Computer extended series solution for unsteady flow in a contracting or expanding pipe

N. M. Bujurke, N. P. Pai, G. Jayaraman

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Unsteady flow in a semi-infinite contracting or expanding pipe is reinvestigated using long series analysis. The proposed series method is useful in analysing the problem for a moderately large constant α (α = aȧ/v, where a = a(t), the radius of the pipe is a function of time, ȧ(t) is the velocity of the wall, and v is kinematic viscosity). For positive values of α (expansion of the pipe) accuracy of the series representing shear stress and pressure gradient is increased from α = 2·89 to α = 6·0 by extracting the singularity followed by completion of the series. For negative values of α (contraction of the pipe), we revert the series which results into the increase of the region of validity of the transposed series from α = -25·0 to α -2·89. Later we use Padé approximants for summing them. Also, the asymptotic solution for large values of α is obtained and it agrees closely with pure numerical values of shear stress at the wall and pressure gradient.

Original languageEnglish
Pages (from-to)151-165
Number of pages15
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume60
Issue number2
DOIs
Publication statusPublished - 01-01-1998

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Series Solution
Unsteady Flow
Unsteady flow
Pipe
Series
Pressure gradient
Shear stress
Pressure Gradient
Shear Stress
Asymptotic Solution
Viscosity
Completion
Contraction
Kinematics
Radius
Singularity

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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Computer extended series solution for unsteady flow in a contracting or expanding pipe. / Bujurke, N. M.; Pai, N. P.; Jayaraman, G.

In: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), Vol. 60, No. 2, 01.01.1998, p. 151-165.

Research output: Contribution to journalArticle

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