1. bookVolume 25 (2020): Issue 3 (September 2020)
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Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure

Published Online: 17 Aug 2020
Page range: 181 - 197
Received: 04 Nov 2019
Accepted: 03 Mar 2020
Journal Details
License
Format
Journal
First Published
19 Apr 2013
Publication timeframe
4 times per year
Languages
English
Copyright
© 2020 Sciendo

An unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

Keywords

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