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Abstract (ger): Die Flüssigkeitsschichten, die um ein sich bewegendes Molekül herumfließen, haben infolge der endlichen Abmessungen der Flüssigkeitsmolekeln eine endliche Dicke. Die Berücksichtigung dieses Umstandes führt zu einer Modifikation der Stokesschen Gesetze der Kontinuumstheorie für den Zusammenhang zwischen Reibung und Viskosität. Es ergibt sich die richtige Größenordnung und ungefähr die richtige Radienabhängigkeit der beobachteten Mikroreibung, und zwar sowohl für die Rotation als auch für die Translation.
Kausalität – Streitgespräch
(2007)
Modelle in der Physik
(2005)
Der Energiebedarf der Menschen wird heute überwiegend durch die Verbrennung von Kohle, Erdöl und Erdgas gedeckt. Das Bewusstsein der Endlichkeit dieser wertvollen Rohstoffe hat die Energiefrage zu einem zentralen Begriff für alle Überlegungen gemacht, die auf die langfristige Zukunft des Lebens auf unserem Planeten gerichtet sind. Vor 150 Jahren haben zuerst Physiologen die Bedeutung der Energie für den Stoffwechsel von Lebewesen erkannt, Physiker bestimmten den für die Umwelt kritischen Energiehaushalt der Erde. Sie stellten Überlegungen dazu an, welche Auswirkung die Ausbeutung der fossilen Energievorräte hat und welche Aufgaben von der Menschheit gelöst werden müssen, wenn ihre Zukunft gesichert werden soll. Schon heute erkennbare Aufgaben für Wissenschaft, Technik und Wirtschaft werden genannt, sie müssen von der Energiepolitik gefördert werden.
We expose analogies between turbulence in a fluid heated from below (Rayleigh-Bénard (RB) flow) and shear flows: The unifying theory for RB flow (S.Grossmann and D.Lohse, J.Fluid Mech. 407, 27-56 (2000) and subsequent refinements) can be extended to the flow between rotating cylinders (Taylor-Couette flow) and pipe flow. We identify wind dissipation rates and momentum fluxes that are analogous to the dissipation rate and heat flux in RB flow. The proposed unifying description for the three cases is consistent with the experimental data.
Non-Oberbeck-Boussinesq (NOB) effects on the Nusselt number Nu and Reynolds number Re in strongly turbulent Rayleigh-Benard convection in liquids were investigated both experimentally and theoretically. In the experiment, the heat current, the temperature difference, and the temperature at the horizontal mid-plane were measured. Three cells of different heights L, all filled with water and all with aspect ratio T close to 1 were used. For each L, about 1.5 decades in Ra were covered, together spanning the ränge 108 < Ra < 1011. For the largest temperature difference between the bottom and top plates of ? = 40K the kinematic viscosity and the thermal expansion coefficient, due to their temperature dependence, varied by more than a factor of two. The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus was no longer valid. The ratio Ï? of the temperature drops across the bottom and top thermal boundary layers became as small as Ï? = 0.83, as compared to the ratio Ï? = 1 in the OB case. Nevertheless, the Nusselt number Nu was found to be only slightly smaller (at most 1.4%) than in the next larger cell with the same Rayleigh number, where the material parameters were still nearly height-independent. The Reynolds numbers in the OB and NOB case agreed with each other within the experimental resolution of about 2%, showing that NOB effects for this parameter were small as well. Thus Nu and Re are rather insensitive against even significant deviations from OB conditions. Theoretically, we first account for the robustness of Nu with respect to NOB corrections: the NOB effects in the top boundary layer cancel those which arise in the bottom boundary layer as long as they are linear in the temperature difference ?. The net effects on Nu are proportional to ?2 and thus increase only slowly and still remain minor despite drastic material parameter changes. We then extend the Prandtl-Blasius boundary-layer theory to NOB Rayleigh-Benard flow with temperature dependent viscosity and thermal diffusivity. This allows the calculation of the shift of the bulk temperature, the temperature drops across the boundary layers, and the ratio Ï? without introducing any fitting parameter. The calculated quantities are in very good agreement with experiment. When in addition we use the experimental finding that for water the sum of the top and bottom thermal boundary-layer widths (based on the slopes of the temperature profiles at the plates) remains unchanged under NOB effects within experimental resolution, the theory also gives the measured small Nusseltnumber reduction for the NOB case. In addition, it predicts an increase by about 0.5% of the Reynolds number, which is also consistent with the experimental data. By theoretically studying hypothetical liquids with only one of the material parameters being temperature dependent, we shed further light on the origin of NOB corrections in water: While the NOB deviation of x from its OB value Ï? = 1 mainly originates from the temperature dependence of the viscosity, the NOB correction of the Nusselt number primarily originates from the temperature dependence of the thermal diffusivity. Finally, we give the predictions from our theory for the NOB corrections if glycerol is used as operating liquid.