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On the eigenvalue problems of Poiseu...

Maserumule, Motodi Samuel.

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On the eigenvalue problems of Poiseuille flows in a circular pipe.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On the eigenvalue problems of Poiseuille flows in a circular pipe./
Author:	Maserumule, Motodi Samuel.
Description:	133 p.
Notes:	Adviser: Isom Herron.
Contained By:	Dissertation Abstracts International63-03B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3045449
ISBN:	0493595937

On the eigenvalue problems of Poiseuille flows in a circular pipe.
Maserumule, Motodi Samuel.

On the eigenvalue problems of Poiseuille flows in a circular pipe. - 133 p.

Adviser: Isom Herron.

Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2002.

In this work we introduce a novel formulation of Sexl's equations obtained by expanding three dimensional infinitesimal disturbances about the axisymmetric Hagen-Poiseuille flow in a pipe of circular cross section. The formulation is based on a representation theorem of solenoidal vector fields due to Schmitt and von Wahl [53]. We use the new formulation to prove that the linear nonaxisymmetric eigenvalue problem associated with Hagen-Poiseuille flow has infinitely many eigenfunctions which form a complete set. The method of proof includes the DiPrima-Habetler completeness theorem [14]. A nontrivial transformation that links the new formulation with the formulation used by Salwen et al [50] is presented.

ISBN: 0493595937Subjects--Topical Terms:

1018410
Applied Mechanics.

On the eigenvalue problems of Poiseuille flows in a circular pipe.
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005 20110509
008 110509s2002 eng d
020 $a 0493595937
035 $a (UnM)AAI3045449
035 $a AAI3045449
040 $a UnM $c UnM
100 1 $a Maserumule, Motodi Samuel. $3 1258484
245 1 0 $a On the eigenvalue problems of Poiseuille flows in a circular pipe.
300 $a 133 p.
500 $a Adviser: Isom Herron.
500 $a Source: Dissertation Abstracts International, Volume: 63-03, Section: B, page: 1390.
502 $a Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2002.
520 $a In this work we introduce a novel formulation of Sexl's equations obtained by expanding three dimensional infinitesimal disturbances about the axisymmetric Hagen-Poiseuille flow in a pipe of circular cross section. The formulation is based on a representation theorem of solenoidal vector fields due to Schmitt and von Wahl [53]. We use the new formulation to prove that the linear nonaxisymmetric eigenvalue problem associated with Hagen-Poiseuille flow has infinitely many eigenfunctions which form a complete set. The method of proof includes the DiPrima-Habetler completeness theorem [14]. A nontrivial transformation that links the new formulation with the formulation used by Salwen et al [50] is presented.
520 $a The relationship between axisymmetric eigenfunctions associated with Hagen-Poiseuille flow and their counterparts associated with parabolic Poiseuille flow is explored by means of a numerical study. We use a modified Chebyshev tau numerical scheme to compute eigenvalues and eigenfunctions of the two problems. The parabolic Poiseuille flow is easier to deal with because of the absence of a singularity in the differential equations. An exact solution to the axisymmetric parabolic Poiseuille flow problem is presented for the first time.
590 $a School code: 0185.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Fluid and Plasma. $3 1018402
690 $a 0346
690 $a 0405
690 $a 0759
710 2 0 $a Rensselaer Polytechnic Institute. $3 1019062
773 0 $t Dissertation Abstracts International $g 63-03B.
790 $a 0185
790 1 0 $a Herron, Isom, $e advisor
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3045449