Asymptotic Analyses of the Start-Up Stage of Couette Flow Subjected to Different Boundary Conditions

Chen Lei, Gang Liu, Guozhong Zhang, Yuannan Tang, John Chai

Research output: Contribution to journalArticle

Abstract

In this article, the process for reaching “developed” stage was investigated under both imposed shear stress and specified velocity boundary conditions. Four specific situations are investigated. These are (1) constant shear stress, (2) linearly increasing shear stress from zero shear, (3) constant velocity and (4) linearly increasing velocity from stationary. Analytical solutions of velocity distributions under these four situations were obtained. A dimensionless viscosity, defined as the ratio of the measured viscosity calculated based on the measuring principle of Couette-type viscometer to the true viscosity of fluid was proposed to describe the initial transient period. We define the “developed” stage when the dimensionless viscosity is 1% away from its final value or when it reaches 1.01. By analyzing Stokes’ first problem, compact models of the dimensionless viscosity were expressed and exact quantitative relations among the initial values of dimensionless viscosity under these four specific situations were found. Time periods for Couette flow to reach the “developed” stage was calculated. The development time is the shortest under the constant velocity boundary and is the longest under the linearly increasing shear stress boundary.
LanguageEnglish
Pages177-182
Number of pages6
JournalInternational Communications in Heat and Mass Transfer
Volume88
Early online date26 Sep 2017
DOIs
Publication statusPublished - Nov 2017

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Couette flow
Boundary conditions
Viscosity
viscosity
boundary conditions
shear stress
Shear stress
viscometers
Viscometers
Velocity distribution
velocity distribution
shear
Fluids
fluids

Cite this

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abstract = "In this article, the process for reaching “developed” stage was investigated under both imposed shear stress and specified velocity boundary conditions. Four specific situations are investigated. These are (1) constant shear stress, (2) linearly increasing shear stress from zero shear, (3) constant velocity and (4) linearly increasing velocity from stationary. Analytical solutions of velocity distributions under these four situations were obtained. A dimensionless viscosity, defined as the ratio of the measured viscosity calculated based on the measuring principle of Couette-type viscometer to the true viscosity of fluid was proposed to describe the initial transient period. We define the “developed” stage when the dimensionless viscosity is 1{\%} away from its final value or when it reaches 1.01. By analyzing Stokes’ first problem, compact models of the dimensionless viscosity were expressed and exact quantitative relations among the initial values of dimensionless viscosity under these four specific situations were found. Time periods for Couette flow to reach the “developed” stage was calculated. The development time is the shortest under the constant velocity boundary and is the longest under the linearly increasing shear stress boundary.",
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Asymptotic Analyses of the Start-Up Stage of Couette Flow Subjected to Different Boundary Conditions. / Lei, Chen; Liu, Gang; Zhang, Guozhong; Tang, Yuannan ; Chai, John.

In: International Communications in Heat and Mass Transfer, Vol. 88, 11.2017, p. 177-182.

Research output: Contribution to journalArticle

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AU - Chai, John

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