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  • 1985-1989  (11)
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  • 1
    Electronic Resource
    Electronic Resource
    An exact solution for non-darcy free convection from a horizontal line source of heat (1988)
    Springer
    Heat and mass transfer 22 (1988), S. 125-127 
    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 dem Aufsatz wird die freie Konvektion von einer horizontalen, linienförmigen Wärmequelle untersucht, die in ein unbegrenztes poröses Medium eingebettet ist. Die Poren des porösen Mediums sind mit einem Fluid gefüllt, das unter Schwerkrafteinfluß ruht. Das strömende Fluid und das poröse Medium sind örtlich im thermischen Gleichgewicht.
    Notes: Abstract In this paper we consider the free convection from a horizontal line source of heat which is embedded in an unbounded porous medium saturated with a fluid at rest under gravity. The convective fluid and the porous medium are in local thermal equilibrium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01052976
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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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  • 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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  • 4
    Electronic Resource
    Electronic Resource
    Higher-order effects in natural convection flow over uniform flux inclined flat plates in porous media (1988)
    Springer
    Heat and mass transfer 22 (1988), S. 239-242 
    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 werden Grenzschichteinflüsse höherer Ordnung für die freie Konvektionsströmung über schrägen ebenen Platten (sowohl für positive als auch für negative Schräge) bei gleichmäßigem Wärmestrom in einem gesättigten porösen Medium untersucht. Mit Hilfe der Methode der angepaßten asymptotischen Entwicklungen werden drei Terme der inneren und äußeren Entwicklung bestimmt. Es wird gezeigt, daß die erste Eigenfunktion für
    Notes: Abstract Higher-order boundary-layer effects for natural convection flow along inclined flat plates (of both positive and negative inclinations) with a uniform heat flux surface condition in a saturated porous medium are studied. Using the method of matched asymptotic expansions the three terms in inner and outer expansions have been obtained. It is shown that the first eigenfunction for this considered problem coincides with 0(ɛ 2)-term in the inner expansion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01377247
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  • 5
    Electronic Resource
    Electronic Resource
    Mixed convection similarity solutions on a horizontal surface (1987)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 38 (1987), S. 102-116 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die Grenzschicht an einer horizontalen Platte mit gemischter Konvektion wird für zwei Fälle untersucht: Für eine ruhende Platte bei gleichförmiger Außenströmung und für eine Platte, die sich kontinuierlich mit konstanter Geschwindigkeit in ihrer eigenen Ebene bewegt, ohne Außenströmung. Für beide Fälle wählen wir ein Potenzgesetz für die Temperaturverteilung entlang der Wand, für welche die Grundgleichungen eine Ähnlichkeitslösung zulassen. In der ersten Problemstellung betrachten wir einen Bereich des Auftriebsparameters, für den zweifache Lösungen existieren. Wir zeigen, wie diese doppelten Lösungen aus einer Bifurkation entstehen und wie der untere Lösungszweig endet, wenn der Auftriebsparameter gegen Null strebt. Für die zweite Problemstellung zeigen wir, daß eine eindeutige Lösung existiert für alle positiven Werte des Auftriebsparameters und daß für negative Werte eine singuläre Lösung mit algebraischem Zerfall erreicht wird.
    Notes: Abstract The mixed convection boundary layer on a horizontal plate is considered for the two separate cases when there is a uniform free stream with the plate held fixed and when there is no outer flow but the plate is moving continuously with a uniform velocity along its length. In both cases we assume that power law temperature distribution on the plate which enables the governing equations to be reduced to similarity form. For the first problem we consider the range of buoyancy parameter for which there are dual solutions, showing how these dual solutions arise from a bifurcation and how the lower branch of solutions terminate as the buoyancy parameter tends to zero. For the second problem we show that there is a unique solution for all positive values of the buoyancy parameter and that for negative values the solution terminates at a singular solution with algebraic decay.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944924
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Flow past a suddenly cooled horizontal flat surface in a saturated porous medium (1985)
    Springer
    Acta mechanica 56 (1985), S. 205-217 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The problem considered is that of the cooling of an impermeable horizontal surface embedded in a saturated porous medium, the temperature of which is instantaneously reduced to that of the ambient fluid. Solutions valid for small and large times are obtained. It is found that it is not possible to join these two solutions by a numerical integration of the equations either by using direct integration or by using any of the indirect methods that have been suggested for impulsive heating problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177118
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  • 8
    Electronic Resource
    Electronic Resource
    Natural convection from a semi-infinite flat plate inclined at a small angle to the horizontal in a saturated porous medium (1985)
    Springer
    Acta mechanica 57 (1985), S. 183-202 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The free convection boundary layer on a semi-infinite heated flat plate which is inclined at a small angle to the horizontal in a saturated porous medium is considered. When the plate is inclined upwards, series solutions, one valid near the leading edge and the other valid at large distances from it, are obtained. Sufficient terms in the leading edge solution are taken so that the two asymptotic solutions may be joined. When the plate is inclined downwards the series solution valid near the leading edge is again obtained and sufficient terms are again employed to investigate the nature of the boundary layer separation. There is no evidence of a singularity at the separation point and a mathematical explanation of the behaviour at separation is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01176917
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  • 9
    Electronic Resource
    Electronic Resource
    The sudden melting of a thin vertical flat plate in a Darcian free convection flow (1988)
    Springer
    Acta mechanica 71 (1988), S. 77-93 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary In this paper a solution of the unsteady free convection boundary-layer equations in porous media is presented for the sudden melting of a thin semi-infinite vertical flat plate. It is assumed that fort〈0 that the steady state temperature and velocity has been obtained and at timet=0 the plate starts to melt. Three distinct phases of the temporal development of the flow are considered. An analytical solution is presented which is valid fort≪1 and which shows the initial decay of the boundary-layer. At very large values oft the boundary-layer will disappear and an analytical solution showing this approach is obtained. A numerical solution which matches these two limiting solutions has been obtained by means of a step-by-step method and these results show good agreement with the theoretical results that are valid at small and large values of time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01173939
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  • 10
    Electronic Resource
    Electronic Resource
    Two dimensional combined convection in vertical parallel plate ducts, including situations of flow reversal (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1645-1664 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical solutions are presented for the problem of steady laminar combined convection flows in vertical parallel plate ducts. Axial diffusion is neglected in the analysis and the resulting governing equations, which are of a parabolic nature, are expressed in an implicit finite difference scheme using a vorticity-stream function formulation and are solved using a marching technique. A constant wall temperature boundary condition is used and investigations are restricted to the case Pr = 0.72. A large range of values of the ratio Gr/Re is considered, -300 ≤ Gr/Re ≤ 70, and comparisons are made with the case of pure forced convection. For large values of the ratio |Gr/Re| reverse flow occurs in the duct. A modification to the standard marching technique is introduced and complete solutions are achieved for these situations for the first time. Results are presented in terms of velocity profiles, Nusselt numbers, friction factors and temperature distributions.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260713
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