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Proceedings - Mathematical Sciences - 相似文献
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Henning Rasmussen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(2):187-195
Zusammenfassung Die Strömung zwischen zwei porösen Scheiben in der Nähe der Symmetrieachse wird untersucht. Die Navier-Stokes'schen Gleichungen werden auf eine nichtlineare gewöhnliche Differentialgleichung dritter Ordnung reduziert, die mit Störungsmethoden für grosse Reynolds-Zahlen gelöst wird. Numerische Lösungen werden auch berechnet. 相似文献
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Low-Reynolds-number flow plays an important role in the centrifugal separation of fluid particles under microgravity conditions and also in micromechanics due to the miniaturization of fluid mechanical parts. In this situation, the governing equations may be simplified. Here an analytical solution is presented for the steady flow of an incompressible viscous fluid between two finite disks enclosed by a cylindrical container for small Reynolds number (Re 10). The general solution is valid for all choices of the aspect ratio () and different cases of disk to cylinder rotation rates (s). An expression for the torque acting on the disk is obtained. The tangential velocity distribution is calculated and presented graphically for different values of ands. Known results in the literature for a single rotating disk and similar problems follow as a particular case of the general solution presented.
Zusammenfassung Zahlreiche hydrodynamische Vorgänge unter der Bedingung verminderter Schwerkraft aber auch Vorgänge in der Mikromechanik finden im Bereich kleiner Reynoldszahlen statt. In solchen Situationen können die Bewegungsgleichungen vereinfacht und eventuell analytische Lösungen gefunden werden. In dieser Arbeit wird die stationäre Strömung einer viskosen, inkompressiblen Flüssigkeit für kleine Reynolds- und unterschiedliche Aspektzahlen untersucht. Die Flüssigkeit ist zwischen zwei rotierenden Scheiben und einem zylindrischen Behälter eingeschlossen. Eine analytische Lösung für die Tangentialkomponente des Geschwindigkeitsvektors ist für den allgemeinen Fall, dass die Scheiben und der Behälter unterschiedliche Winkelgeschwindigkeiten besitzen können, dargestellt. Des weiteren wurde eine Beziehung für das Widerstandsmoment der rotierenden Scheibe angegeben. Der Verlauf der Tangentialgeschwindigkeiten für verschiedene Rotations- und Aspektverhältnisse wird graphisch dargestellt und diskutiert. Bereits angegebene Lösungen in der Literatur bezüglich dieser Geometrie können als Sonderfall der hier dargestellten Lösung entwickelt werden.相似文献
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The present work investigates the effects of disks contracting, rotation and heat transfer on the viscous fluid between heated contracting rotating disks. By introducing the Von Kármán type similarity transformations through which we reduced the highly nonlinear partial differential equation to a system of ordinary differential equations. This system of differential equations with appropriate boundary conditions is responsible for the flow behavior between large but finite coaxial rotating and heated disks. It is important to note that the lower disk is rotating with angular velocity Ω while the upper one with SΩ, the disks are also contracting and the temperatures of the upper and lower disks are T1 and T0, respectively. The agents which driven the flow are the contraction and also the rotation of the disks. On the other hand the velocity components and especially radial component of velocity strongly influence the temperature distribution inside the flow regime. The basic equations which govern the flow are the Navier Stokes equations with well known continuity equation for incompressible flow. The final system of ordinary differential equations is then solved numerically with given boundary conditions. In addition, the effect of physical parameters, the Reynolds number (Re), the wall contraction ratio (γ) and the rotation ratio (S) on the velocity and pressure gradient, as well as, the effect of Prandtl number (Pr) on temperature distribution are also observed. 相似文献
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The present work investigates the effects of the disks contracting, rotation, heat transfer and different permeability on the viscous fluids and temperature distribution between two heated contracting rotating disks. Two cases are considered. For the first case, we neglect the viscous dissipation effects in the energy equation and reduce the Navier-Stokes equations and energy equation into nonlinear coupled ODEs by introducing the Von Kármán type similarity transformations. The effects of various physical parameters like expansion ratio, Prandtl number, Reynolds number and rotation ratio on the velocity and temperature are discussed in detail. The second and more general case is that we consider the viscous dissipation in the energy equation. Under this assumption, the energy equation is reduced to a ordinary differential equation including the Eckert number, whose solution also is solved by HAM. 相似文献
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William W. Wood 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1964,15(3):313-314
Zusammenfassung Ein Beweis des Rayleighschen Kriteriums der Stabilität einer zähen Strömung zwischen zwei unendlichen, coaxialen, rotierenden Zylindern, der auf einer einfachen Abänderung des Energieintegrals für die Perturbationsgeschwindigkeit begründet ist, wird dargestellt. 相似文献
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Flow and heat transfer of an elastico-viscous liquid between two parallel uniformly porous disks rotating about a common axis,
are studied by perturbation technique. It is seen that for such a fluid, drag increases with suction and decreases with injection,
while the rate of heat transfer increases in the presence of either suction or injection. 相似文献
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Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically. 相似文献
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The problem of injection (suction) of a viscous incompressible fluid through a rotating porous disc onto a rotating co-axial
disc is studied using computer extended series. The universal coefficients in the low Reynolds number perturbation expansion
are generated by delegating the routine complex algebra to computer. Various cases leading to specific types of flows are
studied. Analytic continuation of the series solution yields results which agree favourably with pure numerical findings up
to moderately large Reynolds number. The precise variation of lift as a function of R is established in each case. 相似文献
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Markus Bause 《PAMM》2004,4(1):696-697
The extensive application of mathematical and computational methods has become an efficient and powerful approach to the investigation and solution of many problems and processes in fluid dynamics from qualitative as well as quantitative point of view. In this work a new class of advanced numerical approximation schemes to isothermal compressible viscous flow is presented. The schemes are based on an iteration between an Oseen like problem for the velocity and a hyperbolic transport equation for the density. Such schemes seem attractive for computations because they offer a reduction to simpler problems for which highly refined numerical methods either are known or can be built from existing approximation schemes to similar equations, and because of the guidance that can be drawn from an existence theory based on them. For the generalized Oseen subproblem a Taylor–Hood finite element method is proposed that is stabilized by a reduced SUPG and grad‐div technique (cf. [1, 4]) in the convection‐dominated case. Results of theoretical investigations and numerical studies are presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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This article provides an analytical solution of the Navier–Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of unknown components of velocity and pressure in a radial direction – in contrast to the Briter–Pohlhausen analytical solution, which is supported by simplified Navier–Stokes equations. The obtained infinite system of ordinary differential equations forms recurrent relations from which unknown functions can be calculated successively. The first and second approximations of solution are solved analytically and the third and fourth approximations of solutions are solved numerically. The numerical example demonstrates agreements with results obtained by other authors using different methods. 相似文献
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P. Raghupathi Rao A. Ramachandra Rao 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1983,34(4):550-555
Heat transfer in a MHD flow between two infinite eccentric disks rotating with different speeds is considered when the plates are maintained at different temperatures. The results for the corresponding nonmagnetic case presented wrongly by Banerjee and Borkakati [7] are corrected. It is observed that the eccentric rotation reduces the heat transfer on the disks. 相似文献
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B. Banerjee A. K. Borkakati 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1982,33(3):414-418
Heat transfer in the flow between two infinite eccentric disks rotating with different speeds is considered when the plates are maintained at different temperatures.
Zusammenfassung Es wird die Wärmeübertragung im Fluid zwischen zwei unendlichen Platten mit verschiedenen Temperaturen berechnet, die exzentrisch mit verschiedenen Winkelgeschwindigkeiten rotieren.相似文献
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N. M. Bujurke N. N. Katagi V. B. Awati 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(5):836-851
The computer extended perturbation series method is used to analyze the problem of steady viscous flow in slender tubes. The objective is to obtain an expansion in a power series of λ (= ɛ R, ɛ is a small parameter and
is a streamwise Reynolds number) and look for its analytic continuation. Such an expansion was usually terminated at the second or third order term and consequently they have a very limited utility. Sufficiently large number of terms in the series, representing physical quantities are, generated for the detail analysis which enables to get converging Pade’ sums for large λ. Domb-Sykes plot enables in finding singularity restricting the convergence of the series. Useful results valid up to λ = 15 are obtained for different derived quantities whereas in earlier findings [6], analysis could be done only up to λ = 10 resulting into a substantial improvement in the present study.Received: September 17, 2003; revised: July 5, 2004 相似文献
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《Comptes Rendus Mathematique》2008,346(17-18):935-938
The equations describing similarity solutions for flow between infinite parallel permeable disks with equal rates of suction or injection at the walls is derived using the stream function. This leads to a fourth order non-linear Ordinary Differential Equation. This equation is shown to admit anti-symmetric solutions using the moving plane method. To cite this article: Adimurthi, A. Karthik, C. R. Acad. Sci. Paris, Ser. I 346 (2008). 相似文献
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N. M. Bujurke N. N. Katagi V. B. Awati 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,61(2):836-851
The computer extended perturbation series method is used to analyze the problem of steady viscous flow in slender tubes. The objective is to obtain an expansion in a power series of λ (= ɛ R, ɛ is a small parameter and
R = \fracMLnR = \frac{M}{{L\nu }}
is a streamwise Reynolds number) and look for its analytic continuation. Such an expansion was usually terminated at the second or third order term and consequently they have a very limited utility. Sufficiently large number of terms in the series, representing physical quantities are, generated for the detail analysis which enables to get converging Pade’ sums for large λ. Domb-Sykes plot enables in finding singularity restricting the convergence of the series. Useful results valid up to λ = 15 are obtained for different derived quantities whereas in earlier findings [6], analysis could be done only up to λ = 10 resulting into a substantial improvement in the present study. 相似文献