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Solution analytique tridimensionnelle en convection naturelle stationnaire

Grundmann, Miloslav and Mojtabi, Abdelkader Solution analytique tridimensionnelle en convection naturelle stationnaire. (1998) Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy, 326 (7). 423-428. ISSN 1287-4620

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Official URL: https://doi.org/10.1016/S1287-4620(98)80011-2


An analytical study of free convection in a cubic cavity of fluid-saturated porous material is reported. The analytical algorithm integrates the Darcy-Boussinesq equations formulated in terms of pressure and temperature. The dependent variables (P, T) are expressed using an asymptotic development in the parameter ξ = (Ra - Rac)1/2/π where Rac = 4 π2 denotes the value of the critical Rayleigh number, in a cubic cavity (Rac1 = 4 π2 for the 2D flow and Rac2 = 4.5 π2 for 3D flow). Terms up to order 48 for the 2D flow and up to order 16 for the 3D flow are computed. The analytical value of the Nusselt number is in good agreement with a numerical one obtained using a Legendre spectral collocation method.

Item Type:Article
HAL Id:hal-01891921
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:08 Oct 2018 11:40

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