Elbows for Accelerated Flow

Abstract It is of interest in the field of fluid mechanics to determine the shape of that two-dimensional channel which will most effectively turn a stream of fluid through an angle β while simultaneously increasing its velocity by a factor r. In the present paper, criteria which such a channel should satisfy are suggested and an elbow which meets these requirements is obtained. The solution is carried out first for a nonviscous incompressible fluid and then for the compressible medium using the Karmen-Tsien linearized pressure-volume relation.

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Effects of Heat Transfer During Peristaltic Transport in Nonuniform Channel With Permeable Walls

Journal of Heat Transfer ◽

10.1115/1.4034551 ◽

2016 ◽

Vol 139 (1) ◽

Cited By ~ 2

Author(s):

Siddharth Shankar Bhatt ◽

Amit Medhavi ◽

R. S. Gupta ◽

U. P. Singh

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Incompressible Fluid ◽

Friction Force ◽

Viscous Incompressible Fluid ◽

Peristaltic Transport ◽

Two Dimensional ◽

Peristaltic Motion ◽

Long Wavelength ◽

Permeable Walls

In the present investigation, problem of heat transfer has been studied during peristaltic motion of a viscous incompressible fluid for two-dimensional nonuniform channel with permeable walls under long wavelength and low Reynolds number approximation. Expressions for pressure, friction force, and temperature are obtained. The effects of different parameters on pressure, friction force, and temperature have been discussed through graphs.

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Internal waves in a viscous atmosphere

Journal of Fluid Mechanics ◽

10.1017/s0022112075003278 ◽

1975 ◽

Vol 72 (4) ◽

pp. 773-786 ◽

Cited By ~ 6

Author(s):

W. L. Chang ◽

T. N. Stevenson

Keyword(s):

Energy Source ◽

Incompressible Fluid ◽

Internal Waves ◽

Infinite Number ◽

Similarity Solution ◽

Small Amplitude ◽

Horizontal Plane ◽

Two Dimensional ◽

The Waves ◽

Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

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p-version least squares finite element formulation for two-dimensional, incompressible fluid flow

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.1650180104 ◽

1994 ◽

Vol 18 (1) ◽

pp. 43-69 ◽

Cited By ~ 38

Author(s):

Daniel Winterscheidt ◽

Karan S. Surana

Keyword(s):

Finite Element ◽

Fluid Flow ◽

Incompressible Fluid ◽

Least Squares ◽

Finite Element Formulation ◽

Element Formulation ◽

Two Dimensional ◽

Incompressible Fluid Flow

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The inf-sup stability of the lowest order Taylor–Hood pair on affine anisotropic meshes

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drz028 ◽

2019 ◽

Vol 40 (4) ◽

pp. 2377-2398

Author(s):

Gabriel R Barrenechea ◽

Andreas Wachtel

Keyword(s):

Finite Element ◽

Fluid Mechanics ◽

Incompressible Fluid ◽

Stokes Equations ◽

Sufficient Conditions ◽

Navier Stokes ◽

Element Solution ◽

Navier Stokes Equations ◽

Anisotropic Meshes ◽

Theoretical Results

Abstract Uniform inf-sup conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier–Stokes equations. In this work we prove a uniform inf-sup condition for the lowest-order Taylor–Hood pairs $\mathbb{Q}_2\times \mathbb{Q}_1$ and $\mathbb{P}_2\times \mathbb{P}_1$ on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalize Verfürth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.

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