Analytical solutions of upper-convected Maxwell fluid flow with exponential dependence of viscosity on the pressure
type: Item
instance of: scholarly article
title: Analytical solutions of upper-convected Maxwell fluid flow with exponential dependence of viscosity on the pressure
zbMATH Open document ID: 1498.76007
author: Abdul Rauf
author: Tahir Mushtaq Qureshi
author: Obaid Ullah Mehmood
author: Constantin Fetecau
published in: European Journal of Mechanics. B. Fluids
publication date: 2021-12-01T00:00:00Z
review text: Starting from basic models according to [\textit{S. Bair} and \textit{P. Kottke}, ``Pressure-viscosity relationships for elastohydrodynamics'', Tribol. Trans. 46, 289--295 (2003); \textit{P. W. Bridgman}, The physics of high pressure. New York, NY: MacMillan Company (1931); \textit{G. G. Stokes}, ``On the theories of the internal friction of fluids in motion, and motion of elastic solids'', Trans. Camb. Phil. Soc. 8, 287--305 (1845)] and from a model according to [\textit{S. Karra} et al., ``On Maxwell fluids with relaxation time and viscosity depending on the pressure'', Int. J. Non-Linear Mech. 46, No. 1, 819--827 (2011; \url{doi:10.1016/j.ijnonlinmec.2011.02.013})], the authors considered the following model, more specifically, they consider the constitutive equations of incompressible upper-convected Maxwell (UCM) fluids with pressure-dependent viscosity given by the relations \[ T=-pI+S, \quad S+\lambda((\delta S)/(\delta t))=\eta(p)A, \tag{1}\] where \(S\) is the extra-stress tensor, \(\lambda\) is the relaxation time, \(\eta(p)\) is the pressure-dependent viscosity, and the upper convected derivative \((\delta/(\delta t))\) is defined by \[ ((\delta S)/(\delta t))=((dS)/(dt))-LS-SL^{T}. \] The tensor \(L\) is the gradient of the velocity vector \(v\), and the Laplace multiplier \(p\) is not the same as the mean normal stress, as shown by Karra et al. [loc. cit.]. They will study some unsteady motions of incompressible UCM fluids whose pressure-dependent viscosity \(\eta(p)\) is of the exponential form \[ \eta(p)=\mu e^{\alpha(p-p_0)}. \] If \(\alpha\to 0\) in this relation, then \(\eta(p)\to\mu\), and Equations (1) reduce to the constitutive equations of ordinary imcompressible UCM fluids. Exact and simple expressions for the stationary solutions corresponding to two oscillatory motions of incompressible upper-convected Maxwell fluids with exponential dependence of viscosity on the pressure between parallel plates have been established using suitable changes …
reviewed by: Noureddine Daili
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 7436719
zbMATH Keywords: parallel plates
zbMATH Keywords: Laplace transform
zbMATH Keywords: pressure-viscosity coefficient
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.euromechflu.2021.04.001
OpenAlex ID: W3153194044
Wikidata QID: Q115575283
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DOI: 10.1016/J.EUROMECHFLU.2021.04.001
description: scientific article; zbMATH DE number 7436719