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  • 1
    Electronic Resource
    Electronic Resource
    Analytical solution for transient laminar fully developed free convection in vertical channels (1995)
    Springer
    Heat and mass transfer 30 (1995), S. 241-248 
    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 Für oben und unten offene vertikale Kanäle mit Kreisquerschnitt bzw. als Parallelplattenanordnung werden unter Verwendung der Methode der Greenschen Funktionen analytische Lösungen für die nichtstationäre, vollausgebildete, natürliche Konvektion gefunden und zwar unter Zugrundelegung verschiedener Fundamental-Randbedingungen bezüglich beider Konfigurationen. Die so ermittelten Fundamentallösungen können zur Gewinnung von Lösungen für allgemeine Randbedingungen dienen. Der zeitlich veränderliche Volumenstrom, die Mischtemperatur und die Nusselt-Zahl werden mit Bezug auf die erhaltenen nichtstationären Profile für Temperatur und Geschwindigkeit näher analysiert.
    Notes: Abstract Using Green's function method, analytical solutions for transient fully developed natural convection in open-ended vertical circular and two-parallel-plate channels are presented. Different fundamental boundary conditions for these two configurations have been investigated and the corresponding fundamental solutions are obtained. These fundamental solutions may be used to obtain solutions satisfying more general thermal boundary conditions. In terms of the obtained unsteady temperature and velocity profiles, the transient volumetric flow rate, mixing cup emperature and local nusselt number are estimated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01602770
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  • 2
    Electronic Resource
    Electronic Resource
    Unsteady conduction in eccentric annuli (1995)
    Springer
    Heat and mass transfer 30 (1995), S. 249-257 
    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 Der Wärmetransport durch Leitung in exzentrischen Ringspalten mit inneren Wärmequellen wurde für zwei Randbedingungen des Fundamentaltyps 4 untersucht. Man erhält diese, indem eine Ringspaltberandung von einem konstanten Wärmefluß durchsetzt wird, während die gegenüberliegende adiabat sein soll. Für den stationären Fall lassen sich exakte Lösungen finden, während das transiente Problem numerisch gelöst werden muß.
    Notes: Abstract Conduction heat transfer in eccentrically hollow cylindrical shafts with internal generation of heat has been investigated under two boundary conditions of the fourth type. These two boundary conditions are obtained by keeping one of the boundary surfaces at uniform heat flux while the opposite boundary is perfectly insulated (adiabatic). Exact analytical solutions are obtained to the steady state problem while the transient problem is numerically investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01602771
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  • 3
    Electronic Resource
    Electronic Resource
    Transient combined natural convection-conduction in open-ended vertical concentric annuli (1999)
    Springer
    Heat and mass transfer 35 (1999), S. 133-141 
    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
    Notes: Abstract Transient conjugate natural convection heat transfer in open-ended vertical concentric annuli is investigated numerically. The governing equations of an induced laminar flow for a fluid of Pr=0.7 are solved using a finite-difference technique. The heating is achieved by a step change in the temperature of the outer surface of the outer tube while the inner surface of the inner tube is kept adiabatic. The range of Grashof number considered is 500≤Gr*≤105. The effects of solid-fluid conductivity ratio and diffusivity ratio on the transient induced flow characteristics are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002310050306
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  • 4
    Electronic Resource
    Electronic Resource
    Steady and transient liquid sphere heating in a convective gas stream (2000)
    Springer
    Heat and mass transfer 36 (2000), S. 147-158 
    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
    Notes: Abstract  A finite-difference scheme has been developed to solve the equations governing the laminar forced convection heat transfer around and inside a spherical fluid droplet moving steadily in another immiscible fluid for both steady and transient thermal conditions. For large values of the external flow Reynolds number (Re), results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ*). Detailed results over a wide range of viscosity ratio (μ*) and for 200≤Re≤1000 are presented for the temperature profiles outside and inside the sphere, Nusselt number, the time required to attain a uniform surface temperature and the time required to reach the steady-state temperature. Results show that convective heating is dependent on the external flow Reynolds number (Re) and the interior-to-exterior viscosity ratio (μ*) where increasing Re or decreasing μ* result in increasing heat transfer rate convected to the liquid sphere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002310050377
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  • 5
    Electronic Resource
    Electronic Resource
    Laminar forced convection about rotating bodies at low Pr-number (1997)
    Springer
    Heat and mass transfer 33 (1997), S. 81-84 
    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
    Notes: Abstract Nusselt number is presented as a function of Reynolds number and Prandtl number (Pr) for a laminar flow about a non- rotating and rotating sphere. The sphere rotation is expressed in terms of Taylor number. Pr is ranging between 0.7 and 0.2. The governing equations were solved numerically using finite difference method for constant wall temperature and constant heat flux conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002310050163
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  • 6
    Electronic Resource
    Electronic Resource
    Developing laminar forced convection in eccentric annuli (1998)
    Springer
    Heat and mass transfer 33 (1998), S. 353-362 
    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
    Notes: Abstract The paper presents a boundary-layer model describing the laminar forced convection heat transfer in the entry region of eccentric annuli. A finite-difference numerical algorithm is developed for solving this model. Numerical results are presented for the developing velocity profiles and the pressure drop in annuli of radius ratio 0.5 and 0.9 over a dimensionless eccentricity ranged from 0.1 to 0.8. Heat transfer parameters are presented for a fluid of Pr=0.7 under the conditions of an isothermally heated inner wall while the outer wall is kept at the inlet fluid temperature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002310050201
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  • 7
    Electronic Resource
    Electronic Resource
    Consistency, stability and convergence of the finite-difference equations for flow about a rotating sphere in an axial stream (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 825-831 
    Details
    ISSN: 0271-2091
    Keywords: Finite-difference Stability ; Rotating Sphere in Stream ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite-difference equations which have previously been developed to solve the problem of laminar boundary layer flow about a rotating sphere in an axial stream are analysed according to the available numerical stability theories. This analysis is necessary to determine the restrictions on velocities and mesh sizes required to obtain a convergent numerical solution. Convergence can be achieved if both consistency and stability of the finite-difference equations are fulfilled. The analysis reported in the present paper shows that the developed finite-difference equations are consistent with their original partial differential equations. Also, the analysis proves that the developed finite-difference procedure is numerically stable for all mesh sizes as long as the downstream meridional velocity is non-negative, i.e.as long as no flow reversals occur within the domain of solution.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070804
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  • 8
    Electronic Resource
    Electronic Resource
    An improved implicit finite-difference scheme for boundary-layer flows (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 715-728 
    Details
    ISSN: 0271-2091
    Keywords: Iterative ; Finite-difference ; Confined ; Unconfined ; Boundary-layer flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper presents a modification to two well-known non-iterative implicit finite-difference schemes for confined and unconfined boundary-layer-type flows. The modification aims at improving the accuracy of these schemes by reducing the adverse effect of linearization, which is inherent in both of them. Using the present improved scheme, the same level of accuracy of the results could be obtained with large mesh sizes in the flow direction (coarse grid). The modification is done by adding a local iterative procedure at each computational step in the flow (marching) direction. As an example, to demonstrate the proposed modification, the simple case of developing forced convection in the entry region of concentric annuli has been considered. The results are presented, which prove the applicability of the proposed modification and show its effect on the obtained accuracy and on the required computer time.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150606
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  • 9
    Electronic Resource
    Electronic Resource
    Finite difference analysis for laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 17-38 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a finite difference analysis are presented for the problem of incompressible laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers, the boundary conditions of one wall being isothermal and the other wall adiabatic. This corresponds to the fundamental solution of the third kind according to the four fundamental solutions classified by Reynolds, Lundberg and McCuen1.Firstly, the hydrodynamic entry length problem, based on the boundary layer simplifications of the Navier-Stokes equations, was solved by means of an extension of the linearized finite difference scheme used previously by Bodia and Osterle2 to solve a similar problem between parallel plates. The energy equation is then solved, using the velocity profiles previously obtained, by means of an implicit finite difference technique.The accuracy of the numerical solution was checked by comparing results for the annulus of radius ratio 0.25 with the avaiable solution of Shumway and McEligot3.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090103
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  • 10
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    Developing laminar forced convection in eccentric annuli (1998)
    Springer
    Details
    Publication Date: 1998-04-23
    Print ISSN: 0042-9929
    Electronic ISSN: 1432-1181
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Springer
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