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• W2102025969 abstract "We consider free convection driven by a heated vertical plate immersed in a nonlinearly stratified medium. The plate supplies a uniform horizontal heat flux to a fluid, the bulk of which has a stable stratification, characterized by a non-uniform vertical temperature gradient. This gradient is assumed to have a typical length scale of variation, denoted Z 0 , while Ψ 0 is the order of magnitude of the related heat flux that crosses the medium vertically. We derive an analytic solution to the Boussinesq equations that extends the classical solution of Prandtl to the case of nonlinearly stratified media. This novel solution is asymptotically valid in the regime Ra S ≫ 1, where Ra S denotes the Rayleigh number of nonlinear stratification, based on Z 0 , Ψ 0 , and the physical properties of the medium. We then apply the new theory to the natural convection affecting the vapour phase in a liquefied pure gas tank (e.g. the cryogenic storage of hydrogen). It is assumed that the cylindrical storage tank is subject to a constant uniform heat flux on its lateral and top walls. We are interested in the vapour motion above a residual layer of liquid in equilibrium with the vapour. High-precision axisymmetric numerical computations show that the flow remains steady for a large range of parameters, and that a bulk stratification characterized by a quadratic temperature profile is undoubtedly present. The application of the theory permits a comparison of the numerical and analytic results, showing that the theory satisfactorily predicts the primary dynamical and thermal properties of the storage tank." @default.
• W2102025969 created "2016-06-24" @default.
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• W2102025969 date "2007-09-24" @default.
• W2102025969 modified "2023-09-27" @default.
• W2102025969 title "Natural convection along a heated vertical plate immersed in a nonlinearly stratified medium: application to liquefied gas storage" @default.
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• W2102025969 doi "https://doi.org/10.1017/s0022112007007458" @default.
• W2102025969 hasPublicationYear "2007" @default.
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