Abstract. Heat conduction is considered in a semi-infinite solid subjected to a high step change in surface heat flux, such that melting occurs. A time-dependent relaxation model for the energy flux is assumed, leading to a non-Fourier, non-linear equation for the thermal field, which is solved under suitable conditions on the interface displacement.1. Introduction. Criticism to the Fourier model for heat conduction, which leads to a physically unacceptable infinite speed of propagation of the energy transfer, was put forward, in the past, by several authors. Such a criticism, initially based on purely speculative grounds, follows from a variety of approaches to the problem, from the first consideration in a work by Cattaneo [1], where a model for the heat conduction process was substantiated-in the case of gaseous media-by means of the kinetic theory, to the statistical mechanics of nonequilibrium irreversible processes [2].1In any case, when the Fourier law is rebuted, a time-dependent relaxation model is proposed for the heat flux and the thermal field, which, in the Fourier case, is governed by a parabolic equation, obeys to a hyperbolic wave equation.The temperature distribution evaluated by the latter model more significantly differs from the Fourier model predictions as the involved fluxes of heat and their time variations increase. Recent technological developments have drawn increasing attention to non-Fourier heat transfer models as situations where their effects can start playing a significant role

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