Abstract
Explicit solutions of similarity-type are obtained for a model conduction heat transfer with phase change into a semi-infinite slab, where the thermal conductivities and specific heats of both phases are a linear function of the temperature. The lower and upper bounds for the solutions of this model are also obtained.
•Phase change problems in a semi-infinite slab is considered.•Explicit solutions of similarity-type are obtained.•The lower and upper bounds for the solutions are also obtained.•The existence and uniqueness of the solution is proved.