On the Nonlinear Generalized Maxwell Fluid Model

2003 ◽  
Vol 70 (2) ◽  
pp. 309-310 ◽  
Author(s):  
H. Hu
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Constant Rate ◽  
Comparison Of The Results ◽  
Generalized Maxwell Fluid

An equation describing a nonlinear generalized Maxwell fluid model is presented. Model behavior, for constant rate elongations, is investigated. A comparison of the results in this study with those in the literature has been given. The conclusion of Corr et al. that the model has two solutions is questionable.

A Nonlinear Generalized Maxwell Fluid Model for Viscoelastic Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 787-790 ◽  
Author(s):  
D. T. Corr ◽  
M. J. Starr ◽  
R. Vanderby, ◽  
T. M. Best
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Viscoelastic Materials ◽  
Force Equation ◽  
Constant Rate ◽  
Parallel Arrangement ◽  
Noteworthy Feature ◽  
In Series ◽  
Linear Spring ◽  
Generalized Maxwell Fluid

A nonlinear Maxwell fluid model consisting of a linear dashpot in series with a parallel arrangement of a linear spring and a second-order nonlinear spring, was developed. This configuration provides the flexibility necessary to describe both the stiffening and the softening responses of some viscoelastic materials. A noteworthy feature of the model is that under constant rate displacement, the force equation can be solved in closed form, thereby providing a continuous, exact general solution.

scholarly journals On the flow of MHD generalized maxwell fluid via porous rectangular duct

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 989-1002
Author(s):  
Aamir Farooq ◽  
Muhammad Kamran ◽  
Yasir Bashir ◽  
Hijaz Ahmad ◽  
Azeem Shahzad ◽  
...  
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Rectangular Duct ◽  
Modified Darcy’S Law ◽  
Initial Boundary Value ◽  
Generalized Maxwell Fluid ◽  
Limiting Case ◽  
The Impact

Abstract The purpose of this proposed investigation is to study unsteady magneto hydrodynamic (MHD) mixed initial-boundary value problem for incompressible fractional Maxwell fluid model via oscillatory porous rectangular duct. Considering the modified Darcy’s law, the problem is simplified by using the method of the double finite Fourier sine and Laplace transforms. As a limiting case of the general solutions, the same results can be obtained for the classical Maxwell fluid. Also, the impact of magnetic parameter, porosity of medium, and the impact of various material parameters on the velocity profile and the corresponding tangential tensions are illuminated graphically. At the end, we will give the conclusion of the whole paper.

scholarly journals A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS

2019 ◽  
Vol 81 (4) ◽  
pp. 501-512
Author(s):  
I.A. Zhurba Eremeeva ◽  
D. Scerrato ◽  
C. Cardillo ◽  
A. Tran
Keyword(s):  
Mathematical Model ◽  
Viscoelastic Fluid ◽  
Viscoelastic Properties ◽  
Fluid Model ◽  
Maxwell Fluid ◽  
Initial Boundary ◽  
Deborah Number ◽  
Nonstationary Motion ◽  
Friction Forces ◽  
Roller Bearings

Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.

On the Flow of a Polymer Melt Passing Over a Transverse Slot

1999 ◽  
Vol 19 (3) ◽  
pp. 175-196 ◽  
Author(s):  
G.H. Wu ◽  
C.K. Chen ◽  
S.H. Ju
Keyword(s):  
Fluid Model ◽  
Polymer Melt ◽  
Maxwell Fluid ◽  
Creeping Flow ◽  
Analytical Prediction ◽  
Hole Pressure ◽  
Fluid Elasticity ◽  
Conduit Wall ◽  
Liquid Flows ◽  
Transverse Slot

Abstract The phenomenon of hole pressure occurs whenever a polymeric or viscoelastic liquid flows over a depression in a conduit wall. Numerical simulations undertaken for the flow of an aqueous polyacrylamide melt passing over a transverse slot arc considered here. The fluid model used for this study is a White-Metzner constitutive equation describing the non-Newtonian behavior of the melt. The results were computed by an elastic-viscous split-stress finite clement method (EVSS-FEM). a mixed finite clement method incorporating the non-consistent streamline upwind scheme. For verification, the numerical algorithm was first applied to compute the corresponding flow of the upper-convected Maxwell fluid model, a special case of the Whitc-Metzner model characterized by constant viscosity and relation time. The resulting hole pressure (Ph) was evaluated for various Deborah numbers (De) and compared with the analytical prediction derived from the Higashitani-Pritchard (HP) theory. The agreement was found to be satisfactory for creeping flow in the low De range, for which the HP theory is valid. Subsequently, the hole pressure of this flow problem was predicted. The streamlines and pressure distribution along the channel walls arc also presented. Furthermore, the effects of fluid elasticity, shear thinning, the exponent in the viscosity function and the relaxation-time function, and slot geometry on the hole pressure were investigated.

scholarly journals Temperature variation in the dark cosmic fluid in the late universe

2016 ◽  
Vol 31 (08) ◽  
pp. 1650050 ◽  
Author(s):  
Iver Brevik
Keyword(s):  
Dark Energy ◽  
Time Dependence ◽  
Entropy Production ◽  
Temperature Variation ◽  
Temperature Jump ◽  
Fluid Model ◽  
Maxwell Fluid ◽  
Positive Temperature ◽  
Turbulent Transition ◽  
Big Rip

A one-component dark energy fluid model of the late universe is considered [Formula: see text] when the fluid, initially assumed laminar, makes a transition into a turbulent state of motion. Spatial isotropy is assumed so that only the bulk viscosities are included ([Formula: see text] in the laminar epoch and [Formula: see text] in the turbulent epoch). Both viscosities are assumed to be constants. We derive a formula, new as far as we know, for the time dependence of the temperature [Formula: see text] in the laminar case when viscosity is included. Assuming that the laminar/turbulent transition takes place at some time [Formula: see text] before the big rip is reached, we then analyze the positive temperature jump experienced by the fluid at [Formula: see text] if [Formula: see text]. This is just as one would expect physically. The corresponding entropy production is also considered. A special point emphasized in the paper is the analogy that exists between the cosmic fluid and a so-called Maxwell fluid in viscoelasticity.

Helices of fractionalized Maxwell fluid

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Muhammad Jamil ◽  
Kashif Ali Abro ◽  
Najeeb Alam Khan
Keyword(s):  
Angular Velocity ◽  
General Solution ◽  
Circular Cylinder ◽  
Special Function ◽  
Fluid Model ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Initial Moment ◽  
Special Cases ◽  
In Series

AbstractIn this paper the helical flows of fractionalized Maxwell fluid model, through a circular cylinder, is studied. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Omegatp, and to slide along the same axis with linear velocity Utp. The solutions that have been obtained using Laplace and finite Hankel transforms and presented in series form in terms of the newly defined special function M(z), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for ordinary Maxwell and Newtonian fluid obtained as special cases of the present general solution. Finally, the influence of various pertinent parameters on fluid motion as well as the comparison among different fluids models is analyzed by graphical illustrations.

scholarly journals Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Changfeng Xue ◽  
Junxiang Nie
Keyword(s):  
Exact Solutions ◽  
Half Space ◽  
Stokes Problem ◽  
Maxwell Fluid ◽  
Constitutive Relationship ◽  
Classical Solutions ◽  
Maxwell Fluids ◽  
Fourier Sine Transform ◽  
Porous Half Space ◽  
Generalized Maxwell Fluid

The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.

scholarly journals Unsteady Flows of a Generalized Fractional Burgers’ Fluid between Two Side Walls Perpendicular to a Plate

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jianhong Kang ◽  
Yingke Liu ◽  
Tongqiang Xia
Keyword(s):  
Unsteady Flows ◽  
Maxwell Fluid ◽  
Second Grade ◽  
Burgers Fluid ◽  
Double Fourier Transform ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Side Walls ◽  
Generalized Maxwell Fluid ◽  
Stokes Second Problem

The unsteady flows of a generalized fractional Burgers’ fluid between two side walls perpendicular to a plate are studied for the case of Rayleigh-Stokes’ first and second problems. Exact solutions of the velocity fields are derived in terms of the generalized Mittag-Leffler function by using the double Fourier transform and discrete Laplace transform of sequential fractional derivatives. The solution for Rayleigh-Stokes’ first problem is represented as the sum of the Newtonian solutions and the non-Newtonian contributions, based on which the solution for Rayleigh-Stokes’ second problem is constructed by the Duhamel’s principle. The solutions for generalized second-grade fluid, generalized Maxwell fluid, and generalized Oldroyd-B fluid performing the same motions appear as limiting cases of the present solutions. Furthermore, the influences of fractional parameters and material parameters on the unsteady flows are discussed by graphical illustrations.

Statistical Response of a Simplified Nonlinear Fluid Model Under Random Parameters

2007 ◽  
Author(s):  
T-P. Chang
Keyword(s):  
Fluid Model ◽  
Closed Form Solution ◽  
Mean Value ◽  
Form Solution ◽  
Viscoelastic Materials ◽  
Nonlinear Springs ◽  
Constant Rate ◽  
Viscoelastic Modeling ◽  
Spring Constants ◽  
Nonlinear Fluid

In this paper, a simplified spring-dashpot model is proposed to represent the complicated nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been adopted by many researchers to characterize some parts of human body in bioengineering. Among others, the following researchers have already contributed to the development of this field (Weiss et al., [1]; Guedes et al., [2]). Sometimes it is impossible to estimate the constant parameters in the model deterministically, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to characterize the random properties of the viscoelastic materials. The mean value of the displacement of the nonlinear model, subjected to constant rate displacement, can be solved analytically. Based on the closed-form solution, the proposed method produces the statistical responses of the simplified nonlinear fluid model, which is fairly useful in estimating the reliability of the nonlinear system.

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