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The Quarterly Journal of Mechanics and Applied Mathematics 1970 23(2):225-246; doi:10.1093/qjmam/23.2.225
© 1970 by Oxford University Press
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STARTING SOLUTIONS FOR MELTING OF A SLAB UNDER PLANE OR AXISYMMETRIC HOT SPOTS

HARVEY P. YAGODA and BRUNO A. BOLEY

( Stevens Institute of Technology Hoboken, New Jersey
College of Engineering, Cornell University Ithaca, New York )

A short-time closed-form solution is developed for two-dimensional heat conduction problems with change of phase for a half-space. The heat is applied in such a manner that melting starts at a point of the surface, and then spreads simultaneously both towards the interior of the body and along its surface. Concerning the surface variation, only the plane and radially-symmetric cases are considered in detail, while a generalization to arbitrary variations is briefly discussed.

The solution is obtained by the embedding technique, and shows that the shape of the interface is, when suitably normalized, a universal function, i.e. it is independent of the applied heat input and of the material properties. Initial melt propagation in directions normal to and along the surface are respectively proportional to (t–tm)1/2 and (t–tm)1/2, where tm is the time of start of melting.


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