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Exact solution for the unsteady flow of a semi-infinite micropolar fluid

Acta mechanica sinica 2011年第3期27卷 354-359页

作者： H.H. sherief m.s. faltas E.A. Ashmawy Department of mathematics Faculty of ScienceAlexandria University

The unsteady motion of an incompressible micropolar fluid filling a half-space bounded by a horizontal infinite plate that started to move suddenly is considered. Laplace transform techniques are used. The solution in the Laplace transform domain is obtained by using a direct approach. The inverse Laplace transforms are obtained in an exact manner using the complex inversion formula of the transform together with contour integration techniques. The solution in the case of classical viscous fluids is recovered as a special case of this work when the micropolarity coecient is assumed to be zero. Numerical computations are carried out and represented graphically.

关键词： Unsteady motion . Laplace transform . microp-olar fluid

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Fundamental solutions for axi-symmetric translational motionof a microstretch fluid

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Acta mechanica sinica 2012年第3期28卷 605-611页

作者： H.H.sherief m.s.faltas E.A.Ashmawy Department of mathematics Faculty of ScienceAlexandria University

The fundamental solution for the axi-symmetric translational motion of a microstretch fluid due to a concen- trated point body force is obtained. A general formula for the drag force exerted by the fluid on an axi-symmetric rigid par- ticle translating in it is then deduced. As an application to the obtained drag formula, this paper has discussed the problem of creeping translational motion of a rigid sphere in a mi- crostretch fluid. The slip boundary condition on the surface of the spherical particle is applied. The drag force and the other physical quantities are obtained and represented graph- ically for various values of the micropolarity and slip param- eters.

关键词： Drag force Fundamental solution mi-crostretch fluid slip condition

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Unsteady unidirectional micropolar fluid flow

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Theoretical & Applied mechanics Letters 2011年第6期1卷 36-40页

作者： m. s. faltas H. H. sherief E. A. Ashmawy m. G. Nashwan Department of mathematics Faculty of Science Alexandria University Alexandria Egypt

This paper considers the unsteady unidirectional flow of a micropolar fluid, produced by the sudden application of an arbitrary time dependent pressure gradient, between two parallel plates. The no-slip and the no-spin boundary conditions are used. Exact solutions for the velocity and microrotation distributions are obtained based on the use of the complex inversion formula of Laplace transform. The solution of the problem is also considered if the upper boundary of the flow is a free surface. The particular cases of a constant and a harmonically oscillating pressure gradient are then examined and some numerical results are illustrated graphically.

关键词： Laplace transform micropolar fluid unidirectional flow

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