Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment

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Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment. / Moshkin, N. P.

In: Journal of Applied and Industrial Mathematics, Vol. 16, No. 1, 02.2022, p. 105-115.

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

BibTeX

@article{e53290e1cdc345879bf5858809dc0b89,

title = "Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment",

abstract = "Two-dimensional unsteady stagnation-point flow of a viscoelastic fluid is studied assumingthat it obeys the upper-convected Maxwell (UCM) model. The solutions of constitutive equationsare found under the assumption that the components of the extra stress tensor are polynomials inthe spatial variable along a rigid wall. The class of solutions for unsteady flows in aneighbourhood of the front or rear stagnation point on a plane boundary is considered, and therange of possible behaviors is revealed depending on the initial stage (initial data) and on whetherthe pressure gradient is an accelerating or decelerating function of time. The velocity and stresstensor component profiles are obtained by numerical integration of the system of nonlinearordinary differential equations. The solutions of the equations exhibit finite-time singularitiesdepending on the initial data and the type of dependence of pressure gradient on time.",

keywords = "blow-up solution, Maxwell viscoelastic medium, Riccati equation, unsteady critical-point flow, upper convective derivative",

author = "Moshkin, {N. P.}",

note = "Funding Information: This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00096. Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = feb,

doi = "10.1134/S1990478922010100",

language = "English",

volume = "16",

pages = "105--115",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment

AU - Moshkin, N. P.

PY - 2022/2

Y1 - 2022/2

N2 - Two-dimensional unsteady stagnation-point flow of a viscoelastic fluid is studied assumingthat it obeys the upper-convected Maxwell (UCM) model. The solutions of constitutive equationsare found under the assumption that the components of the extra stress tensor are polynomials inthe spatial variable along a rigid wall. The class of solutions for unsteady flows in aneighbourhood of the front or rear stagnation point on a plane boundary is considered, and therange of possible behaviors is revealed depending on the initial stage (initial data) and on whetherthe pressure gradient is an accelerating or decelerating function of time. The velocity and stresstensor component profiles are obtained by numerical integration of the system of nonlinearordinary differential equations. The solutions of the equations exhibit finite-time singularitiesdepending on the initial data and the type of dependence of pressure gradient on time.

AB - Two-dimensional unsteady stagnation-point flow of a viscoelastic fluid is studied assumingthat it obeys the upper-convected Maxwell (UCM) model. The solutions of constitutive equationsare found under the assumption that the components of the extra stress tensor are polynomials inthe spatial variable along a rigid wall. The class of solutions for unsteady flows in aneighbourhood of the front or rear stagnation point on a plane boundary is considered, and therange of possible behaviors is revealed depending on the initial stage (initial data) and on whetherthe pressure gradient is an accelerating or decelerating function of time. The velocity and stresstensor component profiles are obtained by numerical integration of the system of nonlinearordinary differential equations. The solutions of the equations exhibit finite-time singularitiesdepending on the initial data and the type of dependence of pressure gradient on time.

KW - blow-up solution

KW - Maxwell viscoelastic medium

KW - Riccati equation

KW - unsteady critical-point flow

KW - upper convective derivative

UR - http://www.scopus.com/inward/record.url?scp=85134224318&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/266650b8-9ae6-3f11-a618-409d89c33312/

U2 - 10.1134/S1990478922010100

DO - 10.1134/S1990478922010100

M3 - Article

AN - SCOPUS:85134224318

VL - 16

SP - 105

EP - 115

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -

ID: 36770798