Flow of a particular class of non-Newtonian visco-elastic and visco-inelastic fluids near a stagnation point

Zusammenfassung Die Bewegungsgleichungen für die stationären Strömungen einer besonderen Klasse nichtnewtonscher viskoelastischer und viskounelastischer Flüssigkeiten nahe einem Staupunkt sind nach der Kármán-Pohlhausen-Methode integriert worden. Es hat sich gezeigt, dass der Effekt der Querviskosität und Viskoelastizität durch den dimensionslosen ParameterR=a/ beziehungsweiseK=a/ dargestellt werden. Aus der Betrachtung der Dissipationsfunktion folgern wir, dass der ganze Umfang der negativen Werte vonK undR physikalisch zulässig ist. Die zweidimensionalen Grenzschichtgleichungen für viskoelastische Flüssigkeiten sind abgeleitet worden.     

Radiation effects on the MHD flow near the stagnation point of a stretching sheet

The radiation effects using the Rosseland approximation on the flow of an incompressible viscous electrically conducting fluid over a stretching sheet near the stagnation point in the presence of uniform transverse magnetic field is studied. The governing equations transform to ordinary differential equation by using suitable similarity transformation and then by a perturbation technique the numerical results for temperature distribution were obtained and discussed graphically.     

Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited

This paper considers the effects of radiation on the flow near the two-dimensional stagnation point of a stretching sheet immersed in a viscous and incompressible electrically conducting fluid in the presence of an applied constant magnetic field. The external velocity and the stretching velocity of the sheet are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by the Keller-box method. The features of the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The results indicate that the heat transfer rate at the surface decreases in the presence of radiation.     

Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited

This paper considers the effects of radiation on the flow near the two-dimensional stagnation point of a stretching sheet immersed in a viscous and incompressible electrically conducting fluid in the presence of an applied constant magnetic field. The external velocity and the stretching velocity of the sheet are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by the Keller-box method. The features of the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The results indicate that the heat transfer rate at the surface decreases in the presence of radiation.     

The flow of an electrically conducting fluid at a rear stagnation point

Summary We consider the impulsively generated magnetohydrodynamic flow at a rear stagnation point. The work of Leibovich is carried further by formulating the inner viscous problem and providing analytical solutions and complete numerical solutions for the entire range of the interaction parameter. It is shown that the present results are consistent with previously obtained numerical solutions to the steady equations of both similarity and non-similarity form.

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Résumé Nous considérons l'écoulement magneto-hydrodynamique impulsivement engendré à un point de stagnation arrière. On porte plus loin l'étude de Leibovich par la formulation du problème visqueux intérieur et en fournissant des solutions analytiques et numériques complètes correspondantes au champ entier du paramètre d'interaction. On montre que les résultats actuels sont en accord avec les solutions numériques, et de similitude et de non-similitude, déjà connues des équations stationnaires.

     

Dynamics of flow near a separation point

Dynamical behavior of a boundary layer separation is studied using the experimental approach. The dynamical nature of the phenomenon is demonstrated on a simple case of a flat–plate boundary layer in adverse pressure gradient. The Time–Resolved PIV technique was utilized for monitoring instantaneous structure of the separation region and its time development. Distinctive coherent structures and their dynamical behavior were identified using the Proper Orthogonal Decomposition method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The flow of a visco-elastic fluid near a point of re-attachment

The flow of a visco-elastic fluid near a point of re-attachment is examined to see how elasticity affects the constant slope-ratio relationship which Newtonian fluids exhibit. The slope of the dividing streamline at the point of re-attachment divided by the slope of the same streamline far from the wall is found to be constant in the visco-elastic case, as well, for all angles of incidence. The slope ratio depends solely on the Weissenberg number which measures the extent to which viscous effects dominate elasticity effects.     

Axially-symmetric stagnation point flow of power law fluids

Zusammenfassung Mit Hilfe von Ähnlichkeitsbetrachtungen wird in der Gegend eines Staupunktes die rotationssymmetrische Strömung einer nicht Newtonschen Flüssigkeit mit Potenzgesetz diskutiert. Es zeigt sich, dass im Gegensatz zu der Newtonschen Flüssigkeit die Dicke der Grenzschicht mit dem Abstand vom Staupunkt variiert. Die Bewegungsdifferentialgleichungen werden mittels der Kármán-Pohlhausen-Methode integriert. Es stellt sich heraus, dass die Schubspannung an der Platte mitn, dem charakteristischen Index der Flüssigkeit, zunimmt.     

Approximate analytic solutions of stagnation point flow in a porous medium

An efficient and new implicit perturbation technique is used to obtain approximate analytical series solution of Brinkmann equation governing the two-dimensional stagnation point flow in a porous medium. Analytical approximate solution of the classical two-dimensional stagnation point flow is obtained as a limiting case. Also, it is shown that the obtained higher order series solutions agree well with the computed numerical solutions.     

The influence of turbulence on the transfer of heat to cylinders near the stagnation point

Zusammenfassung Es wird das problem des Einflusses der Turbulenz auf den Wärmeübergang an einem quer angeströmten Zylinder untersucht. Die Untersuchung beschränkt sich auf den Teil des Umfangs, über den sich die laminare Grenzschicht erstreckt. Einige ältere Messungen an der Vorderseite eines Zylinders werden miteinander verglichen, und es zeigt sich, dass ein wichtiger Parameter, nämlich die Intensität der Vorturbulenz bei den Untersuchungen nicht berücksichtigt worden ist. Die bekannten Messungen von Schmidt und Wenner werden kritisch untersucht und der genannte Effekt wird an ihnen aufgezeigt.Weiter werden eigene Messungen der lokalen Nusseltschen Zahl beschrieben. Die Messungen waren durchgeführt worden an der Vorderseite eines einzelnen Zylinders im Querstrom, und zwar in drei sich nicht überdeckenden Gebieten der Intensität der Vorturbulenz. Die Versuchsanordnung wird beschrieben und mögliche Einflüsse der Veränderung der Druckverteilung am Zylinder werden diskutiert. Obwohl dieser letztere Effekt nicht völlig eliminiert worden war, zeigen die Versuche doch klar, dass steigende Turbulenz ein starkes Anwachsen der lokalen Nusselt-Zahl bedingt. Dieses Anwachsen ist bei kleiner Turbulenz besonders stark. Ein Vergleich mit der theoretischen Lösung Froesslings, die für Turbulenz 0 gilt, zeigt, dass die Turbulenz den Wärmeübergang in der Staulinie bis zu 80% erhöhen kann, bei einer Turbulenzvariation von 0–3%.Diese Ergebnisse, die qualitativ interpretiert werden, stützen die Hypothese einer früheren Veröffentlichung, die annimmt, dass der Effekt durch Änderungen der laminaren Grenzschicht, die hervorgerufen werden durch Schwankungen von zunehmender Amplitude, wie sie bei zunehmenden Vorturbulenzen auftreten, bedingt ist.     

Heat-transfer near the stagnation point of a body of revolution in the presence of a magnetic field

Zusammenfassung Die affine Lösung vonNeuringer undMcIlroy [1] für die ebene, laminare Staupunktströmung einer elektrisch leitenden Flüssigkeit in einem magnetichen Feld wird auf den rotationssymmetrischen Fall erweitert. Die gemäss dem Jouleschen Gesetz umgesetzte Wärme sowie die Wärmezufuhr durch Reibung werden dabei ohne Vernachlässigung berücksichtigt.Die Randbedingungen werden neu formuliert, und Lösungen werden erhalten in der Gestalt von gewöhnlichen Differentialgleichungen, die numerisch integriert werden.Die Grössenordnung der auftretenden Parameter wird abgeschätzt in Fällen, welche physikalisches Interesse haben. In den meisten Fällen ist es möglich, eine Grenzschicht-Annäherung einzuführen. Die Resultate hängen dann im wesentlichen nur von einem einzigen Parameter ab. Die Geschwindigkeitsverteilung, das magnetische Feld und der Wärmeübergang an der Körperoberfläche werden berechnet.     

Note on an integral equation occurring in stagnation point flow

Zusammenfassung Die Differentialgleichung der Staupunktströmung wird nach einer Methode vonWeyl behandelt, und es wird gezeigt, dass das Weylsche Verfahren für elektronische Rechenautomaten besonders geeignet ist.     

Volume flowrate in a plane convergent forced flow of an incompressible non-Newtonian liquid

A study is made of the plane convergent forced flow of an incompressible liquid with anomalous viscosity, whose rheological properties obey a power law. A reduction in flow cross section leads to the development of a counterpressure whose existence produces near the inlet a counterflow in the region adjacent to the fixed wall. By analogy with the case of plane-parallel flow an equation is derived for the volume flowrate per unit width of a plane convergent flow.Mekhanika Polimerov, Vol. 2, No. 1, pp. 116–122, 1966     

Laminar compressible boundary layer flow at a three-dimensional stagnation point with vectored mass transfer

The effect of surface mass transfer velocities having normal, principal and transverse direction components (‘vectored’ suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.     

Non-Darcy unsteady mixed convection flow near the stagnation point on a heated vertical surface embedded in a porous medium with thermal radiation and variable viscosity

The unsteady mixed convection boundary layer flow near the stagnation point on a heated vertical plate embedded in a fluid saturated porous medium is studied. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature. Both the buoyancy assisting and the buoyancy opposing flow situations are considered with combined effects of the first and second order resistance of solid matrix of non-Darcy porous medium, variable viscosity and radiation. The problem is reduced to a system of non-dimensional partial differential equations, which is solved numerically using the Keller-box method. The features of the flow and the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The surface shear stress and the heat transfer of the present study are compared with the available results and a good agreement is found.     

Some problems for a non-Newtonian liquid and their application to the study of polycarbonate flow

Approximate solutions are obtained for problems of polymer flow in certain cylindrical channels. The polymer is regarded as an isotropic viscoelastic medium. Solutions are constructed by the method of perturbations from the corresponding solutions for a Newtonian liquid. The velocity distribution is calculated for a polycarbonate melt flowing in circular, elliptical and square channels.Mekhanika Polimerov, Vol. 2, No. 4, pp. 603–610, 1966     

Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the homotopy analysis method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the magnetic parameter, buoyancy parameter and rotation parameter on the surface shear stresses and surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear stresses and surface heat transfer is in good agreement with the numerical solution given in reference [H. S. Takhar, A. J. Chamkha, G. Nath, Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat Mass Transfer 37 (2001) 397].     

The point source field near a concave boundary

A new representation for the field emitted by a short-wave source placed near a concave boundary is obtained by the hybrid method. A Dirichlet problem is considered. The representation obtained provides an efficient algorithm for numerical experiments. Bibliography: 2 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 212–219.