Related papers: Two-phase Stefan problem for generalized heat equa…
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…
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…
The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell--Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases…
In this paper we elaborate a hybrid classical-quantum framework which allows one to model and solve heat and mass transfer problems occurring in electric contacts. We utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum…
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…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry…
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step…
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…
A general theory of photon-mediated energy and momentum transfer in N-body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in…
We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium…
We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently…
A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…
The classical Stefan problem is reduced as the singular limit of phase-field equations. These equations are for temperature $u$ and the phase-field $\varphi$, consists of a heat equation: $$ u_t+\ell\varphi_t=\Delta u, $$ and a…
This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a…
The technique of periodic homogenization with two-scale convergence is applied to the analysis of a two-phase Stefan-type problem that arises in the study of a periodic array of melting ice bars. For this "reduced model" we prove results on…
We investigate the steady state of heat conduction in general relativity using a variational approach for two-fluid dynamics. We adopt coordinates based on the Landau-Lifschitz observer because it allows us to describe thermodynamics with…