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Transport in Porous Media - 相似文献
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Transport in Porous Media - The Horton–Rogers–Lapwood problem with strong heterogeneity and anisotropy is examined for a simple case, namely where the heterogeneity is provided by two... 相似文献
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Donald A. Nield 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1966,17(2):226-232
Résumé L'équation différentielle obtenue en appliquant la théorie des perturbations au problème de la convection cellulaire a déjà été résolue par rapport aux valeurs propres définissant le début de l'instabilité. Dans ce travail on cherche les fonctions propres correspondant à diverses combinaisons des forces de poussée et de tension superficielle et différentes conditions thermiques à la surface libre. On discute la relation entre la disposition des lignes de courant et le degré d'interdépendance des deux agents d'instabilité. On a tracé les lignes de courant dans le cas où la convection résulte de la tension superficielle seule sur une surface libre isolée thermiquement. Ces lignes sont peu différentes de celles qu'on trouve dans les mêmes conditions lorsque la convection est due à la poussée seule. Ceci explique le haut degré d'interdépendance entre les deux phénomènes, lorsque la surface supérieure est isolée thermiquement. 相似文献
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The effects of hydrodynamic and thermal heterogeneity, for the case of variation in both the horizontal and vertical directions,
on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, with weak vertical
throughflow, are studied analytically for the case of weak heterogeneity. It is found that when the boundary conditions at
the upper and lower boundaries are symmetric, the throughflow magnitude and the permeability and conductivity gradients enter
the expression for the critical Rayleigh number at second order. The throughflow on its own is stabilizing but the combination
of throughflow and heterogeneity may be either stabilizing or destabilizing. 相似文献
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This short note is a response to the comment on our recently published paper cited in the title. All points raised by the
author of the comment are discussed. It is shown that one of the remarks, concerning eigenflow solutions in the limiting case
of forced convection, does not have a sound physical basis. In fact, it refers to a circumstance, a fluid with a thermal expansion
coefficient greater than that of a perfect gas, of marginal or no interest in the framework of convection in porous media. 相似文献
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A linear instability analysis has been performed for the onset of convection in a horizontal layer of a porous medium whose permeability pulsates with time as a result of vertical movement of one of the boundaries. It was found that, to a first-order approximation in the pulsation amplitude, the effect of deformation is destabilizing for disturbances whose period is of the order of the thermal diffusion time scale. The effects of the average porosity, pulsation amplitude, and pulsation frequency were investigated. 相似文献
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The problem for determining the critical Rayleigh number for the onset of convection in a horizontal porous layer with vertical
throughflow is re-examined with the aim of obtaining analytical formulas applicable in the cases of weak and strong throughflow.
For the case of strong throughflow an asymptotic analysis is performed. 相似文献
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An analytic solution is obtained for forced convection flow in a parallel-plates channel or a circular duct occupied by a
hyper-porous medium saturated with a rarefied gas in the slip-flow regime, for the case of uniform flux boundary conditions.
As expected, it is found that velocity slip leads in general to increased heat transfer and temperature slip leads to reduced
heat transfer. 相似文献