Onset of Buoyancy-driven Instability in Porous Media Melted from Below |
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Authors: | Joung Sook Hong Min Chan Kim Chang Kyun Choi |
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Affiliation: | (1) ARC Center, Korea University, Seoul, 136-701, Korea;(2) Department of Chemical Engineering, Cheju National University, Cheju, 690-756, Korea;(3) School of Chemical and Biological Engineering, Seoul National University, Seoul, 151-744, Korea |
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Abstract: | When a nonhomogeneous solid is melting from below, convection may be induced in a thermally–unstable melt layer. In this study, the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance equations. The critical Darcy–Rayleigh numbers based on the melt-layer thickness, Ra H,c, are found numerically for various conditions. For small superheats, the present predictions show that Ra H,c is located between 27.1 and 4π 2 and it approaches the well-known results of the original Horton–Rogers–Lapwood problem. However, for high superheats, it is dependent on the phase change rate λ and the relation of Ra H,c λ = 25.89 is shown. |
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Keywords: | Buoyancy-driven convection Melting Porous medium Stefan problem Similarity transform |
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