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In this paper, a one-phase Stefan-type problem for a semi-infinite materialwhich has as its main feature a variable latent heat that depends on the powerof the position and the velocity of the moving boundary is studied. Exactsolutions of similarity type are obtained for the cases when Neumann or Robinboundary conditions are imposed at the fixed face. Required relationshipsbetween data are presented in order that these problems become equivalent tothe problem where a Dirichlet condition at the fixed face is considered.Moreover, in the case where a Robin condition is prescribed, the limitbehaviour is studied when the heat transfer coefficient at the fixed face goesto infinity.

mathematical problems in engineering

One-phase Stefan-like problems with a latent heat depending on the  position and velocity of the free boundary, and with Neumann or Robin  boundary conditions at the fixed face