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

TL;DR

This paper investigates a one-phase Stefan problem with a position- and velocity-dependent latent heat, providing exact similarity solutions under Neumann or Robin boundary conditions and analyzing boundary condition limits.

Contribution

It introduces a novel Stefan problem with variable latent heat depending on position and velocity, deriving exact solutions and boundary condition relationships.

Findings

Exact similarity solutions for Neumann and Robin conditions

Relationships between data for equivalence with Dirichlet problem

Limit behavior analysis as heat transfer coefficient approaches infinity

Abstract

In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions of similarity type are obtained for the cases when Neumann or Robin boundary conditions are imposed at the fixed face. Required relationships between data are presented in order that these problems become equivalent to the problem where a Dirichlet condition at the fixed face is considered. Moreover, in the case where a Robin condition is prescribed, the limit behaviour is studied when the heat transfer coefficient at the fixed face goes to infinity.