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Heat Transfer Research
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ISSN Druckformat: 1064-2285
ISSN Online: 2162-6561

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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2018019154
pages 773-786

ON THE ONSET OF NATURAL CONVECTION IN A PARTIALLY COOLED CYLINDER

Jose Nuñez
Escuela Nacional de Estudios Superiores, Unidad Morelia, Universidad Nacional Autónoma de México, Antigua Carretera a Pátzcuaro No. 8701, Col. Ex Hacienda de San José de la Huerta, 58190, Morelia, Michoacán, México
Alberto Beltrán
Instituto de Investigaciones en Materiales, Unidad Morelia, Universidad Nacional Autónoma de México, Antigua Carretera a Pátzcuaro No. 8701, Col. Ex Hacienda de San José de la Huerta, C.P. 58190, Morelia, Michoacán, México

ABSTRAKT

Recent experimental configurations like the liquid metal electrode for the development of a liquid metal battery and the inverted Bridgman configuration for growing crystals involve natural convection of fluids confined in vertical cylinders heated from below and partially cooled from above. A cylindrical cavity subjected to such conditions is studied from a numerical point of view, assuming the Rayleigh number, the noncooled size, and the aspect ratio (height/diameter) parameters over ranges 103 ≤ Ra ≤ 105, 0 ≤ γ ≤ 0.875, and 0.5 ≤ α ≤ 1.25, respectively, for all cases with Pr = 6.67 being assumed. The governing equations for natural convection are discretized employing a mixed Fourier–Finite volume method using the SIMPLEC algorithm as velocity decoupling strategy. Steady flow transitions from axisymmetric to nonaxisymmetric were obtained; interestingly, the average Nusselt number shows a monotonic de-creasing behavior as a function of while an increasing behavior as function of Ra is observed. In particular, symmetry breaking instability as a function of critical parameters of the convective flow is determined by a numerical stability analysis. Finally, a stability map for Ra vs. γ is constructed for α = 1.0.


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