesekus constitutive equation in a concentric annulus with inner cylinder rotation. An approximation is used for the estimation of radial normal stress. The effect of Weissenberg number ( We), radius ratio ( κ) and mobility factor ( α) on velocity distribution and fRe are investigated. The results show that the velocity gradient near the inner cylinder increases as the fluid elasticity increases. The results also show that fRe decreases with increasing fluid elasticity.

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number ( Wi > 1).

Swirling Flow of a Viscoelastic Fluid With Free Surface—Part II: Numerical Analysis With Extended Marker-and-Cell Method

In Part I [Wei et al., 2004, 2004 ASME Int. Mech. Eng. Conference], we presented the experimental results for swirling flows of water and cetyltrimethyl ammonium chloride (CTAC) surfactant solution in a cylindrical vessel with a rotating disk located at the bottom for a Reynolds number of around 4.3×104 based on the viscosity of solvent. For the large Reynolds number, violent irregular instantaneous secondary flows at the meridional plane were observed by use of a particle image velocimetry system. Because of the limitations of our computer resources, we did not carry out direct numerical simulation for such a large Reynolds number. The LES and turbulence model are alternative methods, but a viscoelastic LES/turbulence model has not yet been developed for the surfactant solution. In this study, therefore, we limited our simulations to a laminar flow. The marker-and-cell method proposed for Newtonian flow was extended to the viscoelastic flow to track the free surface, and the effects of Weissenberg number and Froude number on the flow pattern and surface shape were studied. Although the Reynolds number is much smaller than that of the experiment, the major experimental observations, such as the inhibition of primary and secondary flows and the decrease of the dip of the free surface by the elasticity of the solution, were qualitatively reproduced in the numerical simulations.

Effect of Weissenberg number on the flow structure: DNS study of drag-reducing flow with surfactant additives

A second-order finite difference scheme was employed for the DNS study of drag-reducing flow with surfactant additives. We focus on the effect of Weissenberg number (nondimensional relaxation time) on the flow structures. The instantaneous flow structures and stress distribution at different elasticities are compared. The effects of Weissenberg number on turbulence statistics such as turbulence intensities, Reynolds shear stress and two-point correlation coefficients are also presented.