A Criterion of Onset of Free Convection in a Horizontal Melted Water Layer With Free Surface

[+] Author and Article Information
N. Seki, S. Fukusako, M. Sugawara

Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan

J. Heat Transfer 99(1), 92-98 (Feb 01, 1977) (7 pages) doi:10.1115/1.3450661 History: Received March 03, 1976; Online August 11, 2010


The problem considered in this paper is the determination of the Rayleigh number marking the onset of free convection in a horizontal melted layer of ice heated from above under uniform radiant heat flux. In this analysis, linear perturbation techniques are used to derive a sixth-order differential equation subject to hydrodynamic and thermal boundary conditions. The series-solution method is utilized to obtain an eigenvalue equation for the case where the lower surface (ice surface) is kept at 0°C and the upper free surface is subjected to the general thermal conditions. An experimental determination of the onset of free convection, when the heat transfer mode changes from conduction to convection, is obtained from the fact that the temperature distribution in a melted water layer starts to deviate from its linear profile. At the same time, a peculiar variational inflection of the water-surface temperature occurs. From the present investigation, it can be demonstrated both analytically and experimentally that the critical Rayleigh number Ra c in a horizontal melted water layer with a density inversion is dependent on the free water-surface temperature T2 for T2 < 8°C, while Ra c for T2 ≧ 8°C is independent of T2 .

Copyright © 1977 by ASME
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