Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour

Dennis A. Siginer, Mario F. Letelier

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

The fully developed steady velocity field in pressure gradient driven laminar flow of non-linear viscoelastic fluids with instantaneous elasticity constitutively represented by a class of single mode, non-affine quasilinear constitutive equations is investigated in straight pipes of arbitrary contour ∂D. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at O(1). Field variables are expanded in asymptotic series in terms of the Weissenberg number Wi. The analysis does not place any restrictions on the smallness of the driving pressure gradients which can be large and applies to dilute and weakly elastic non-linear viscoelastic fluids. The velocity field is investigated up to and including the third order in Wi. The Newtonian field in general arbitrary contours is obtained and longitudinal velocity field components due to shear-thinning and to non-linear viscoelastic effects are identified. Third order analysis shows a further contribution to the longitudinal field driven by first normal stress differences. Secondary flows driven by unbalanced second normal stresses in the cross-section manifest themselves as well at this order. Longitudinal equal velocity contours, the secondary flow field structure, the first and the second normal stress differences as well as wall shear stress variations are discussed for several non-circular contours some for the first time.

Original languageEnglish
Pages (from-to)2188-2202
Number of pages15
JournalInternational Journal of Heat and Mass Transfer
Volume54
Issue number9-10
DOIs
Publication statusPublished - Apr 1 2011

Fingerprint

laminar flow
Laminar flow
tubes
Fluids
fluids
velocity distribution
Secondary flow
Pressure gradient
secondary flow
pressure gradients
Shear thinning
asymptotic series
base flow
Constitutive equations
shear thinning
cross sections
constitutive equations
Shear stress
Elasticity
Flow fields

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

@article{d1653a1e02294153a2d5d7043bd9ab32,
title = "Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour",
abstract = "The fully developed steady velocity field in pressure gradient driven laminar flow of non-linear viscoelastic fluids with instantaneous elasticity constitutively represented by a class of single mode, non-affine quasilinear constitutive equations is investigated in straight pipes of arbitrary contour ∂D. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at O(1). Field variables are expanded in asymptotic series in terms of the Weissenberg number Wi. The analysis does not place any restrictions on the smallness of the driving pressure gradients which can be large and applies to dilute and weakly elastic non-linear viscoelastic fluids. The velocity field is investigated up to and including the third order in Wi. The Newtonian field in general arbitrary contours is obtained and longitudinal velocity field components due to shear-thinning and to non-linear viscoelastic effects are identified. Third order analysis shows a further contribution to the longitudinal field driven by first normal stress differences. Secondary flows driven by unbalanced second normal stresses in the cross-section manifest themselves as well at this order. Longitudinal equal velocity contours, the secondary flow field structure, the first and the second normal stress differences as well as wall shear stress variations are discussed for several non-circular contours some for the first time.",
author = "Siginer, {Dennis A.} and Letelier, {Mario F.}",
year = "2011",
month = "4",
day = "1",
doi = "10.1016/j.ijheatmasstransfer.2010.11.041",
language = "English",
volume = "54",
pages = "2188--2202",
journal = "International Journal of Heat and Mass Transfer",
issn = "0017-9310",
publisher = "Elsevier Ltd",
number = "9-10",

}

Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour. / Siginer, Dennis A.; Letelier, Mario F.

In: International Journal of Heat and Mass Transfer, Vol. 54, No. 9-10, 01.04.2011, p. 2188-2202.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour

AU - Siginer, Dennis A.

AU - Letelier, Mario F.

PY - 2011/4/1

Y1 - 2011/4/1

N2 - The fully developed steady velocity field in pressure gradient driven laminar flow of non-linear viscoelastic fluids with instantaneous elasticity constitutively represented by a class of single mode, non-affine quasilinear constitutive equations is investigated in straight pipes of arbitrary contour ∂D. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at O(1). Field variables are expanded in asymptotic series in terms of the Weissenberg number Wi. The analysis does not place any restrictions on the smallness of the driving pressure gradients which can be large and applies to dilute and weakly elastic non-linear viscoelastic fluids. The velocity field is investigated up to and including the third order in Wi. The Newtonian field in general arbitrary contours is obtained and longitudinal velocity field components due to shear-thinning and to non-linear viscoelastic effects are identified. Third order analysis shows a further contribution to the longitudinal field driven by first normal stress differences. Secondary flows driven by unbalanced second normal stresses in the cross-section manifest themselves as well at this order. Longitudinal equal velocity contours, the secondary flow field structure, the first and the second normal stress differences as well as wall shear stress variations are discussed for several non-circular contours some for the first time.

AB - The fully developed steady velocity field in pressure gradient driven laminar flow of non-linear viscoelastic fluids with instantaneous elasticity constitutively represented by a class of single mode, non-affine quasilinear constitutive equations is investigated in straight pipes of arbitrary contour ∂D. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at O(1). Field variables are expanded in asymptotic series in terms of the Weissenberg number Wi. The analysis does not place any restrictions on the smallness of the driving pressure gradients which can be large and applies to dilute and weakly elastic non-linear viscoelastic fluids. The velocity field is investigated up to and including the third order in Wi. The Newtonian field in general arbitrary contours is obtained and longitudinal velocity field components due to shear-thinning and to non-linear viscoelastic effects are identified. Third order analysis shows a further contribution to the longitudinal field driven by first normal stress differences. Secondary flows driven by unbalanced second normal stresses in the cross-section manifest themselves as well at this order. Longitudinal equal velocity contours, the secondary flow field structure, the first and the second normal stress differences as well as wall shear stress variations are discussed for several non-circular contours some for the first time.

UR - http://www.scopus.com/inward/record.url?scp=79952282017&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952282017&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2010.11.041

DO - 10.1016/j.ijheatmasstransfer.2010.11.041

M3 - Article

VL - 54

SP - 2188

EP - 2202

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

IS - 9-10

ER -