scholarly journals An Integral of the Two-Dimensional Stationary Viscous Fluid Flow Equations

2021 ◽  
Vol 1945 (1) ◽  
pp. 012019
Author(s):  
D V Knyazev
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Viscous Fluid Flow ◽  
Flow Equations

scholarly journals A New Technique to Solve Two-Dimensional Viscous Fluid Flow Among Slowly Expand or Contract Walls

2020 ◽  
Vol 7 (4) ◽  
pp. 631-641
Author(s):  
Abdul-Sattar J. Al-Saif ◽  
Takia Ahmed J. Al-Griffi
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
New Method ◽  
New Technique ◽  
Two Dimensional ◽  
Viscous Fluid Flow ◽  
Homotopy Perturbation ◽  
A New Technique ◽  
Expanding Or Contracting Walls ◽  
Method Show

In this research, we have proposed a new technique to solve two-dimensional (2D) viscous fluid flow among slowly expanding or contracting walls. The new technique depends on combining the algorithms of Yang transform and the homotopy perturbation methods. The results, obtained from the first iteration and by using the new method, show the accuracy and efficiency of this method compared to the other methods, used to find the analytical approximate solution for the problem caused by the 2D viscous fluid flow. Moreover, the graphs of the new solutions show the validity, usefulness and necessity of the new method.

The Stability of Viscous Fluid Flow under Pressure between Parallel Planes

1936 ◽  
Vol 32 (1) ◽  
pp. 40-54 ◽  
Author(s):  
S. Goldstein
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Exponential Factor ◽  
Small Oscillations ◽  
Viscous Fluid Flow ◽  
The Stability ◽  
Image Position ◽  
Disturbed Motion

If we consider, by the method of small oscillations, the stability of a viscous fluid flow in which the undisturbed velocity is parallel to the axis ofxand its magnitudeUis a function ofyonly (x, y, zbeing rectangular Cartesian co-ordinates), and if we assume that any possible disturbance may be analysed into a number (usually infinite) of principal disturbances, each of which involves the time only through a single exponential factor, then it has been proved by Squire, by supposing the disturbance analysed also into constituents which are simple harmonic functions ofxandz, and considering only a single constituent, that if instability occurs at all, it will occur for the lowest Reynolds number for a disturbance which is two-dimensional, in thex, yplane. Hence only two-dimensional disturbances need be considered. The velocity components in the disturbed motion will be denoted by (U+u, v). Since only infinitesimal disturbances are considered, all terms in the equations of motion which are quadratic inuandvare neglected. Whenuandvare taken to be functions ofymultiplied byei(αx−βi), the equation of continuity becomesand the result of eliminating the pressure in the equations of motion then gives the following equation forv, where ν is the kinematic viscosity of the fluid:

Sign in / Sign up

Export Citation Format

Share Document