Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to s...

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Bibliographic Details
Published in:Mathematical Problems in Engineering 2008-01, Vol.2008 (2008), p.1445-1457
Main Authors: Rashidi, Mohammad Mehdi, Shahmohamadi, Hamed, Dinarvand, Saeed
Format: Article
Language:English
Subjects:
Algorithms
Axisymmetric flow
Boundary conditions
Differential equations
Dynamical systems
Fluid dynamics
Fluid flow
Homotopy theory
Incompressible flow
Incompressible fluids
Injection molding
Mathematical problems
Methods
Nonlinear equations
Ordinary differential equations
Parallel plates
Runge-Kutta method
Similarity solutions
Studies
Thrust bearings
Two dimensional analysis
Two dimensional flow
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Summary:The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.
ISSN:1024-123X
1563-5147
DOI:10.1155/2008/935095