Stefan problem for a heat-generating cylindrical sample with boundary conditions of the third kind: calculation of melting time

Abstract

We determine the kinetic patterns of melting in a heat-generating cylindrical element under invariable supercritical conditions using numerical modelling. The study focuses on the melting process in a homogeneous sample that generates heat either through a chemical reaction or electromagnetic heating. The thermophysical properties of the sample were assumed to be constant in both solid and liquid phases. The main tool used in the study was a numerical model based on the nonstationary Stefan problem in a heat-generating body, which incorporates the descriptions of heat conduction and melting processes. The phase transition was described in terms of enthalpy. In order to select the parameters of the numerical model (grid steps), the accuracy of the difference scheme was investigated. The study presents calculated dependencies of the main melting characteristics (melting time and the maximum sample temperature at melting) on control parameters (heat generation intensity, the heat effect of melting and the ratio of thermal conductivity coefficients of the phases). By using specified approximations (temperature averaging and quasi-stationary distribution), formulas were derived to estimate the melting time of the sample. The calculations showed that the variations in the thermal properties of the sample (thermal conductivity coefficients and heat effect) significantly influence the melting rate. It was demonstrated that although the relationship between the melting time and the intensity of heat generation and the thermal effect of the phase transition is consistent with the approximate models, there is a significant quantitative difference between them, in particular, for small deviations from the critical heat generation intensity. The calculations can be used to assess the thermomechanical stability of materials with internal heat generation. The developed numerical model allows melting processes to be investigated under a wide range of conditions, including varying boundary conditions.