On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium

S. V. Meleshko; N. P. Moshkin; V. V. Pukhnachev

doi:10.1016/j.ijnonlinmec.2018.06.002

On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium

S. V. Meleshko, N. P. Moshkin, V. V. Pukhnachev

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson–Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solutions were derived.

Original language	English
Pages (from-to)	152-157
Number of pages	6
Journal	International Journal of Non-Linear Mechanics
Volume	105
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2018.06.002
Publication status	Published - 1 Oct 2018

Keywords

Invariant solution
Johnson–Segalman convected derivative
Lagrangian coordinates
Lie group
Stagnation point flow
UCM
Viscoelastic fluid
Johnson-Segalman convected derivative
FLUID
MODEL
FLOW

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10.1016/j.ijnonlinmec.2018.06.002

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title = "On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium",

abstract = "Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson–Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solutions were derived.",

keywords = "Invariant solution, Johnson–Segalman convected derivative, Lagrangian coordinates, Lie group, Stagnation point flow, UCM, Viscoelastic fluid, Johnson-Segalman convected derivative, FLUID, MODEL, FLOW",

author = "Meleshko, {S. V.} and Moshkin, {N. P.} and Pukhnachev, {V. V.}",

year = "2018",

month = oct,

day = "1",

doi = "10.1016/j.ijnonlinmec.2018.06.002",

language = "English",

volume = "105",

pages = "152--157",

journal = "International Journal of Non-Linear Mechanics",

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T1 - On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium

AU - Meleshko, S. V.

AU - Moshkin, N. P.

AU - Pukhnachev, V. V.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson–Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solutions were derived.

AB - Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson–Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solutions were derived.

KW - Invariant solution

KW - Johnson–Segalman convected derivative

KW - Lagrangian coordinates

KW - Lie group

KW - Stagnation point flow

KW - UCM

KW - Viscoelastic fluid

KW - Johnson-Segalman convected derivative

KW - FLUID

KW - MODEL

KW - FLOW

UR - http://www.scopus.com/inward/record.url?scp=85049022317&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2018.06.002

DO - 10.1016/j.ijnonlinmec.2018.06.002

M3 - Article

AN - SCOPUS:85049022317

VL - 105

SP - 152

EP - 157

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

ER -