186,943 research outputs found
The Generalized Graetz Problem in Finite Domains
No full textWe consider the generalized Graetz problem associated with stationary convection-diffusion inside a domain having any regular three-dimensional translationally invariant section and finite or semi-infinite extent. Our framework encompasses any previous “extended” and “conjugated” Graetz generalizations and provides theoretical bases for computing the orthogonal set of generalized two-dimensional Graetz modes. The theoretical framework includes both heterogeneous and possibly anisotropic diffusion tensors. In the case of semi-infinite domains, the existence of a bounded solution is shown from the analysis of two-dimensional operator eigenvectors which form a basis of L2 . In the case of finite domains a similar basis can be exhibited, and the mode’s amplitudes can be obtained from the inversion of newly defined finite domain operator. Our analysis includes both the theoretical and practical issues associated with this finite domain operator inversion as well as its interpretation as a multireflection image method. Error estimates are provided when numerically truncating the spectrum to a finite number of modes. Numerical examples are validated for reference configurations and provided in nontrivial cases. Our methodology shows how to map the solution of stationary convection-diffusion problems in finite three-dimensional domains into a two-dimensional operator spectrum, which leads to a drastic reduction in computational cost
Mathematical analysis of parallel convective exchangers with general lateral boundary conditions using generalized graetz modes
No full textWe propose a mathematical analysis of parallel convective exchangers for any general but longitudinally invariant domains. We analyze general Dirichlet or Neumann prescribed boundary conditions at the outer solid domain. Our study provides general mathematical expressions for the solution of convection/diffusion problems. Explicit form of generalized solutions along longitudinal coordinate are found from convoluting elementary base Graetz mode with the applied sources at the boundary. In the case of adiabatic zero flux counter-current configuration, we recover the longitudinally linearly varying solution associated with the zeroth eigenmode which can be considered as the fully developed behavior for heat-exchangers. We also provide general expression for the infinite asymptotic behavior of the solutions which depends on simple parameters such as total convective flux, outer domain perimeter and the applied boundary conditions. Practical considerations associated with the numerical precision of truncated mode decomposition is also analyzed in various configurations for illustrating the versatility of the formalism. Numerical quantities of interest are investigated, such as fluid/solid internal and external fluxes
Aplicação do método variacional à solução do problema de graetz generalizado
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-graduação em Engenharia Mecânica
Numerical Analysis of a New Mixed Formulation for Eigenvalue Convection-Diffusion Problems
No full textA mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization
G.d.K. Prinz Ludwig Windisch-Graetz's Kindheit und Jugendzeit : 1839-1850.
No full text"Aus dem Lesejournal Ludwig Windisch-Graetz' 1842-1850": p. 246-255.Mode of access: Internet
Geschichte der Juden von den ältesten Zeiten bis auf die Gegenwart : /
No full text"Biographie des Dr. H. Graetz, verfasst von Dr. Ph. Bloch"--V. 1, p. 1-72.Originally published: Leipzig : Leiner, 1890-1909, Ausg. letzter Hand.Includes bibliographical references.01. Geschichte der Israeliten, von ihren Uranfängen (um 1500) bis zum Tode des Königs Salomo (um 977 vorchristlicher Zeit) nebst synchronistischen Zeittafeln / H. Graetz; mit einem Vorw. von Reuven Michael.02.1-2. Geschichte der Israeliten, von Tode des Königs Salomo (um 977 vorchristlicher Zeit) bis zum Tode des Juda Makkabi (160) / H. Graetz.03.1-2. Geschichte der Judäer, von dem Tode Juda Makkabis bis zum Untergange des judäischen Staates / H. Graetz.04. Geschichte der Juden, von Untergange des judäischen Staates bis zum Abschluss des Talmud / H. Graetz.05. Geschichte der Juden, vom Abschluss des Talmuds (500) bis zum Aufblühen der Jüdisch-Spanischen Kultur (1027) / H. Graetz.06. Geschichte der Juden, vom Aufblühen der Jüdisch-Spanischen Kultur (1027) bis Maimunis Tod / H. Graetz.09. Geschichte der Juden, von der Verbannung der Juden aus Spanien und Portugal (1494) bis zur dauernden Ansiedelung der Marranen in Holland (1618) / H. Graetz.10. Geschichte der Juden, von der dauernden Ansiedelung der Marranen in Holland (1618) bis zum Beginne der Mendelssohnschen Zeit (1750) / H. Graetz.11. Geschichte der Juden, vom Beginn der Mendelssohnschen Zeit (1750) bis in die Neueste Zeit (1848) / H. Graetz.7-8. Geschichte der Juden, von Maimunis Tod (1205) bis zur Verbannung der Juden aus Spanien und Portugal / H. Graetz
Transports couplés en géométries complexes
No full textCes travaux s'intéressent aux questions de transports non stationnaires et de transferts stationnaires de chaleur et de masse par convection-diffusion au sein de géométries complexes. Par complexe, nous entendons d'une part pour le transport que le fluide est convecté au sein d'une cavité de section quelconque lentement variable dans la direction longitudinale, c'est à dire ayant des variations longitudinales grandes devant hauteur et largeur moyennes. Nous considérons d'autre part le transfert au sein de domaines non-axisymétriques dans lesquels sont plongés un ou plusieurs tubes où le fluide porteur s'écoule. Pour ce qui concerne le transfert, ce travail a consisté à montrer comment étendre le principe, valider l'utilisation, et illustrer l'efficacité d'une décomposition en mode de Graetz pour la prédiction des échanges dans des configurations réalistes d'échangeurs. Cette décomposition permet de formuler le problème initial 3D comme un problème aux valeurs propres généralisées en 2D dont la résolution numérique est drastiquement moins coûteuse. Nous généralisons la notion de mode de Graetz à des conditions aux limites latérales quelconques et, en particulier pour le cas d'échangeurs équilibrés où nous avons mis en évidence un nouveau mode linéairement variables dans la direction longitudinale. Nous mettons en oeuvre le calcul de ces modes de Graetz dans le cas de configurations semi-infinies pour traiter, par exemple, des configurations transversalement périodiques (types plancher chauffant) et montrons qu'un faible nombre de modes suffit pour donner une très bonne approximation des transferts. Dans le cas d'échangeurs finis couplé avec des tubes en entrée/sortie, nous montrons comment déterminer les amplitudes des modes de Graetz dans les différents domaines par la minimisation d'une fonctionnelle associée aux conditions d'entrée sorties retenues. Ces modes permettent l'étude paramétrique systématique des champs de température, des flux de chaleurs entre les domaines fluides et solides ainsi que des rendements thermiques d'un échangeur à deux tubes. Nos résultats indiquent que la longueur d'échange caractéristique est gouvernée par le premier mode de Graetz généralisé à grand nombre de Péclet. Nous montrons aussi, en particulier, qu'un échangeur symétrique possède un spectre symétrique, et une évolution amont/aval symétrique. Dans le cas de la dispersion de Taylor, nous avons établi une forme conservative 3D des équations de dispersion de Taylor en géométrie variable généralisant le cas 2D déjà connu. Nous avons ensuite implémenté en éléments finis puis validé numériquement ces équations de dispersion en 2D et 3D. Nous montrons que les variations longitudinales 3D de la cavité peuvent considérablement augmenter la dispersion longitudinale.This work interest is about stationary transfer and non-stationary transport by convection-diffusion onto complex geometries. For transport issues, complex refers to convection into flattened cavity of arbitrary transverse shape, slowly varying along the longitudinal direction. In the context of transfer, complex refers to non-axisymmetric domains of arbitrary transverse shape along which one or several parallel tubes convect heat or mass. For the transfer problem, this work extends the principle, validates the use, and illustrates the efficiency of Graetz modes decompositions for exchanges prediction in realistic exchangers configurations. This decomposition permits to formulate the initial 3D problem as a generalysed 2D eigenvalue problem, the numerical evaluation of which is drastically reduced. We generalyze Graetz modes solutions for arbitrary applied lateral boundary conditions. In the particular case of balanced exchangers, we bring to the fore a new neutral mode whose longitudinal variations are linear as opposed to classical Graetz modes displaying exponential decay. The numerical computation of those modes for semi-infinite configurations with lateral periodic boundary conditions shows that a few number of those provides a very good approximation for exchanges. In the case of finite exchangers coupled with inlet/oulet tubes, we show how to evaluate the amplitudes of Graetz modes in the various domains (inlet, exchanger, outlet) from functional minimization associated with input/output boundary conditions. The evaluation of these amplitudes permit a systematic parametric study of temperature fields, heat fluxes between fluid and solid, and hot/cold performance of a couple-tube exchanger. Our results indicate that the typical exchange length is governed by the first Graetz mode at large P\'eclet number. We also show that a symmetric exchanger has a symmetric spectrum and a upward/backward symmetric evolution. In the case transport we elaborate theoretically the conservative form of 3D Taylor dispersion equations into variable cavities which generalyzes the framework already known in 2D. We numerically implement these averaged dispersion equations with finite element, and validate in 2D the obtained results. We show that 3D longitudinal variations of a cavity has a strong impact on the longitudinal dispersion
Graetz (Michael) L'Alliance israélite universelle et l'héritage de la Révolution française
No full textGraetz (Michael) L'Alliance israélite universelle et l'héritage de la Révolution française. In: Archives de sciences sociales des religions, n°68/2, 1989. p. 184
Graetz (Michael) L'Alliance israélite universelle et l'héritage de la Révolution française
No full textGraetz (Michael) L'Alliance israélite universelle et l'héritage de la Révolution française. In: Archives de sciences sociales des religions, n°68/2, 1989. p. 184
Determining child mental health
No full textThe definitive version is available at www.blackwell-synergy.comFocuses on the approach that should be used to identify children and adolescents with mental health problems. Dimensional approach in which data is collected using self-report measure; Categorical approach employed in DSM-IVMichael Sawyer, Brian Graetz and Peter Baghurs
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