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1

Zuckerwar, Allan J. New constitutive equation for the volume viscosity in fluids. National Aeronautics and Space Administration, Langley Research Center, 1994.

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2

Stephan, K. Thermal conductivity and viscosity data of fluid mixtures. Dechema, 1988.

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3

A, Siginer Dennis, Kim J. H, Bajura R. A, American Society of Mechanical Engineers. Fluids Engineering Division., and Fluids Engineering Conference (1993 : Washington, D.C.), eds. Electro-rheological flows, 1993: Presented at the Fluids Engineering Conference, Washington, D.C., June 20-24, 1993. American Society of Mechanical Engineers, 1993.

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4

L, Streett Craig, Hussaini M. Yousuff, and Langley Research Center, eds. An analysis of artificial viscosity effects on reacting flows using a spectral multi-domain technique. National Aeronautics and Space Administration, Langley Research Center, 1987.

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5

Borman, V. D. Dynamics of infiltration of a nanoporous media with a nonwetting liquid. Nova Science Publishers, 2010.

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6

Lewis Research Center. Institute for Computational Mechanics in Propulsion., ed. Effects of artificial viscosity on the accuracy of high-Reynolds-number [kappa-epsilon] turbulence model. NASA, Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1994.

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7

Gretar, Tryggvason, and Lewis Research Center. Institute for Computational Mechanics in Propulsion., eds. The flow induced by the coalescence of two initially stationary drops. National Aeronautics and Space Administration, Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1994.

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8

Yudaev, Vasiliy. Hydraulics. INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/996354.

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The textbook corresponds to the general education programs of the general courses "Hydraulics" and "Fluid Mechanics". The basic physical properties of liquids, gases, and their mixtures, including the quantum nature of viscosity in a liquid, are described; the laws of hydrostatics, their observation in natural phenomena, and their application in engineering are described. The fundamentals of the kinematics and dynamics of an incompressible fluid are given; original examples of the application of the Bernoulli equation are given. The modes of fluid motion are supplemented by the features of the
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9

Institute for Computer Applications in Science and Engineering., ed. Modelling the transitional boundary layer. National Aeronautics and Space Administration, Langley Research Center, Institute for Computer Applications in Science and Engineering, 1990.

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10

Leonov, A. I. Nonlinear phenomena in flows of viscoelastic polymer fluids. Chapman & Hall, 1994.

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11

R, Menter F., and United States. National Aeronautics and Space Administration., eds. Computation of separated and unsteady flows with one- and two-equation turbulence models: 32nd Aerospace Sciences meeting & exhibit, January 10-13, 1994/Reno, NV. [National Aeronautics and Space Administration, 1994.

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12

T, Papageorgiou Demetrios, Smyrlis Yiorgos S, and Institute for Computer Applications in Science and Engineering., eds. Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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13

A, Wakeham W., and Ho C. Y. 1928-, eds. Transport properties of fluids: Thermal conductivity, viscosity, and diffusion coefficient. Hemisphere Pub. Corp., 1988.

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14

Rishell, Amy, and Theodore Selby, eds. Viscosity and Rheology of In-Service Fluids as They Pertain to Condition Monitoring. ASTM International, 2013. http://dx.doi.org/10.1520/stp1564-eb.

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15

Rishell, Amy. Viscosity and rheology of in-service fluids as they pertain to condition monitoring. ASTM International, 2013.

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16

United States. National Aeronautics and Space Administration., ed. Numerical solutions of the complete Navier-Stokes equations: Progress report no. 16 for the period July 1, 1998 to December 31, 1989. Dept. of Mechanical and Aerospace Engineering, North Carolina State University, 1989.

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17

United States. National Aeronautics and Space Administration., ed. Numerical solutions of the complete Navier-Stokes equations: Progress report no. 27 for the period October 1, 1995 to September 30, 1996. Dept. of Mechanical and Aerospace Engineering, North Carolina State University, 1996.

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18

Yeh, Chou, and Institute for Computer Applications in Science and Engineering., eds. Analytical and phenomenological studies of rotating turbulence. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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19

P, Ryan Michael. The viscosity of synthetic and natural silicate melts and glasses at high temperatures and 1 bar (10⁵ Pascals) pressure and at higher pressures. U.S. G.P.O., 1987.

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20

P, Ryan Michael. The viscosity of synthetic and natural silicate melts and glasses at high temperatures and 1 bar (10⁵ Pascals) pressure and at higher pressures. U.S. Dept. of the Interior, 1987.

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21

P, Ryan Michael. The viscosity of synthetic and natural silicate melts and glasses at high temperatures and 1 bar (10p5s. Dept. of the Interior, U.S. Geological Survey, 1987.

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22

Murthy, S. N. B. Application of large eddy interaction model to a mixing layer. Lewis Research Center, 1989.

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23

Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. American Mathematical Society, 2013.

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24

Free surface flows with viscosity. Computational Mechanics Publications, 1998.

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25

Dynamics of compressible viscous fluid. CSP, 2009.

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26

Escudier, Marcel. Fluids and fluid properties. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0002.

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In this chapter it is shown that the differences between solids, liquids, and gases have to be explained at the level of the molecular structure. The continuum hypothesis makes it possible to characterise any fluid and ultimately analyse its response to pressure difference Δ‎p and shear stress τ‎ through macroscopic physical properties, dependent only upon absolute temperature T and pressure p, which can be defined at any point in a fluid. The most important of these physical properties are density ρ‎ and viscosity μ‎, while some problems are also influenced by compressibility, vapour pressure
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27

Ovarlez, Guillaume, and Sarah Hormozi. Lectures on Visco-Plastic Fluid Mechanics. Springer, 2018.

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28

Ovarlez, Guillaume, and Sarah Hormozi. Lectures on Visco-Plastic Fluid Mechanics. Springer, 2019.

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29

Effects of Higher Order Viscosity Terms on Fluid Flow. Creative Media Partners, LLC, 2021.

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30

Stewart, Charles Wayne. Coalescence of ellipsoidal bubbles rising freely in low-viscosity liquids. 1993.

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31

Guo, Boling, Chunxiao Guo, Qiaoxin Li, Yaqing Liu, and China Science China Science Publishing & Media Ltd. Non-Newtonian Fluids: A Dynamical Systems Approach. de Gruyter GmbH, Walter, 2018.

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32

Guo, Boling, Chunxiao Guo, Qiaoxin Li, Yaqing Liu, and China Science China Science Publishing & Media Ltd. Non-Newtonian Fluids: A Dynamical Systems Approach. de Gruyter GmbH, Walter, 2018.

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33

Non-Newtonian Fluids: A Dynamical Systems Approach. De Gruyter, Inc., 2018.

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34

Stephen, K., and T. Heckenberger. Thermal Conductivity and Viscosity Data of Fluid Mixtures (Chemistry Data Series). Scholium Intl, 1989.

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35

Rajeev, S. G. Ideal Fluid Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0004.

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Some solutions of Euler’s equations are found here. The simplest are the steady flows: water flowing out of a tank at a constant rate, the Venturi and Pitot tubes. Another is the static solution of a self-gravitating fluid of variable density (e.g., a star). If the total mass is too large, such a star can collapse (Chandrasekhar limit). If the flow is both irrotational and incompressible, it must satisfy Laplace’s equation. Complex analysismethods can be used to solve for the flow past a cylinder or inside a disk with a stirrer. Joukowski used conformal transformations on the cylinder to find
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36

Tyvand, Peder A. Free Surface Flows with Viscosity (Advances in Fluid Mechanics Ser., V.16). WIT Press (UK), 1997.

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37

Escudier, Marcel. Basic equations of viscous-fluid flow. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0015.

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In this chapter it is shown that application of the momentum-conservation equation (Newton’s second law of motion) to an infinitesimal cube of fluid leads to Cauchy’s partial differential equations, which govern the flow of any fluid satisfying the continuum hypothesis. Any fluid flow must also satisfy the continuity equation, another partial differential equation, which is derived from the mass-conservation equation. It is shown that distortion of a flowing fluid can be split into elongational distortion and angular distortion or shear strain. For a Newtonian fluid, the normal and shear stres
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38

Escudier, Marcel. Introduction to Engineering Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.001.0001.

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Turbojet and turbofan engines, rocket motors, road vehicles, aircraft, pumps, compressors, and turbines are examples of machines which require a knowledge of fluid mechanics for their design. The aim of this undergraduate-level textbook is to introduce the physical concepts and conservation laws which underlie the subject of fluid mechanics and show how they can be applied to practical engineering problems. The first ten chapters are concerned with fluid properties, dimensional analysis, the pressure variation in a fluid at rest (hydrostatics) and the associated forces on submerged surfaces, t
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39

Cowan, Martin E. Synthesis and characterization of high molecular weight water-soluble polymers to study the role of extensional viscosity in polymeric drag reduction. 2000.

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40

Schiesser, W. E., and C. A. Silebi. Computational Transport Phenomena: Numerical Methods for the Solution of Transport Problems. Cambridge University Press, 2018.

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41

Rajeev, S. G. Euler’s Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0002.

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Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the evolution of vorticity (Helmholtz equation). Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates density to pressure). Of special interest is the case of incompressible flow; when the fluid velocity is small compared to the speed of sound, the density may be treated as a constant. In this limit, Euler’s equations have scale invariance in addi
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42

Rajeev, S. G. Viscous Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0005.

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Here some solutions of Navier–Stokes equations are found.The flow of a fluid along a pipe (Poisseuille flow) and that between two rotating cylinders (Couette flow) are the simplest. In the limit of large viscosity (small Reynolds number) the equations become linear: Stokes equations. Flow past a sphere is solved in detail. It is used to calculate the drag on a sphere, a classic formula of Stokes. An exact solution of the Navier–Stokes equation describing a dissipating vortex is also found. It is seen that viscosity cannot be ignored at the boundary or at the core of vortices.
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43

Rajeev, S. G. Shocks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0006.

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When the speed of a fluid exceeds that of sound, discontinuities in density occur, called shocks.The opposite limit from incompressibility (constant density) is constant pressure. In this limit, we get Burgers equation. It can be solved exactly in one dimension using the Cole–Hopf transformation. The limit of small viscosity is found not to be the same as zero viscosity: there is a residual drag no matter how small it is. The Maxwell construction of thermodynamics was adapted by Lax and Oleneik to derive rules for shocks in this limit. The Riemann problem of time evolution with a discontinuous
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44

Escudier, Marcel. Internal laminar flow. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0016.

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In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraul
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45

Allen, Michael P., and Dominic J. Tildesley. Nonequilibrium molecular dynamics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803195.003.0011.

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This chapter explains some of the fundamental issues associated with applying perturbations to a molecular dynamics simulation, along with practical details of methods for studying systems out of equilibrium. The main emphasis is on fluid flow and viscosity measurements. Spatially homogeneous perturbations are described to study shear and extensional flow. Non-equilibrium methods are applied to the study of heat flow and the calculation of the thermal conductivity. Issues of thermostatting, and the modelling of surface-fluid interactions for inhomogeneous systems, are discussed. The measuremen
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46

Stephan, Karl. Viscosity of Dense Fluids. Springer, 2013.

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47

Stephan, K. Viscosity of Dense Fluids. Springer London, Limited, 2013.

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48

Rajeev, S. G. Boundary Layers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0007.

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It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall invalidate Euler’s equations. Prandtl proposed that viscosity has negligible effect except near a thin region near a wall. Prandtl’s equations simplify the Navier-Stokes equation in this boundary layer, by ignoring one dimension. They have an unusual scale invariance in which the distances along the boundary and perpendicular to it have different dimensions. Using this symmetry, Blasius reduced Prandtl’
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49

Rajeev, S. G. The Navier–Stokes Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0003.

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When different layers of a fluid move at different velocities, there is some friction which results in loss of energy and momentum to molecular degrees of freedom. This dissipation is measured by a property of the fluid called viscosity. The Navier–Stokes (NS) equations are the modification of Euler’s equations that include this effect. In the incompressible limit, the NS equations have a residual scale invariance. The flow depends only on a dimensionless ratio (the Reynolds number). In the limit of small Reynolds number, the NS equations become linear, equivalent to the diffusion equation. Id
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50

Brummer, Rüdiger. Rheology Essentials of Cosmetic and Food Emulsions. Springer, 2005.

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