Unsteady multiple boundary layers on a porous plate in a rotating system
TL;DR: In this paper, an initial value investigation is made of the motion of an incompressible, homogeneous, viscous fluid bounded by a porous plate with uniform suction or blowing.
Abstract: An initial value investigation is made of the motion of an incompressible, homogeneous, viscous fluid bounded by a porous plate with uniform suction or blowing. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about the z axis normal to the plate, and additionally a nontorsional oscillation of a given frequency is superimposed on the plate for the generation of an unsteady flow in the rotating system. By using the Laplace transform technique, an exact solution of the three dimensional Navier‐Stokes equations for unsteady flow is obtained. The structure of the associated multiple boundary layers is determined. Effects of uniform suction (or blowing) and rotation on the flow phenomena are analyzed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.
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TL;DR: In this paper, the MHD flow of an electrically conducting second order incompressible fluid bounded by an infinite nonconducting porous plate subjected to a uniform suction or blowing has been analyzed.
81 citations
TL;DR: In this article, an infinite porous plate exhibiting non-torsional oscillation of a given frequency was used to study the effect of material parameters on the flow and several limiting cases were deduced.
Abstract: A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.
50 citations
TL;DR: In this article, the effects of non-Newtonian fluid characteristics and uniform acceleration of a porous disk on the velocity field were analyzed both analytically and numerically, and a very good accuracy has been seen.
44 citations
TL;DR: In this article, the Laplace transform treatment is used to obtain exact solutions of the boundary layer equations for hydrodynamic and hydromagnetic boundary layer flows, including the effects of uniform suction or blowing, resonant and non-resonant frequencies.
Abstract: This paper provides a general study of the unsteady hydrodynamic and hydromagnetic boundary layer flows including the effects of the pressure gradient and uniform suction or blowing. Exact solutions of the boundary layer equations are obtained by using the Laplace transform treatment. Asymptotic analysis is carried out to determine the unsteady flow field for small and large times. The structure of the velocity distribution and the associated boundary layers is investigated for resonant and, non-resonant cases with physical significance. The ultimate steady-state hydrodynamic and hydromagnetic boundary layer flows are examined for various cases related to uniform suction or blowing, resonant and non-resonant frequencies. It is shown that the ultimate steady-state flows are eventually established through inertial oscillations and the propagation of diffused waves. The non-existence of the ultimate steady-state hydrodynamic solution for the case of resonance and blowing is investigated with physical significance. In the hydromagnetic situation, the ultimate boundary layer flow is found to exist for all cases involved in the problem including the case of blowing and resonance. Several special results of interest are discussed.
Es handelt sich um eine allgemeine Untersuchung der hydrodynamischen und der magneto-hydrodynamischen Grenzschichtstromungen einschlieslich des Einflusses eines Druckgradienten und gleichformigen Absaugens bzw. Ausblasens. Es wurden exakte Losungen der Grenzschichtgleichungen durch Benutzung der Laplace-Transformation erhalten. Eine asymtotische Betrachtung wurde durchgefuhrt, um das instationare Stromungsfeld fur kleine und grose Zeiten zu gewinnen.
Die Struktur der Geschwindigkeitsverteilung und der zugeordneten Grenzschichten wurde fur die physikalisch bedeutungsvollen Falle der Resonanz und der Nicht-Resonant untersucht.
Der stationare Endzustand der hydrodynamischen und magnetohydrodynamischen Grenzschichtstromungen wurde untersucht fur verschiedene Falle des Absaugens und Ausblasens, sowohl fur Resonanz- als auch fur Nicht-Resonanz-frequenzen. Es wird gezeigt, das die stationaren Stromungen moglicherweise durch Tragheitsschwingungen und durch die Ausbreitung von Diffusionswellen aufrechterhalten werden. Die Nichtexistenz einer Losung, welche den stationaren Endzustand im hydrodynamischen Fall fur Resonanz und Ausblasen beschreibt, wird in bezug auf ihre physikalische Bedeutung untersucht. Im magnetohydrodynamischen Fall haben wir gefunden, das die stationare Grenzschichtstromung in allen Fallen existiert, einschlieslich Ausblasen und Resonanz. Es wird eine Reihe von Einzelergebnissen diskutiert.
39 citations
TL;DR: In this paper, the Laplace transform technique was used to investigate the hydromagnetic convective flow of an incompressible homogeneous viscous liquid over an accelerated porous plate with suction/injection.
29 citations
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