Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure

Unsteady motion between two infinite horizontal parallel plates of incompressible viscous fluids with a power-law dependence of viscosity on the pressure is studied analytically. The fluid motion is generated by the lower plate that is moving in its plane with a time dependent velocity. General solu...

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Autores principales:	Constantin Fetecau, Dumitru Vieru
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2020
Materias:	General solutions Unsteady motions: Viscous fluids Pressure dependent viscosity Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/931a1fa380f240f7b61a08d726ac3eb5
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spelling	oai:doaj.org-article:931a1fa380f240f7b61a08d726ac3eb52021-12-01T05:05:15ZExact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure2666-496810.1016/j.apples.2020.100003https://doaj.org/article/931a1fa380f240f7b61a08d726ac3eb52020-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496820300030https://doaj.org/toc/2666-4968Unsteady motion between two infinite horizontal parallel plates of incompressible viscous fluids with a power-law dependence of viscosity on the pressure is studied analytically. The fluid motion is generated by the lower plate that is moving in its plane with a time dependent velocity. General solutions for dimensionless velocity and shear stress fields are established using suitable changes of independent variable and unknown function. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion of this kind of respective fluids. Consequently, the problem in discussion is completely solved. For illustration, three particular cases with engineering applications are considered and graphical representations are presented and discussed. The solutions corresponding to some motions due to an accelerated plate are connected to those of the simple Couette flow by means of Riemann-Liouville fractional integral operator. The solutions corresponding to oscillating motions are presented as sums of steady-state and transient components and, for the validation of results that have been obtained, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The required time to reach the steady-state is graphically determined both for oscillating motions and the simple Couette flow.Constantin FetecauDumitru VieruElsevierarticleGeneral solutionsUnsteady motions: Viscous fluidsPressure dependent viscosityEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 1, Iss , Pp 100003- (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	General solutions Unsteady motions: Viscous fluids Pressure dependent viscosity Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	General solutions Unsteady motions: Viscous fluids Pressure dependent viscosity Engineering (General). Civil engineering (General) TA1-2040 Constantin Fetecau Dumitru Vieru Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
description	Unsteady motion between two infinite horizontal parallel plates of incompressible viscous fluids with a power-law dependence of viscosity on the pressure is studied analytically. The fluid motion is generated by the lower plate that is moving in its plane with a time dependent velocity. General solutions for dimensionless velocity and shear stress fields are established using suitable changes of independent variable and unknown function. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion of this kind of respective fluids. Consequently, the problem in discussion is completely solved. For illustration, three particular cases with engineering applications are considered and graphical representations are presented and discussed. The solutions corresponding to some motions due to an accelerated plate are connected to those of the simple Couette flow by means of Riemann-Liouville fractional integral operator. The solutions corresponding to oscillating motions are presented as sums of steady-state and transient components and, for the validation of results that have been obtained, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The required time to reach the steady-state is graphically determined both for oscillating motions and the simple Couette flow.
format	article
author	Constantin Fetecau Dumitru Vieru
author_facet	Constantin Fetecau Dumitru Vieru
author_sort	Constantin Fetecau
title	Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
title_short	Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
title_full	Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
title_fullStr	Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
title_full_unstemmed	Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
title_sort	exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure
publisher	Elsevier
publishDate	2020
url	https://doaj.org/article/931a1fa380f240f7b61a08d726ac3eb5
work_keys_str_mv	AT constantinfetecau exactsolutionsforunsteadymotionbetweenparallelplatesofsomefluidswithpowerlawdependenceofviscosityonthepressure AT dumitruvieru exactsolutionsforunsteadymotionbetweenparallelplatesofsomefluidswithpowerlawdependenceofviscosityonthepressure
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Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure

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