Rayleigh–Stokes problem for non‐Newtonian medium with memory

Zierep, Jürgen; Bohning, R.; Fetecău, Constantin

doi:10.1002/zamm.200710328

Cited by 11 publications

(6 citation statements)

References 6 publications

(8 reference statements)

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“…[1,2,3,4,12,16]. Regarding analytic representation for solution of this problem in linear form, we refer to [7,8,13,15,17,18]. Recently, the final value problem involving (1) has been addressed in [9,10,14], as an interesting supplement to qualitative investigation for this equation.…”

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confidence: 99%

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Lân¹

2022

EECT

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We study the generalized Rayleigh-Stokes problem involving a fractional derivative and nonlinear perturbation. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and asymptotic stability of solutions. In particular, if the nonlinearity is Lipschitzian then the mild solution of the mentioned problem becomes a classical one and its convergence to equilibrium point is proved.

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confidence: 99%

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Lân¹

2022

EECT

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“…We have for example a third order differential eq. for a second grade medium [14,15,16]. Another important eq.…”

Section: Energy Balance For Flows Of Non-newtonian Mediamentioning

confidence: 99%

Supervision of two fundamental problems in modern fluid dynamics for sparing energy

Zierep

2009

J. Therm. Sci.

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The normal shock at a curved surface in transonic flow leads to a superdetermined boundary value problem. A bump behind the shock decreases the drag of the airfoil and reduces the necessary energy.Flows of non-Newtonian media lead in the contrary to subdetermined boundary initial problems. The energy balance for these fluids is of great interest for chemical engineering.Keywords: Transonic flow, Shock at a curved wall, Superdetermined problem, Non-Newtonian media, Subdetermined problem, Energy balance.In the following we describe only the ideas of fundamental problems by discussing two actual examples of the energy balance and their importance for modern fluid dynamics and applications. The expert reader will soon add more examples. The details are given in [1, 2, 3] and the additional references given there. Normal shock at a curved surfaceFor high subsonic flow of an airfoil of a commercial air-liner (M = 0.85) we have in the neighbourhood of the maximum thickness a local supersonic region that is usually limited downstream by a normal shock. This shock needs strong energy and by this increases the drag considerably. The theoretical solution for the problem of a normal shock at a curved surface (airfoil) leads with the nonlinear differential eqs. and the shock eqs. finally to a superdetermined problem. This strange behaviour is a very singular property that is a consequence of the nonlinearity of the eqs. To get the analytical solution of this problem needed a long time. At the beginning we found a singularity for the pressure decrease ( = velocity increase) behind the shock of the type of Neil´s parabola [4,5,6]. This solution is only possible for the same convex curvature in front of and behind the shock at the airfoil and a special interval of the Mach number (1.662≤ M≤2) in front of the shock. This solution is not useful for technical applications especially for a commercial airplane. Therefore we pass over to the simpler eqs. of small disturbance theory (SDT) for transonic flow. The differential eqs. and the shock eqs. lead to a logarithmic singularity behind the shock for any curvature of the airfoil and transonic Mach number in front of the shock [6,7,8,9]. This well known singularity in the transonic subsonic area is unfortunately not correct. The reason for that is that the transonic approximation is not valid for strong Neil´s parabola singularity. Some of the terms that are neglected by this transonic approximation had to be considered if we use the exact singularity of the full Euler eqs. That means that this is the properly posed formulation of all details of our problem [1,2]. A consequence is that our problem is superdetermined. That means for example that the curvature of the wall of the airfoil can only be given in front of the shock (convex) and the Mach number there. The wall curvature behind the shock is calculated by the solution. In the transonic case we get a concave curved surface element. This leads to the beginning of a so-called bump. This small bump

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“…Using the same fluid model as that of author [10] Foote et al [11] studied the extension of Stokes solution for the oscillations of a porous plate. Zierep et al [12] obtained solution of Rayleigh-Stokes problem for a non-Newtonian medium with memory. The flow of a viscoelastic second grade fluid near an oscillating porous plate was studied by Hayat et al [13,14] while analytical solution of Stokes second problem for a second grade fluid was discussed by Asghar et al [15].…”

Section: Introductionmentioning

confidence: 99%

On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate

Ghosh

Sana²

2009

Acta Astronautica

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Rayleigh–Stokes problem for non‐Newtonian medium with memory

Abstract: The solution of the governing equation for second grade fluid is discussed analytical by Fourier sine transform and numerical. We found an interesting memory behaviour for the Rayleigh-Stokes problem.

Cited by 11 publications

References 6 publications

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Supervision of two fundamental problems in modern fluid dynamics for sparing energy

On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate

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