Convective Instability in a Melt Layer Heated From Below

[+] Author and Article Information
E. M. Sparrow, L. Lee, N. Shamsundar

Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minn.

J. Heat Transfer 98(1), 88-94 (Feb 01, 1976) (7 pages) doi:10.1115/1.3450475 History: Received August 15, 1975; Online August 11, 2010


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.

Copyright © 1976 by ASME
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In