TY - JOUR

T1 - CONVECTIVE INSTABILITY IN A MELT LAYER HEATED FROM BELOW.

AU - Sparrow, E. M.

AU - Lee, L.

AU - Shamsundar, N.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1976

Y1 - 1976

N2 - This paper is concerned with the conditions marking the onset of convective motions in a horizontal, liquid melt layer. The melt layer is created when a solid, initially at its saturation temperature, is heated from below. The analysis is carried out for liquid melts whose densities decrease with increasing temperature. Linear stability theory is employed to determine the conditions marking the onset of motion. The results of the analysis are expressed in terms of two Rayleigh numbers. One of these, the internal Rayleigh number, is based on the instantaneous thickness and instantaneous temperature difference across the layer. The other, the external Rayleigh number, is more convenient to use in applications problems since it contains quantities which are constant and a priori prescribable. For a melting problem where the external Rayleigh number is large, instability occurs soon after the start of heating. At smaller external Rayleigh numbers, the duration time of the regime of no motion increases markedly. At large times, the stability results for convective heating coincide with those for stepped wall temperature. In addition to the results for the stability problem, results for conduction phase change (in the absence of motion) are also presented for the surface convection boundary condition.

AB - This paper is concerned with the conditions marking the onset of convective motions in a horizontal, liquid melt layer. The melt layer is created when a solid, initially at its saturation temperature, is heated from below. The analysis is carried out for liquid melts whose densities decrease with increasing temperature. Linear stability theory is employed to determine the conditions marking the onset of motion. The results of the analysis are expressed in terms of two Rayleigh numbers. One of these, the internal Rayleigh number, is based on the instantaneous thickness and instantaneous temperature difference across the layer. The other, the external Rayleigh number, is more convenient to use in applications problems since it contains quantities which are constant and a priori prescribable. For a melting problem where the external Rayleigh number is large, instability occurs soon after the start of heating. At smaller external Rayleigh numbers, the duration time of the regime of no motion increases markedly. At large times, the stability results for convective heating coincide with those for stepped wall temperature. In addition to the results for the stability problem, results for conduction phase change (in the absence of motion) are also presented for the surface convection boundary condition.

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M3 - Article

AN - SCOPUS:0016882072

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 76 -HT-BB

ER -