scholarly journals Global well-posedness for 2-D viscoelastic fluid model

2016 ◽  
Vol 10 ◽  
pp. 2661-2670
Author(s):  
Mikhail A. Artemov ◽  
George G. Berdzenishvili
Keyword(s):  
Viscoelastic Fluid ◽  
Fluid Model ◽  
Well Posedness

scholarly journals On a model for internal waves in rotating fluids

2018 ◽  
Vol 3 (2) ◽  
pp. 627-648 ◽  
Author(s):  
A. Durán
Keyword(s):  
Internal Waves ◽  
Fluid Model ◽  
Well Posedness ◽  
Solitary Wave Solutions ◽  
Rotating Fluid ◽  
Rotating Fluids ◽  
Mathematical Properties ◽  
Gravity Effects ◽  
Two Fluid Model ◽  
Two Fluid

AbstractIn this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the dispersion balance. The physical regime of validation is discussed and mathematical properties of the new system, concerning well-posedness, conservation laws and existence of solitary-wave solutions, are analyzed.

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.

scholarly journals Examination of Well-Posedness of Multi-Fluid Model.

1994 ◽  
Vol 60 (580) ◽  
pp. 4010-4015
Author(s):  
Akio Tomiyama ◽  
Nobutake Kanami ◽  
Isao Kataoka ◽  
Hitoshi Higaki
Keyword(s):  
Fluid Model ◽  
Well Posedness

Numerical Study of MHD Viscoelastic Fluid Flow with Binary Chemical Reaction and Arrhenius Activation Energy

2017 ◽  
Vol 15 (1) ◽  
Author(s):  
M. Mustafa ◽  
A. Mushtaq ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Activation Energy ◽  
Fluid Flow ◽  
Chemical Reaction ◽  
Viscoelastic Fluid ◽  
Numerical Study ◽  
Fluid Model ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Large Temperature ◽  
Temperature Function

Abstract Here we address the influence of heat/mass transfer on MHD axisymmetric viscoelastic fluid flow developed by an elastic sheet stretching linearly in the radial direction. Constitutive relations of Maxwell fluid model are utilized in mathematical formulation of the problem. Non-linear radiation heat flux is factored in the model which accounts for both small and large temperature differences. Chemical reaction effects with modified Arrhenius energy function are analyzed which are not yet explored for viscoelastic fluid flows. Highly accurate numerical computations are performed. Our computations show S-shaped profiles of temperature function in case of sufficiently large temperature differences. Species concentration increases when activation energy for chemical reaction is increased. However, both chemical reaction rate and temperature gradient tend to reduce the solute concentration.

Interfacial Pressure Coefficient for Ellipsoids and Its Effect on the Two-Fluid Model Eigenvalues

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Avinash Vaidheeswaran ◽  
Martin Lopez de Bertodano
Keyword(s):  
Fluid Model ◽  
Pressure Coefficient ◽  
Well Posedness ◽  
Virtual Mass ◽  
Two Phase Flows ◽  
Two Phase ◽  
Pressure Coefficients ◽  
Interfacial Pressure ◽  
Two Fluid Model ◽  
Two Fluid

Analytical expressions for interfacial pressure coefficients are obtained based on the geometry of the bubbles occurring in two-phase flows. It is known that the shape of the bubbles affects the virtual mass and interfacial pressure coefficients, which in turn determines the cutoff void fraction for the well-posedness of two-fluid model (TFM). The coefficient used in the interfacial pressure difference correlation is derived assuming potential flow around a perfect sphere. In reality, the bubbles seen in two-phase flows get deformed, and hence, it is required to estimate the coefficients for nonspherical geometries. Oblate and prolate ellipsoids are considered, and their respective coefficients are determined. It is seen that the well-posedness limit of the TFM is determined by the combination of virtual mass and interfacial pressure coefficient used. The effect of flow separation on the coefficient values is also analyzed.

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