Abstract
A method based on coordinate transformation which transforms the time-varying domain into an invariant one, is given for solving multi-dimensional solidification/melting problems. The present method differs from its predecessors in that it transforms one space variable only while others remain unchanged. This results in tremendous amounts of saving in computations in comparison to methods proposed by earlier authors. Two sample problems are treated by the method in two dimensions one concerned with solidification of the square prism and the other with melting in a rectangular prism. The numerical results obtained by the present method are found to be in good agreement with those due to earlier authors. The method is further extended to three dimensions through a problem of cuboid solidification. Obtained in the present paper are perhaps the only available results for the complete solidification of the cuboid.
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