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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| Format: | Article |
| Language: | English |
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Elsevier
2020-03-01
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| Series: | Applications in Engineering Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666496820300030 |
| _version_ | 1818722119083622400 |
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| author | Constantin Fetecau Dumitru Vieru |
| author_facet | Constantin Fetecau Dumitru Vieru |
| author_sort | Constantin Fetecau |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-17T20:49:33Z |
| format | Article |
| id | doaj.art-931a1fa380f240f7b61a08d726ac3eb5 |
| institution | Directory Open Access Journal |
| issn | 2666-4968 |
| language | English |
| last_indexed | 2024-12-17T20:49:33Z |
| publishDate | 2020-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Applications in Engineering Science |
| spelling | doaj.art-931a1fa380f240f7b61a08d726ac3eb52022-12-21T21:33:04ZengElsevierApplications in Engineering Science2666-49682020-03-011100003Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressureConstantin Fetecau0Dumitru Vieru1Academy of Romanian Scientists, Bucharest, RomaniaTechnical University “Gheorghe Asachi” of Iasi, Romania, Department of Theoretical Mechanics; Corresponding Author.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.http://www.sciencedirect.com/science/article/pii/S2666496820300030General solutionsUnsteady motions: Viscous fluidsPressure dependent viscosity |
| spellingShingle | Constantin Fetecau Dumitru Vieru Exact solutions for unsteady motion between parallel plates of some fluids with power-law dependence of viscosity on the pressure Applications in Engineering Science General solutions Unsteady motions: Viscous fluids Pressure dependent viscosity |
| title | 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_short | 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 |
| topic | General solutions Unsteady motions: Viscous fluids Pressure dependent viscosity |
| url | http://www.sciencedirect.com/science/article/pii/S2666496820300030 |
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