Analytical solutions to Stokes-type flows of inhomogeneous fluids

Mehrdad Massoudi; Ashwin Vaidya

doi:10.1016/j.amc.2011.11.110

Analytical solutions to Stokes-type flows of inhomogeneous fluids

Mehrdad Massoudi, Ashwin Vaidya

Mathematics

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

10 Scopus citations

Abstract

In this paper, we study the unsteady motion of an inhomogeneous incompressible viscous fluid, where the viscosity varies spatially according to various models. We study the Stokes-type flow for these types of fluids where in the first case the flow between two parallel plates is examined with one of the plates oscillating and in the second case when the flow is caused by a pulsatile pressure gradient. A general argument establishes the existence of oscillatory solutions to our problem. Exact solutions are obtained in terms of some special functions and comparisons are made with the cases of constant viscosity and the slow flow regimes.

Original language	English
Pages (from-to)	6314-6329
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	218
Issue number	11
DOIs	https://doi.org/10.1016/j.amc.2011.11.110
State	Published - 5 Feb 2012

Keywords

Non-homogenous fluids
Oscillating plate
Stokes second problem
Variable viscosity

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10.1016/j.amc.2011.11.110

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AB - In this paper, we study the unsteady motion of an inhomogeneous incompressible viscous fluid, where the viscosity varies spatially according to various models. We study the Stokes-type flow for these types of fluids where in the first case the flow between two parallel plates is examined with one of the plates oscillating and in the second case when the flow is caused by a pulsatile pressure gradient. A general argument establishes the existence of oscillatory solutions to our problem. Exact solutions are obtained in terms of some special functions and comparisons are made with the cases of constant viscosity and the slow flow regimes.

KW - Non-homogenous fluids

KW - Oscillating plate

KW - Stokes second problem

KW - Variable viscosity

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JO - Applied Mathematics and Computation

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ER -

Analytical solutions to Stokes-type flows of inhomogeneous fluids

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