The flow of a non-Newtonian liquid near a stagnation point

Zusammenfassung Die Bewegungsgleichungen für die Strömung einer nicht-Newtonschen Flüssigkeit nahe einem Staupunkt sind integriert worden nach der Kármán-Pohlhausen-Methode. Es ist gefunden worden, dass der Effekt der Querviskosität von einem dimensionslosen ParameterK=_c a/u abhängt. Die Grenzschichtdicke nimmt ab vonK=0 zuK=0,15 und wächst dann mitK, Die Wand-Scherbeanspruchung nimmt ab mit zunehmendemK, während die Normalkraft an der Wand unabhängig ist von Viskosität und Querviskosität.     

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.     

A wind tunnel investigation on the local heat transfer from a sphere,including the influence of turbulence and roughness

Zusammenfassung Der Wärmeübergang von einer isotherm geheizten Messingkugel an den Luftstrom wurde bei Reynoldszahlen zwischen 4100 und 66000 lokal gemessen und mit der Theorie der laminaren Grenzschicht verglichen. Das Experiment lieferte um 10 bis 15% höhere Resultate als die Theorie. Wurde die Turbulenz der Strömung in der Grössenordnung von 0.1% durch Gitter auf 1% gesteigert, so ergab sich ein bis 40% höherer Wärmeübergang als nach der Theorie für den turbulenzfreien Fall zu erwarten ist. Druckverteilungen um die Kugel wurden gemessen um Einsicht in die realen Strömungsverhältnisse und eine Berechnungsgrundlage zu erhalten.Rauhigkeiten von 0.3 mm auf einer Kugel von 3 cm Durchmesser hatten einen vernachlässigbar kleinen Einfluss im Bereiche kleiner Reynoldszahlen. Bei hohen Reynoldszahlen führten die Rauhigkeiten lokal zu einem turbulenten Wärmeübergang. Der totale Wärmeübergang wurde dabei um 60% gesteigert.Lokale Messungen an einem Modell mit Buckeln und Vertiefungen ergaben im Mittel bei einem Buckel einen 2 bis 3mal grösseren Wärmeübergang als bei einer Vertiefung. Der gesamte Wärmeübergang des buckligen Modells war mindestens 5%, meistens 20%, aber höchstens 72% grösser als derjenige der Kugel bei gleichen Versuchsbedingungen.Die lokalen Nusseltzahlen wurden für alle Versuchsbedingungen in einer Tabelle zusammengefasst, wobei sich die maximalen Messfehler zu einer Unsicherheit von höchstens ±14% aufsummieren.

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List of symbols T Temperature difference between the heated model and the air stream - Polar angle from forward stagnation point - L Characteristic length (diameter of sphere). For the humped modelL is the diameter of the sphere with the same volume - F Surface from which the heating power is conducted to the air stream, respectively its projection on the sphere in the case of humps, hollows or small scale roughness - q Heat conducted from a heater to the air stream through the areaF, divided by T (convective thermal conductance) - Nu Nusselt number, connected withq byq=F··Nu/L. Nu can be physically interpretated as the derivative of the temperature at the surface and normal to the surface brought into a dimensionless form by means of T andL. - Molecular conductivity of heat in air. A value of 0.24 mW/(cm·C) was used for the calculations (0C). - Kinematic viscosity of air. The calculations are based on =0.18 cm²·s^–1 (0C, 740 mb). - U Velocity of the air stream (mean value). - U Fluctuation ofU in the direction ofU, characterising the free stream turbulence. - f Frequency of the fluctuations ofU - Re Reynolds number.Re=L·U/ - Thickness of the viscous boundary layer - h Height of roughness elements - Pr Prandtl number.Pr=··c/ wherec stands for the specific heat - 2p/(·U ²) Pressure at the surface of the sphere in function of , divided by the pressure at the forward stagnation point (dynamic pressures) - Wedge variable according to the notation of Merk - E ₀ First term in the expansion of the Nusselt number Symbols denoting experimental conditions N Normal sphere - BV Model with humps (germanBuckel) and hollows (germanVertiefung) - r Small scaleroughness - G1,G2 Grids made from 1 mm wires and 5 mm rods respectively, producing turbulence     

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.     

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.     

Melting heat and mass transfer in stagnation point micropolar fluid flow of temperature dependent fluid viscosity and thermal conductivity at constant vortex viscosity

Steady mixed convection micropolar fluid flow towards stagnation point formed on horizontal linearly stretchable melting surface is studied. The vortex viscosity of micropolar fluid along a melting surface is proposed as a constant function of temperature while dynamic viscosity and thermal conductivity are temperature dependent due to the influence of internal heat source on the fluid. Similarity transformations were used to convert the governing equation into non-linear ODE and solved numerically. A parametric study is conducted. An analysis of the results obtained shows that the flow-field is influenced appreciably by heat source, melting, velocity ratio, variable viscosity and thermal conductivity.     

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.     

The influence of Hall current and heat transfer on the flow of a fourth grade fluid

In this article, a mathematical model is analyzed to investigate the effects of Hall current and heat transfer on the flow of a fourth grade fluid between two heated and rotating disks. The corresponding problem of velocity and temperature are solved analytically by homotopy analysis method. Comparison is given between the results of velocity in fourth grade, third grade, second grade, and viscous fluids. The variation of pertinent parameters are graphed and discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions

Analysis has been conducted to analyze the stagnation point flow of nanofluid near a permeable stretched surface with convective boundary condition. The relevant problem formulation is presented in the presence of porous medium and internal heat generation/absorption. The effects of Brownian motion and thermophoresis occur in the transport equations. The velocity, temperature and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest namely Brownian motion parameters, thermophoresis parameter, permeability parameter, source/sink parameter, ratio of rate constants to free stream velocity and stretching velocity, Biot number and Prandtl number. A comparative study between the previous published and present results in a limiting sense is found in an excellent agreement.     

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.     

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.     

Numerical experiments on flow control of near wall turbulence

In this paper we demonstrate by means of direct numerical simulations (DNS) of channel flow with surface structuring or modified boundary conditions how turbulence can be controlled by influencing the anisotropy state of near wall turbulence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.

     

The transfer point location problem

In this paper, we introduce the transfer point location problem. Demand for emergency service is generated at a set of demand points who need the services of a central facility (such as a hospital). Patients are transferred to a helicopter pad (transfer point) at normal speed, and from there they are transferred to the facility at increased speed. The general model involves the location of p helicopter pads and one facility. In this paper, we solve the special case where the location of the facility is known and the best location of one transfer point that serves a set of demand points is sought. Both minisum and minimax versions of the models are investigated. In follow up papers we investigate the general model using the results obtained in this paper.     

The influence of loading eccentricity on the buckling of axially compressed imperfect composite cylinders

The buckling of imperfect composite cylinders under concentric and eccentric compression is investigated experimentally and numerically, with particular attention given to the imperfection sensitivity of the shells. A series of glass-fiber-reinforced plastic cylinders have been tested under different load eccentricities to validate the corresponding nonlinear numerical analyses performed in this study. A good agreement between the experimental and numerical results was achieved through use of the ABAQUS/Explicit finite-element code and the introduction of initial imperfections. Both the experimental and the numerical results show that the knockdown factor increases as the loading eccentricity grows.     

The influence of turbulence on a columnar vortex with axial flow

The interaction between a columnar vortex and external turbulence is investigated numerically. A q -vortex is immersed in an initially isotropic homogeneous turbulence field, which itself is produced numerically by a direct numerical simulation of decaying turbulence. The formation of turbulent eddies around the columnar vortex and the vortex-core deformations are studied in detail by visualizing the flow field. In the less-stable case with q = –1.5, small thin spiral structures are formed inside the vortex core. In the unstable case with q = –0.45, the linear unstable modes grow until the columnar vortex make one turn. Its growth rate agrees with that of the linear analysis of Mayer and Powell[1]. After two turns of the vortex, the secondary instability is excited, which causes collapse of the columnar q -vortex and the sudden appearance of many fine scale vortices. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of wall properties on the MHD peristaltic flow of a Maxwell fluid with heat and mass transfer

This article describes the effects of heat and mass transfer on the magnetohydrodynamic (MHD) peristaltic flow in a planar channel with compliant walls. An incompressible Maxwell fluid occupies a porous space. The mathematical formulation is based upon the modified Darcy’s law. The analytic treatment of the solution is given by choosing a small wave number. The expressions of stream function, temperature distribution, concentration field and heat coefficient are constructed. The variations of several interesting parameters are discussed by sketching plots.