A New Similarity Method for Analysis of Multi-Dimensional Solidification

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Abstract
There are many multi-dimensional phase change problems which are of interest in applications but cannot be solved by even the powerful computational techniques that are available today. A new similarity rule is presented in this paper to make the solution of such problems possible. The similarity rule applies to problems in which sensible heat contributions are much smaller than latent heat contributions, and the heat flux distribution on the surface of the phase change substance is more or less uniform. After a derivation of the similarity rule is given, it is verified by application to some problems arising in latent heat storage for which finite-difference computations have been performed previously. The similarity rule is easy to apply, and greatly reduces the effort needed in analysing phase change problems. In conjunction with the energy conservation principle, the similarity rule provides an efficient tool for analysing the time-response of a phase change system to arbitrarily varying heat loads, as is demonstrated by examples.

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