An analytical and numerical study of coupled transient natural convection and solidification in a rectangular enclosure

Michael Vynnycky, Shigeo Kimura

Research output: Contribution to journalArticlepeer-review

Abstract

The transient process of the solidification of a pure liquid phase-change material in the presence of natural convection in a rectangular enclosure is considered both analytically and numerically. One vertical boundary is held at a temperature below the melting-point of the material, the other above; the horizontal boundaries are both assumed adiabatic. A nondimensional analysis of the problem, principally in terms of the Rayleigh (Ra) and Stefan (St) numbers, indicates that some asymptotic simplification is possible for materials often considered in the literature (water, gallium, lauric acid). This observation suggests a way to simplify the full problem when Ra ≫ 1 and St ≪ 1, giving a conventional boundary value problem for the liquid phase and pointwise-in-space first-order ODEs for the evolution in time of the solidification front. The method is tested against full 2D finite-element-based transient numerical simulations of solidification. In addition, simpler approaches for determining the average thickness of the solid layer, based on boundary-layer and enclosure flow correlations, are also investigated.

Original languageEnglish
Pages (from-to)5204-5214
Number of pages11
JournalInternational Journal of Heat and Mass Transfer
Volume50
Issue number25-26
DOIs
Publication statusPublished - Dec 2007
Externally publishedYes

Keywords

  • Asymptotics
  • Finite-element methods
  • Natural convection
  • Solidification

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