Related papers: An Inverse Stefan Problem Relevant to Boilover: He…
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…
In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…
A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity…
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a…
In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem,…
We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay,…
The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann…
From the one-dimensional consolidation of fine-grained soils with threshold gradient, it can be derived a special type of Stefan problems where the seepage front, due to the presence of this threshold gradient, exhibits the features of a…
In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power $P_0$ on fixed face $z=0$ and…
We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions, we…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…
The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
In this paper, we represent the exact solution of a two phase inverse spherical Stefan problem, where along with unknown temperature functions heat flux function has to be determined. Suggested solution is obtained from new form of integral…
This paper develops an input-to-state stability (ISS) analysis of the Stefan problem with respect to an unknown heat loss. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a…
This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…
Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM)…