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The Quarterly Journal of Mechanics and Applied Mathematics 1979 32(2):175-185; doi:10.1093/qjmam/32.2.175
© 1979 by Oxford University Press
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ON SOLIDIFICATION PROBLEMS INCLUDING THE DENSITY JUMP AT THE MOVING BOUNDARY

L. N. TAO

( Illinois Institute of Technology Chicago, Illinois, U.S.A. )

The solidification problem of a semi-infinite medium, including the induced motion caused by the density change of the phase transition, subject to arbitrary initial and boundary conditions is investigated. It is shown that by an appropriate transformation of the space and time variables and the material constants, the solidification problem can be converted to a problem with both phases having equal densities. Hence it is reduced to a classical free-boundary problem. This reduced problem is designated as the associated problem. The associated problems with arbitrarily prescribed initial and boundary conditions are considered and solved; exact solutions are established. It is found that the solution of the interfacial position is of the order of t½ as t -> 0 when the initial temperature at the interface is discontinuous, and is of an order other than t½ when the initial temperature at the interface is continuous.


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