The forces on a flat plate in a couette flow

A bounded shear flow proposed by Glauert is re-examined, to determine more precisely the disturbance caused by the boundary layer on the plate. Toomre and Rott's result, that the pressure gradient due to bounding overtakes the Li-Murray value for an unbounded flow within a surprisingly short distance of the leading edge, is thereby confirmed in a more realistic context. But both of these are found to be less important than that due to the induced circulation predicted by Glauert. While bounding produces a larger leading edge drag than the unbounded theory predicts, circulation gives more lift. The discussion of pressure on and ahead of the plate is given for general bounding. In particular, it shows that the present results are typical and that the anomaly found by Toomre and Rott always disappears when the limit of remote bounding is taken correctly.

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Zusammenfassung Eine seitlich begrenzte Scherströmung, wie sie von Glauert vorgeschlagen wurde, wird neu untersucht, um die Störung, welche durch die Grenzschicht an dieser Platte hervorgerufen wird, genauer zu bestimmen. Toomre und Rotts Resultat, welches besagt, daß der Druckgradient infolge der Begrenzung den von Li-Murray gefundenen Wert für unbegrenzte Strömung in bereits überraschend kurzem Abstand von der Vorderkante übersteigt, wird hierbei in einem etwas realistischeren Zusammenhang bestätigt. Hingegen sind beide Druckgradienten von geringerer Bedeutung als der Einfluß einer auf Glauert zurückgehenden induzierten Zirkulation. Während die begrenzte Strömung zu größerem Widerstand an der Vorderkante führt als eine unbegrenzte, wird durch die Zirkulation mehr Auftrieb erzeugt. Für beliebige Begrenzung wird der Druck an und vor der Platte diskutiert. Insbesondere wird gezeigt, daß die vorliegenden Resultate typisch sind und daß die auf Toomre und Rott zurückgehende Anomalie verschwindet, wenn nur der Grenzübergang für eine Begrenzung im Unendlichen Korrekt ausgeführt wird.

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This research was supported partly by the U.S. Army Research Office-Durham and partly by the National Science Foundation under Grants GP-8711 and 28483.     

Unsteady flow past a flat plate with suction

A solution is given for the transient response for laminar boundary layer flow past a flat plate to a step-function change in suction velocity. An arbitrary but constant suction velocity normal to the plate is allowed prior to step-change. Using the Laplace transform technique the solutions for the unsteady velocity profile and shear stress are obtained and are graphically sketched when the suction velocity doubles in the stepchange. The results show clear evidence of boundary-layer contraction when suction velocity is increased.     

Steady two-dimensional flow past a normal flat plate

A vorticity/stream function formulation is used to obtain a numerical simulation of steady two-dimensional flow of a viscous incompressible fluid past a normal flat plate for a range of Reynolds numbers. A method of Fornberg [J. Fluid Mech. 98, 819 (1980)] is used to determine upstream and downstream boundary conditions on the stream function. Special care is taken in the neighbourhood of the singularities in vorticity at the plate edges and this is very important because any errors introduced are swept downstream and severely affect such quantities as the length and width of the attached eddies. The computed results are compared with those of a laboratory experiment in which a plane strip is drawn through water and ethylene glycol for the range of Reynolds numbers for which the experimental flow is stable.     

Further results concerning the simple queueing loss system

Summary The output or departure process from a single channel queue with independent arrival intervals, exponential service times and no storage is considered. The main result obtained is that successive departure intervals are uncorrelated if and only if the arrival process is Poisson.

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Zusammenfassung Der output bzw. der Abgang eines einzelnen Wartekanals mit unabhängigen Ankunftsintervallen, exponentieller Bedienungszeit und ohne Speicherung wird untersucht. Als wesentliches Resultat ergibt sich, daß sukzessive Abgangsintervalle genau dann unkorreliert sind, wenn der Ankunftsprozeß Poisson-verteilt ist.

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Vorgel. v.:F. Ferschl     

Effect of a standing sound field on the magnetohydrodynamic flow past a flat plate

Zusammenfassung In dieser Arbeit wird die Wirkung eines stationären Schallfeldes auf die magnetohydrodynamische Strömung, die im Bereich eines transversalen Magnetfeldes an einer flachen Platte vorbeifliesst, untersucht. Es ist festgestellt worden, dass, dem nichtmagnetischen Fall unähnlich, die gleichförmige Nebenbewegung nicht existiert. Die geschlossenen Schleifen der Stromlinien neben der Platte verlängern sich mit der Zunahme des Magnetfeldes. Weiter verursacht das Magnetfeld eine bedeutende Abnahme der Geschwindigkeitskomponenten.     

Optimal coordinates for a simple shear flow over a flat plate

Zusammenfassung In eine ebene inkompressible Strömung mit konstantem Geschwindigkeitsgradienten quer zur Strömung sei eine ebene Platte parallel gelegt. Als günstiges Koordinatensystem werden parabolische Koordinaten betrachtet und damit ähnliche Lösungen gefunden. Der Übergang von der Grenzschicht zur äusseren Strömung vollzieht sich glatt, und es können Wandschubspannungen und Verdrängungseffekte bestimmt werden. Vergleiche mit anderen Lösungen, die mit kartesischen Koordinaten gefunden wurden, werden angestellt.

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This research was supported in whole by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. AF 49(638)-23. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

The compressible gas-solid particle flow over a semi-infinite flat plate

Zusammenfassung Es wird gezeigt, dass die Grenzschicht-Approximation auf die Zwei-Phasen-Strömung über eine Halbebene anwendbar ist, wenn die Teilchendichte in der Grenzschicht von der Ordnung ist. Die Bedeutung eines neuen Parameters _m /x wird herausgestellt, wo _m die Länge ist, auf der die Teilchen ihre Geschwindigkeit ume ^–1 verringern, und der Abstand von der Vorderkante. Reihenentwicklungen in diesem Parameter werden benutzt, derart, dass eine Ähnlichkeitsgrösse für die Halbebene gefunden werden kann. Dies reduziert ein System partieller Differentialgleichungen auf ein System gewöhnlicher Differentialgleichungen. Letztere werden numerisch und wenn möglich analytisch gelöst, so dass Schubspannungskoeffizienten und Wärmeübergangskoeffizienten für begrenzte Teile der Wand berechnet werden können. Hierbei wird die Gasdichte nicht als konstant angenommen.     

Parabolic flow over a flat plate with wave disturbance in the main stream

In this paper the effects of unsteady flow past a flat plate, which is at rest, are studied when the steady parabolic flow outside the boundary layer is in a wave disturbance. Solutions are developed for large and small times. The behaviour of the amplitudes and phase leads of skin friction components along chordwise and spanwise directions are studied in detail. Two cases, one when the main stream lines are straight and yawed, and the other when the main stream lines are parabolic and concave with respect to the points on the chordwise direction are studied separately and the results are interpreted graphically.     

Response of heat transfer from a moving flat plate in a parabolic flow

This paper deals with the solutions of steady as well as unsteady three-dimensional incompressible thermal boundary layer equations and the study of the response of heat transfer when there is a parabolic flow over a moving flat plate. The components of velocity in boundary layer are discussed by Sarma and Gupta and those results are used to analyse thermal boundary layer equations. A general analysis is made from which we deduce (i) Solutions of two-dimensional thermal boundary layer on a moving flat plate, (ii) Solutions of thermal boundary layer on a yawed flat plate, (iii) Solutions of thermal boundary layer when there is a parabolic flow over a moving flat plate by giving different values to β and Cx. Solutions are developed for large and small times and curves are drawn representing the variations of heat transfer from the plate with time for all the cases. The limiting time is also calculated.     

Molecular modellingof flow past an inclined flat plate

Molecular flow past an inclined plate is simulated on a scientific personal computer. Wake flow and turbulent effects are described and discussed for various fluid speeds.     

Hydromagnetic flow near an oscillating porous flat plate

A solution in the closed form has been obtained for the flow of a viscous incompressible fluid of small electrical conductivity near an infinite insulated porous flat plate oscillating harmonically in its own plane in the presence of a transverse magnetic field of uniform strength fixed relative to the fluid. Small uniform suction has been imposed along the surface of the plate. This is a generalisation of the result of Ong and Nicholls for the hydromagnetic flow near an oscillating solid flat plate.     

Free molecular flow past a flat plate in the presence of a nontrivial gas-surface interaction

Aerodynamic forces acting on a flat plate, placed in a uniform free molecular flow, are investigated by means of a non trivial gas-surface interaction model proposed by the authors. Drag and lift coefficients and lift to drag ratio are calculated for a large number of values of some meaningful parameters, such as the speed ratio, the gas-wall temperature ratio, the attack angle and two coefficients contained in the reemission model. Simple analytical expressions, different from the classical ones, are obtained for very high or very low speed ratio values.

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Riassunto Le forze aerodinamiche agenti su una lastra piana, posta in una corrente uniforme di gas in regime di molecole libere, sono studiate per mezzo di un modello non banale di interazione gas-superficie solida, già proposta dagli autori. I coefficienti di resistenza e di portanza e il rapporto tra queste due quantità sono calcolati per un notevole numero di valori assegnati ad alcuni parametri significativi, come il rapporto di velocità, il rapporto tra temperatura del gas e della parete, l'angolo di attacco e due coefficienti propri del modello di riemissione. Per velocità molto alte o molto piccole si forniscono delle espressioni analitiche esplicite, differenti da quelle ricavabili dalla teoria classica dei coefficienti di accomodamento.

     

Magnetohydrodynamic flow past a yawed semi-infinite flat plate in the presence of a pressure gradient

Resumé Cet article traite de l'écoulement d'un fluid visqueux avec conductivité électrique au delà d'une plaque plate, en presence d'une pente de pression. L'écoulement du fluid à l'infinit parallèle au bord. L'analyse est presentée pour grandes et petites conductivités et les résultats numériques pour la friction parallèle au bord sont donnés dans les deux cas, celui d'une plaque plate et celui d'un cylindre circulaire dans une écoulement uniforme. Ces résultats sont alors comparéa à la friction perpendiculaire au bord, résultats obtenus auparavant par Glauert et Gribben respectivement.     

Plane couette flow of two immiscible incompressible fluids with uniform suction at the stationary plate

The contact layer in the plane couette flow of two immiscible fluids with uniform suction at the stationary plate has been investigated. The effect of suction is to supply an adverse pressure gradient to the fluid which causes back flow near the stationary plate. The streamlines are drawn to show the effect of uniform suction at the stationary plate on the contact layer.     

On the exact solutions of laminar MHD flow over a stretching flat plate

The magnetohydrodynamic steady-state laminar flow of a viscous incompressible and electrically conducting fluid over a continuous permeable stretching surface is considered. It is shown that in the presence of a vertical inverse-linear magnetic field, we establish a sufficient condition for the existence of exact solutions of this problem with respect to the three parameters: the magnetic parameter M, the suction/injection parameter γ, and the stretching parameter ξ. Numerical results are also obtained and give the effect of the suction parameter and the magnetic parameter on the velocity.