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1

On the dynamics of the recursive sequence ...[wzór]

Erdogan M. E., Cinar C.

Fasciculi Mathematici

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2013

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Nr 50

59--66

EN

In this paper, we investigate the global behavior of the difference equation ...[wzór] where β is a positive parameter and α, γ are non-negative parameters and non-negative initial conditions.

2

On the viscoelastic core of a line vortex embedded in a stagnation point flow

Erdogan M. E.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

577-588

EN

The viscoelastic core of a line vortex embedded in a radially inward axisymmetric stagnation point flow for a Maxwell fluid and an Oldroyd B fluid is considered. Velocity, vorticity and stress distributions are calculated and compared with those of the Newtonian fluid. It is found that there are pronounced effects of viscoelastic properties on these distributions with respect to those of the Newtonian fluid.

3

On the unsteady unidirectional flows due to sudden application of a pressure gradient

Erdogan M. E.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 2

345-368

EN

Some properties of unsteady unidirectional flows of viscous fluids are discussed for flows impulsively started from rest by a constant pressure gradient in the direction of the flow. Three illustrative examples are given. The first example is the unsteady Poiseuille flow, the second is the unsteady generalized Couette flow and the third is the unsteady flow in a circular pipe. It is found that the expressions of the quantities such as velocity, flux and skin friction are in series forms which may be rapidly convergent for large values of the dimensionless time but slowly convergent for small values of the dimensionless time or vice versa. It is shown that if their expressions can be found for one of large values of the dimensionless time or small values of the dimensionless time, these expressions can also be used for the other.

4

Unsteady flow of a viscous fluid due to an oscillating plane wall

Erdogan M. E.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 3

465-478

EN

The flow of a viscous fluid produced by a plane boundary moving in its own plane with a sinusoidal variation of velocity is considered. An analytical solution describing the flow at small and large times after the start of the boundary is obtained by the Laplace transform method. The solution confirms that the intuitive solution known in the literature, which for a long time steady periodic oscillation is set up with the same frequency as the velocity of the plane boundary, is correct. The solution gives not only the steady solution but also the transient solution. The time required to attain steady flow depends on the initial conditions. The time required for the cosine oscillation of the boundary is one-half cycle and it is a full cycle for the sine oscillation of the boundary. It is shown that the time required to attain the steady flow can also be obtained by the variation of the shear stress at the wall with time.

5

Effects of the side walls in generalized Couette flow

Erdogan M. E.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 2

271-286

EN

The effects of the side walls on the flow of an incompressible viscous fluid in a conduit of rectangular cross-section by the combined effect of the velocity of the top wall and a constant pressure gradient along the conduit are considered. For this purpose, four different flow conditions are used. In the first case, a separation occurs at the bottom wall. In the second case, the volume flux is zero. In the third case, a separation occurs at the top wall. In the fourth case, the flow is set up by the motion of the top wall in the absence of the pressure gradient. Furthermore, the effect of the side walls in a channel of rectangular cross-section is discussed.