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  • 11
    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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  • 12
    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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  • 13
    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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  • 14
    Electronic Resource
    Electronic Resource
    Laminar and turbulent radial jets (1998)
    Springer
    Acta mechanica 127 (1998), S. 25-38 
    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 the radial free jet which is produced by a continuous discharge of fluid from the space between two identical, parallel, circular, concentric discs into an infinite region of stagnant fluid of the same density and viscosity is investigated. Both laminar and turbulent jets are considered with analytical solutions being obtained near to the origin of the jet and at large distances along the jet. These asymptotic solutions are matched using a computational technique, and the numerical predictions show very good agreement with all the available experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170360
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  • 15
    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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  • 16
    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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  • 17
    Electronic Resource
    Electronic Resource
    Flow reversal in a combined convection flow of Newtonian fluid in a vertical duct (1993)
    Springer
    Acta mechanica 99 (1993), S. 135-153 
    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 Numerical solutions are presented for the problem of steady laminar combined convection flows in vertical parallel-plate ducts, with linearly varying wall temperatures. Neglecting streamwise diffusion in the analysis leads to a parabolic set of governing equations. These are solved using a marching technique for an implicit finite-difference scheme with vorticity, streamfunction and temperature as variables. A constant wall temperature is applied after a certain height to mimic downhole conditions in an oil well. Various values of the governing parameter,Gr, are considered, including the forced convection solution,Gr=0, whilstPr is set at a value of unity in order to present the numerical method. As |Gr| increases reverse flow regions appear and these are dealt with using a modification of the standard marching technique. Results are obtained in terms of velocity profiles, local Nusselt numbers, flow average temperatures and friction factors, with particular attention applied to the case where the wall temperature decreases with height.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177241
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  • 18
    Electronic Resource
    Electronic Resource
    Combined convection flow of a power-law fluid in a vertical duct with linearly varying wall temperatures (1995)
    Springer
    Acta mechanica 110 (1995), S. 19-32 
    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 This paper considers steady laminar combined convection flows of power-law fluids between vertical parallel-plates with a uniform temperature gradient applied to the walls. The parabolic equations are written in an implicit finite-difference form and are solved using a marching technique. The governing parameters are Gr, Pr, andn. Various values of Gr andn are considered, including the forced convection solution, Gr=0, and the Newtonian case,n=1. Pr is set at a value of unity in order to present the numerical method and to compare with the existing results for Newtonian fluids. Under certain circumstances reverse flow regions appear, either at the centre or adjacent to the walls of the duct and these are present in the fully-developed flow. These reverse flow problems are dealt with using an iterative technique. In order to assess the effects of recirculation and pseudoplasticity on the flow and heat transfer characteristics, flow profiles, Nusselt numbers and friction factors are presented for various values of the governing parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01215412
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  • 19
    Electronic Resource
    Electronic Resource
    Unsteady mixed convection from an isothermal circular cylinder (1981)
    Springer
    Acta mechanica 38 (1981), S. 55-69 
    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
    Description / Table of Contents: Zusammenfassung Es wird eine kombinierte, unstetige Konvektion eines isothermen, horizontalen Zylinders in einer vertikal nach oben gerichteten Strömung untersucht. Numerische Lösungen der unstetigen Grenzschichtgleichungen werden an jeder Stelle längs des Zylinders durch die Verwendung der Reihenabbruchsmethode erhalten. Nahe der Vorderseite und nahe bei den Staupunkten gültige Lösungen werden durch Verwendung üblicher Methoden der finiten Differenzen erhalten. Mit Hilfe einer Reihenlösung in Potenzen der Zeit wird das numerische Ergebnis überprüft.
    Notes: Summary Combined unsteady convection from an isothermal horizontal cylinder in a stream flowing vertically upwards has been investigated. Numerical solutions of the unsteady boundary-layer equations have been obtained at any station along the cylinder using the series truncation method. Solutions which are valid near the front and near stagnation points have been obtained using standard finite-difference methods. A series solution in powers of time has been obtained with which the numerical solutions has been checked.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01351462
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  • 20
    Electronic Resource
    Electronic Resource
    Developing combined convection of non-Newtonian fluids in an eccentric annulus (1997)
    Springer
    Acta mechanica 121 (1997), S. 35-49 
    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 Laminar combined convection of non-Newtonian fluids in vertical eccentric annuli, in which the inner and outer walls are held at different constant temperatures is considered and a new economical method of solution for the three-dimensional flow in the annulus is developed. Assuming that the ratio of the radial to the vertical scale, ε, is small, as occurs frequently in many industrial applications, then the governing equations can be simplified by expanding all the variables in terms of ε. This simplification gives rise to the presence of a dominant cross-stream plane in which all the physical quantities change more rapidly than in the vertical direction. The solution trechnique consists of marching in the vertical streamwise direction using a finite-difference scheme and solving the resulting equations at each streamwise step by a novel technique incorporating the Finite Element Method. The process is continued until the velocity, pressure and temperature fields are fully developed, and results are presented for a range of the governing non-dimensional parameters, namely the Grashof, Prandtl, Reynolds and Bingham numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01262522
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