Decay Properties of Axially Symmetric D-Solutions to the Steady Navier–Stokes Equations

2017 ◽  
Vol 20 (1) ◽  
pp. 7-25 ◽  
Author(s):  
Shangkun Weng
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Decay Properties

Effect of a Time-Dependent Stenosis on Flow Through a Tube

1968 ◽  
Vol 90 (2) ◽  
pp. 248-254 ◽  
Author(s):  
D. F. Young
Keyword(s):  
Stokes Equations ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Arterial System ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Dependent Growth ◽  
Abnormal Tissue

A common occurrence in the arterial system is the narrowing of arteries due to the development of atherosclerotic plaques or other types of abnormal tissue development. As these growths project into the lumen of the artery, the flow is disturbed and there develops a potential coupling between the growth and the blood flow through the artery. A discussion of the various possible consequences of this interaction is given. It is noted that very small growths leading to mild stenotic obstructions, although not altering the gross flow characteristics significantly, may be important in triggering biological mechanisms such as intimal cell proliferation or changes in vessel caliber. An analysis of the effect of an axially symmetric, time-dependent growth into the lumen of a tube of constant cross section through which a Newtonian fluid is steadily flowing is presented. This analysis is based on a simplified model in which the convective acceleration terms in the Navier-Stokes equations are neglected. Effect of growth on pressure distribution and wall shearing stress is given and possible biological implications are discussed.

The axially symmetric flow of a viscous fluid between two infinite rotating disks

1962 ◽  
Vol 266 (1324) ◽  
pp. 109-121 ◽  
Keyword(s):  
Stokes Equations ◽  
Transverse Velocity ◽  
Complete Solution ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Rotating Disks ◽  
Symmetric Flow ◽  
Navier Stokes Equations ◽  
High Reynolds

This is a numerical investigation of the similarity solutions of the Navier-Stokes equations describing the steady axially symmetric flow of a viscous incompressible fluid between two infinite rotating disks. Several cases have been examined in detail and the radial and transverse velocity profiles are displayed; value of the torque experienced in these cases are also given. It is found that at high Reynolds numbers, the main core of the fluid is in a state of solid rotation for practically all values of the ratio of angular velocity of the two disks. When the disks are rotating in the same sense, and when one is at rest and the other is rotating, the results show that edge effects must be taken into account in any complete solution to the problem. However, when the disks rotate in opposite directions, the solutions exhibit features which appear unlikely to occur in practice.

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