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We complete the Solomon-Wilson-Alexiades's mushy zone model (Letters Heat Mass Transfer, 9 (1982), 319-324) for the one-phase Lam\'e-Clapeyron-Stefan problem. We obtain explicit solutions when a convective or heat flux boundary condition is…

Analysis of PDEs · Mathematics 2015-03-11 Domingo Alberto Tarzia

One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face…

Analysis of PDEs · Mathematics 2019-08-29 Julieta Bollati , María Fernanda Natale , José Abel Semitiel , Domingo Alberto Tarzia

The one-dimensional (1D) Stefan problem is a prototypical heat and mass transfer problem that analyzes the temperature distribution in a material undergoing phase change. In addition, it describes the evolution of the phase change front…

Fluid Dynamics · Physics 2026-02-10 Mehran Soleimani , Kimmo Koponen , Nils Tilton , Amneet Pal Singh Bhalla

In this paper a one-phase Stefan problem with size-dependent thermal conductivity is analysed. Approximate solutions to the problem are found via perturbation and numerical methods, and compared to the Neumann solution for the equivalent…

Other Condensed Matter · Physics 2019-01-04 Francesc Font

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…

Analysis of PDEs · Mathematics 2020-02-24 Chifaa Ghanmi , Saloua Mani-Aouadi , Faouzi Triki

The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their…

Analysis of PDEs · Mathematics 2020-07-22 Julieta Bollati , Domingo A. Tarzia

A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered. An integral relationship between the temperature and the free boundary is obtained which is equivalent to the…

Analysis of PDEs · Mathematics 2018-10-25 Sabrina Roscani , Domingo Tarzia

We study the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in $\mathbb{R}^N$. In terms of the enthalpy $h(x,t)$, the evolution equation reads $\partial_t…

Analysis of PDEs · Mathematics 2022-08-22 Félix del Teso , Jørgen Endal , Juan Luis Vázquez

Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the…

Materials Science · Physics 2026-02-11 Yavkreet Swami , Jacob Barajas , Amneet Pal Singh Bhalla

A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first…

Analysis of PDEs · Mathematics 2014-03-26 Sabrina Roscani , Eduardo Santillan Marcus

Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys:2020}, we consider a phase-change problem for a one dimensional material with a non-local flux, expressed in terms of the Caputo derivative, which derives in a…

Analysis of PDEs · Mathematics 2021-11-15 Sabrina Roscani , Katarzyna Ryszewska , Lucas Venturato

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)…

Numerical Analysis · Mathematics 2025-05-20 Francky Luddens , Corentin Lothodé , Ionut Danaila

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…

Materials Science · Physics 2012-08-27 G. L. Buchbinder , V. A. Volkov

We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…

Analysis of PDEs · Mathematics 2024-10-07 Adriana C. Briozzo

We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational formulation of self-similar solutions, which allows to find…

Analysis of PDEs · Mathematics 2023-08-15 Evgeny Yu. Panov

In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values…

Computational Physics · Physics 2019-04-12 Timothy G. Myers , Matthew G. Hennessy , Marc Calvo-Schwarzwälder

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 finite velocities until the contact. Under these assumptions, we construct a smooth…

Mathematical Physics · Physics 2007-05-23 V. G. Danilov

The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed…

Analysis of PDEs · Mathematics 2016-07-05 Mahir Hadzic , Gustavo Navarro , Steve Shkoller

We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem…

Analysis of PDEs · Mathematics 2015-09-15 Domingo Alberto Tarzia

The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…

Analysis of PDEs · Mathematics 2013-10-22 Mahir Hadžić , Steve Shkoller