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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Heat and mass transfer 22 (1988), S. 141-146 
    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 Aufsatz behandelt ein analytisches und numerisches Verfahren zur Lösung des klassischen Graetz-Nusselt-Problems und seine Erweiterung auf konstante Heizflächenbelastung an der Wand. Im Detail ist die Ableitung einer neuen Formulierung dargestellt, welche die Technik der Trennung der Variablen und die Linienmethode kombiniert. Unterschiedlich zu herkömmlichen finiten Differenzen-Näherungsmethoden ist das hier entwickelte Verfahren weder explizit noch implizit. Es weist spezielle Charakteristiken auf und hat den Hauptvorteil, daß das Temperaturprofil direkt an jeder beliebigen axialen Stelle in dem Rohr berechnet werden kann, indem man eine einzige gewöhnliche Differentialgleichung löst, welche die Abmessungen des zu betrachtenden Volumens enthält. Die Ergebnisse für den gesamten Einlaufbereich sowie die Probleme, die in diesem Aufsatz analysiert wurden, stimmen gut mit existierenden Standardlösungen überein.
    Notes: Abstract This paper deals with an analytical and numerical procedure to solve the classical Graetz-Nusselt problem and its natural extension accounting for a uniform heat flux at the wall. The derivation of a new formulation coupling the technique of separation of variables and the method of lines is outlined in detail. Unlike conventional finite difference approaches, the procedure developed here is neither explicit nor implicit. It has special characteristics and its main advantage is that the temperature profile can be calculated directly at any axial station in the pipe by solving a single ordinary differential equation which incorporates the size of the station. Results for the entire thermal entry region of both problems analyzed in this paper agree well with existing benchmark solutions.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Physics and Chemistry of Solids 32 (1971), S. 1025-1038 
    ISSN: 0022-3697
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physica C: Superconductivity and its applications 153-155 (1988), S. 361-362 
    ISSN: 0921-4534
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1415-1427 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Flows in rotating magnetic disk storage systems and similar devices are prone to instabilities and the viscous generation of heat. Serious degradation in the performance of disk storage systems occurs when differential thermal expansion, due to the maldistribution of heat, and flow-induced vibrations result in track misregistration by the magnetic read/write heads. Submicron flying heights and micron track widths exacerbate such alignment difficulties. High rotation speeds, also characterizing the emerging disk storage technology, impose significant torque requirements. Experimental measurements of torque obtained by Daily and Nece [J. Basic Eng. Trans ASME 82, 217 (1960)] for a single disk, and by Hudson and Eibeck [J. Fluids Eng. 113, 648 (1991)] for a disk stack with and without obstructions, both in cylindrical enclosures, are found in this study to be correctly correlated by the analytically derived equation, TNo≡Ttotρ/Nμ2R2 = (2C1 + C2H/R2) × [Re/(1 − tL/HR2)]3/2+m, where TNo is a newly defined dimensionsless torque number, Re is the Reynolds number of the interdisk flow; H, R2, t, and L are geometrical length scales; and, C1, C2, and m are experimentally determined constants of order unity.Regressions to the experimental data of these authors yield values for C1, C2, and m in this equation which offer a combination of accuracy and universality not previously available. Moderate amounts of imposed radially directed flows in the spaces between unobstructed pairs of corotating disks are shown, via numerical calculation, to affect the interdisk flow fields quite notably. Analysis of results obtained solving the Navier–Stokes equations, assuming unsteady, axisymmetric, streamlined flow at low speeds of rotation shows that sucking air radially inward in the interdisk space, rather than blowing it radially outwards, substantially reduces the torque required to rotate the disks relative to the unventilated condition. Notwithstanding, depending on how the sucking condition is implemented, in obstructed geometries the reduction in torque may come at the expense of flow instabilities that could affect magnetic head read/write performance, a problem requiring close attention in the application of present findings to the improved design of disk storage systems.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 1225-1240 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The unsteady streamlined motion of a constant property fluid in the unobstructed space between a pair of disks corotating at angular velocity Ω in a fixed cylindrical enclosure is investigated numerically. Two-dimensional (axisymmetric) and three-dimensional calculations are performed using a second-order accurate time-explicit algorithm. The flow configuration corresponds to that investigated experimentally by Schuler et al. [Phys. Fluids A 2, 1760 (1990)]. The steady flow solutions are characterized by a symmetrical pair of counter-rotating toroidal vortices in the cross-stream (r-z) plane. This secondary motion is driven by the radial imbalance between the outward-directed centrifugal force and the inward-directed pressure gradient force. Axisymmetric calculations predict a flow that is steady for Re〈22 200, where Re is the Reynolds number based on the disk radius, the tip speed of the disks, and the kinematic viscosity of the fluid. Above this value the motion is unsteady periodic and, while the features of the cross-stream flow pattern are broadly preserved, the symmetry of the motion about the midplane is broken by alternating periodic crossings of the toroidal vortices.This instability is maintained through an interaction that arises between outward-directed fluid in the disk Ekman layers and inward-directed fluid in the return core flow. Three-dimensional calculations at Re=22 200 and 44 400 show that the toroidal vortices acquire a time-varying sinuous shape in the circumferential direction. These calculations reveal circumferentially periodic reversals of the axial velocity component in the cross-stream plane, including the detached shear layer separating the region of motion in solid-body rotation near the hub from the potential core, in agreement with the flow visualization observations of Humphrey and Gor [Phys. Fluids A 5, 2438 (1993)]. The wavelength of this oscillation is shown to be twice that of the circumferential velocity component which is responsible for the nodal distribution of axial vorticity. When plotted on the interdisk midplane, the axial component of vorticity manifests itself as an even integer number, 2n (n=1,2,...), of circumferentially periodic foci. Experiments show that the number of foci decreases in a stepwise manner with increasing Reynolds number. For the conditions of this study, the calculated dimensionless angular velocity of the foci, ΩF/Ω, ranges from 0.55 at Re=22 200 to 0.44 at Re=44 400. These values are close to the present experimental estimate ΩF/Ω=0.5. © 1995 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1760-1770 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A model of a computer hard disk drive was constructed and measurements of the air flow in the unobstructed space between a pair of disks were obtained. The disks were centrally clamped to a common hub, and rotated within an axisymmetric (cylindrical) enclosure or shroud. Measurements of the circumferential velocity component were made at five radial locations and three rotation rates (Ω=300, 1200, and 3600 rpm) using a laser-Doppler velocimeter. The resulting mean and rms circumferential velocity profiles are presented and discussed. The data show that the circumferential velocity component profiles are fairly uniform in the axial direction in the space between the disks, except near the shroud where the flow is strongly sheared. The circumferential velocity peaks at a critical radius. Between the hub and the critical radius location the flow is in solid body rotation. Between the critical radius and the shroud the circumferential velocity decreases to zero, gradually at first and then very quickly as the shroud is approached. Analysis based on simplified force balance considerations facilitates the interpretation of the experimental observations and leads to improved understanding of the complex flow phenomena. Numerical calculations of the present configuration assuming axisymmetric steady flow were performed by Chang et al. (submitted to Int. J. Heat Mass Transfer). These calculations show reasonable agreement with the averaged velocity data but, for the reasons discussed, fail to reproduce features of the rms distribution associated with nonturbulent flow unsteadiness.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Earth and Planetary Science Letters 93 (1989), S. 345-358 
    ISSN: 0012-821X
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Solid State Ionics 1 (1980), S. 77-86 
    ISSN: 0167-2738
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Experiments in fluids 6 (1988), S. 568-570 
    ISSN: 1432-1114
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Heat and mass transfer 22 (1988), S. 251-257 
    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 Wechselwirkung zwischen Zwangskonvektion und Wärmestrahlung bei laminarer Strömung in einem Rohr theoretisch mit Hilfe eines numerischen Rechenverfahrens untersucht. Dabei wird ein absorbierendes und emittierendes Gas in der Analyse als grauer Strahler betrachtet. Mit Hilfe der Momentenmethode wird der Strahlungs-Wärmefluß in die Energiegleichung näherungsweise eingeführt. Die das Problem beschreibenden Bilanzgleichungen werden auf ein gekoppeltes System einer partiellen und einer gewöhnlichen Differentialgleichung reduziert. Das so erhaltene Gleichungssystem wurde als Anfangswert-problem mit Hilfe einer Verknüpfung der Kontrollvolumina formuliert. Die Temperaturverteilung im Einlauf der Gasstrümung wurde mit Hilfe des Runge-Kutta-Verfahrens integriert. Ergebnisse für die mittlere Fluidtemperatur und die Nusselt-Zahl zeigten gute quantitative Übereinstimmung mit Rechnungen, die eine exakte Beschreibung des Strahlungswärmeflusses benutzen. Diese einfache Methode gewährt große Einsparung in CPU-Zeit. Deshalb scheint die Verwendung der Momentenmethode in Gasstrümungen kombiniert mit Verfahren des Wärmetransportes gerechtfertigt.
    Notes: Abstract The interaction of forced convection and thermal radiation in laminar pipe flow is numerically studied in this paper. An absorbing and emitting gas is considered for the analysis and treated to be a gray medium. The method of moments is used to describe approximately the radiative heat flux in the energy equation. The conservation equations that govern the problem are reduced to a coupled system consisting of a partial and an ordinary differential equations. The resulting system was reformulated into an initial value problem with the help of the method of lines in conjunction with the control volume approach. Temperature distributions in the thermal entrance region of the gas flow are computed by the Runge-Kutta integration scheme. Results for the mean bulk temperatures and total Nusselt numbers showed a good quantitative agreement with those utilizing an exact description for the radiative heat flux. Moreover, this simple methodology provided great savings in CPU time. Therefore, the use of the method of moments in internal gas flows with combined modes of heat transfer seems justifiable.
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