Consideration is given to the onset of convective motions in a horizontal melt layer created by solid-to-liquid phase change. The melt layer is heated at its lower bounding surface either due to convective transfer from an adjacent fluid medium or to a step change in wall temperature. 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.
Skip Nav Destination
Article navigation
Research Papers
Convective Instability in a Melt Layer Heated From Below
E. M. Sparrow,
E. M. Sparrow
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.
Search for other works by this author on:
L. Lee,
L. Lee
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.
Search for other works by this author on:
N. Shamsundar
N. Shamsundar
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.
Search for other works by this author on:
E. M. Sparrow
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.
L. Lee
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.
N. Shamsundar
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.
J. Heat Transfer. Feb 1976, 98(1): 88-94 (7 pages)
Published Online: February 1, 1976
Article history
Received:
August 15, 1975
Online:
August 11, 2010
Article
Article discussed|
View article
Connected Content
Citation
Sparrow, E. M., Lee, L., and Shamsundar, N. (February 1, 1976). "Convective Instability in a Melt Layer Heated From Below." ASME. J. Heat Transfer. February 1976; 98(1): 88–94. https://doi.org/10.1115/1.3450475
Download citation file:
Get Email Alerts
Cited By
Entropic Analysis of the Maximum Output Power of Thermoradiative Cells
J. Heat Mass Transfer
Molecular Dynamics Simulations in Nanoscale Heat Transfer: A Mini Review
J. Heat Mass Transfer
Related Articles
Laminar Natural Convection of Power-Law Fluids in a Square Enclosure With Differentially Heated Sidewalls Subjected to Constant Wall Heat Flux
J. Heat Transfer (December,2012)
Numerical and Experimental Investigation of Phase Change Heat Transfer in the Presence of Rayleigh–Benard Convection
J. Heat Transfer (June,2020)
Analysis of Solid–Liquid Phase Change Under Pulsed Heating
J. Heat Transfer (March,2007)
Related Proceedings Papers
Related Chapters
Radiation
Thermal Management of Microelectronic Equipment
Energy Balance for a Swimming Pool
Electromagnetic Waves and Heat Transfer: Sensitivites to Governing Variables in Everyday Life
Completing the Picture
Air Engines: The History, Science, and Reality of the Perfect Engine