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  • 1985-1989  (4)
  • 1986  (4)
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  • 1985-1989  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    Singular and non-unique solutions of the boundary-layer equations for the flow due to free convection near a continuously moving vertical plate (1986)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 37 (1986), S. 559-572 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung In diesem Artikel wird mittels eines numerischen Verfahrens gezeigt, daß die Grenzschichtgleichungen für die Strömung in der Nähe einer kontinuierlich bewegten vertikalen Platte mit freier Konvektion nicht eindeutig sind. Weiter wird beobachtet, daß es keine Lösungen gibt, wenn die Auftriebskräfte über die Zähigkeitskräfte dominieren. Wenn jedoch die Auftriebskräfte der Plattenbewegung entgegentreten, wird herausgefunden, daß die numerische Lösung zu einer singulären Lösung wird, welche sich vor allen bisher veröffentlichten Resultaten unterscheidet, die durch Lösung der gewöhnlichen nichtlinearen Differentialgleichungen gefunden worden sind, bei denen singuläre und zweifache Lösungen existieren.
    Notes: Abstract In this paper it is shown, using a numerical technique, that the boundary-layer equations for the flow near a continuously moving vertical plate with free convection are not unique. Further it is observed that when the buoyancy forces dominate the viscous forces there are no solutions. However, when the buoyancy forces oppose the motion of the plate, it is found that the numerical solution terminates in a singular manner which is of a different nature to any previously published results which have been obtained by solving non-linear ordinary differential equations where singular and dual solutions exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945430
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Flow past a suddenly cooled horizontal plate (1986)
    Springer
    Heat and mass transfer 20 (1986), S. 237-241 
    Details
    ISSN: 1432-1181
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung In der Arbeit wird das Problem der freien, inkompressiblen, laminaren und nichtstationären Konvektion über eine halbunendliche waagerechte Platte theoretisch untersucht. Es wird vorausgesetzt, daß die Platte fürt〈0 wärmer als die sie umgebende Flüssigkeit ist und dann im Momentt=0 plötzlich bis auf die Temperatur der Umgebung abgekühlt wird. Es werden drei Lösungen für die Impulsgleichung und die Energiegleichung angegeben, und zwar: (i) eine analytische Lösung für kleine Werte des Zeitparameters, (ii) eine asymptotische analytische Lösung für große Werte des Zeitparameters und (iii) eine numerische Lösung, die sich den beiden analytischen Lösungen anpaßt. Es wird gezeigt, daß sich die numerische Lösung den Lösungen für kleine bzw. große Zeitwerte genau anpaßt. Zum Abschluß wird die Veränderung der Geschwindigkeit, Temperatur, Wandreibung und des Wärmeübergangs an der Platte in Abhängigkeit von der Zeit behandelt.
    Notes: Abstract The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for timet〈0 the plate is hotter than its surroundings and at timet=0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely (i) an analytical solution which is valid for small time, (ii) an asymptotic analytical solution which is valid for large time, and (iii) a numerical solution which matches these two limiting analytical solutions. It is found that the numerical solution matches the small and large time solutions accurately. Finally, the variation of the velocity, temperature, skin friction and heat transfer on the plate with time are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303456
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Free-forced convection from a heated longitudinal horizontal cylinder embedded in a porous medium (1986)
    Springer
    Heat and mass transfer 20 (1986), S. 283-289 
    Details
    ISSN: 1432-1181
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Es wird die Strömung und der Wärmeübergang an einem beheizten, halbunendlichen horizontalen Kreiszylinder betrachtet, der mit konstanter Geschwindigkeit sich in ein poröses Medium bewegt. Dabei wird angenommen, daß die Grashof- und Reynolds-Zahlen groß sind, so daß die Bestimmungsgleichungen von den dreidimensionalen Grenzschichtgleichungen gebildet werden. Es wird ein numerisches Verfahren zur Lösung dieser Gleichungen beschrieben und eine asymptotische Lösung präsentiert, die sowohl in der Nähe als auch in großem Abstand von dem vorderen Ende des Zylinders gültig ist. Der Gültigkeitsbereich dieser asymptotischen Lösungen wird diskutiert und die Ergebnisse werden im Detail mit vollständigen numerischen Lösungen verglichen. Das Problem ist z.B. beim Eindringen von Rohrleitungen in geothermische Reservoire von praktischer Wichtigkeit.
    Notes: Abstract The flow and heat transfer from a heated semi-infinite horizontal circular cylinder which is moving with a constant speed into a porous medium is considered. It is assumed that the Grashof and Reynolds numbers are large so that the governing equations are the three dimensional boundary-layer equations. A numerical procedure for solving these equations is described and the asymptotic solutions which are valid both near and distant from the leading edge of the cylinder are presented. The range of validity of these asymptotic solutions is discussed and the results are compared in detail with the full numerical solution. The problem is of practical importance, for example in the drilling of pipes into a geothermal reservoir.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01002419
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A note on the comparison between bie and fd techniques for solving elliptic BVPs with boundary singularities (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 189-193 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quantative comparison between the boundary integral equation (BIE) method and the finite difference (FD) method is presented in which each technique is applied to an elliptic boundary-value problem (BVP) containing a boundary singularity. Two types of singularity have previously been analysed theoretically, namely those due to a discontinuous boundary potential, which we shall refer to as S1, and those due to a sudden change from the specification of boundary potential flux, an S2 singularity. In this paper the analysis is presented for a third type of boundary singularity, namely an S3 singularity: that arising from a discontinuous boundary flux. Such a condition is frequently encountered in the field of heat transfer where, for example, a system or pipe has a change of lagging material.In general, it is found that the BIE method is superior, with regards to the computational time required to achieve a certain degree of accuracy, over standard FD methods even when there is a boundary singularity. Further, the BIE method determines the solution near the singularity much more accurately than the FD method. The FD method does, however, have advantages for a very restrictive class of problems; for example, when the boundary conditions are of the Dirichlet type and the boundary geometry is rectangular. In this case an optimum relaxation parameter can easily be obtained. A soon as Neumann conditions are prescribed, the BIE is far more efficient than the FD, whatever the boundary geometry.It is concluded that, for fast, accurate solutions of general Laplacian boundary-value problems, the BIE is appreciably superior to the FD and this is even more pronounced when there is a boundary singularity.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020210
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    Paper (German National Licenses)
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