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Download PDF by Collectif: Dictionnaire des Idées d'Encyclopaedia Universalis

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ISBN-10: 2852299348

ISBN-13: 9782852299344

Premiere ouvrage en son style, le Dictionnaire des Idées répertorie et explique l’ensemble des idées qui permettent de comprendre le monde d’hier et d’aujourd’hui. Et ce dans tous les domaines du savoir : politique, économie, philosophie, faith, mais aussi arts, littérature, musique, body ou chimie, astronomie, mathématique, etc.
Qu’il s’agisse de courants et mouvements marquants, de pensées novatrices, d’écoles, d’académies, de filiations, d’idéologies, de traditions, de révolutions, de partis, de croyances…, le Dictionnaire des Idées présente et commente four hundred idées fondamentales : Anarchisme, Cartésianisme, Chiisme, Constructivisme, Dérive des continents, École de Vienne, Encyclopédisme, Figuralisme, Hindouisme, Hippocratisme, Keynésianisme, Kitsch, Lacanisme, Réalisme socialiste, Shinto, Subaltern reports, Surréalisme…

Bienvenue dans le Dictionnaire des Idées d’Encyclopædia Universalis.
Vous pouvez consulter les articles du Dictionnaire des Idées à partir de l. a. desk des matières.
Pour une recherche précise concernant un sujet, vous pouvez vous appuyer sur l'Index.
Vous pouvez bien sûr lire le Dictionnaire des Idées de A à Z, d'Abstraction. arts à Zen, religion.
Parfait complément du Dictionnaire des Idées : le Dictionnaire des Notions.

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110), one notices that a physically plausible solution occurs for both þk2 and Àk2 . In order to investigate this problem further, we analyse in more detail the solutions for the function Gð~yÞ. From Eq. 110) we get G001 ð~yÞ þ k2 G1 ð~yÞ ¼ 0 for þk2 ð2:111Þ G002 ð~yÞ À k2 G2 ð~yÞ ¼ 0 for Àk2 ð2:112Þ which gives rise to the following two possible solutions G1 ð~yÞ ¼ C3 cosðk~yÞ þ C4 sinðk~yÞ ð2:113Þ G2 ð~yÞ ¼ C3 coshðk~yÞ þ C4 sinhðk~yÞ ð2:114Þ If we now reconsider the problem to be solved (Eqs.

3 Separation of Variables 39 where the pressure gradient in the axial direction is constant for a hydrodynamically fully developed flow. The boundary conditions are the no slip conditions at all boundaries of the channel. Thus wðb=2; yÞ ¼ 0; wðx; c=2Þ ¼ 0; wðÀb=2; yÞ ¼ 0 wðx; Àc=2Þ ¼ 0 ð2:130Þ  ¼ À1=l @p=@z, it can be seen If we introduce into Eq. 129) the abbreviation K that the problem for determining the fully developed velocity profile is identical to the heat conduction problem in a plate containing a heat sink with constant sink intensity (the derivation of the fully developed velocity field in a rectangular channel is given for example in Spurk (1987)).

110). 36 2 Linear Partial Differential Equations For the function Fð~xÞ, one obtains from Eq. 110) F 00 ð~xÞ À k2 Fð~xÞ ¼ 0 ð2:115Þ Fð~xÞ ¼ C5 coshðk~xÞ þ C6 sinhðk~xÞ ð2:116Þ which has the solution Combining the solutions for F and G leads to the following expression for Hh Hh ¼ ðC3 cosðk~yÞ þ C4 sinðk~yÞÞðC5 coshðk~xÞ þ C6 sinhðk~xÞÞ ð2:117Þ This expression has to satisfy the boundary conditions given by Eq. 107) À Á À Á   1 À ~y2 ; Hh ðÀA; ~yÞ ¼ ÀK=2 1 À ~y2 Hh ðA; ~yÞ ¼ ÀK=2 Hh ð~x; À1Þ ¼ 0 Hh ð~x; 1Þ ¼ 0; ð2:107Þ Applying the two boundary conditions for fixed values of ~y, the following two equations are obtained C3 cosðkÞ þ C4 sinðkÞ ¼ 0 ð2:118Þ C3 cosðkðÀ1ÞÞ þ C4 sinðkðÀ1ÞÞ ¼ 0 Because cosðkÞ ¼ cosðÀkÞ and sinðkÞ ¼ À sinðÀkÞ, one obtains from the above equations that C4 = 0 and that C3 cosðkÞ ¼ 0 ð2:119Þ From this equation it follows that k¼ 2n À 1 p; 2 n ¼ 1; 2; 3; .

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