Related papers: Two-phase Stefan problem for generalized heat equa…
In this paper we study the distribution of the temperature within a body where the heat is transported only by radiation. Specifically, we consider the situation where both emission-absorption and scattering processes take place. We study…
Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order $ \al \in (0,1) $ is taken in the Caputo's sense. The first one has a constant condition on $ x = 0 $ and the second presents a…
We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a…
We study a space-fractional Stefan problem with the Dirichlet boundary conditions. It is a model that describes superdiffusive phenomena. Our main result is the existence of the unique classical solution to this problem. In the proof we…
We consider an interacting particle system with two species under strong competition dynamics between the two species. Then, through the hydrodynamic limit procedure for the microscopic model, we derive a one-phase Stefan type free boundary…
Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and…
In this article we study a fully relativistic model of a two dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects…
In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish…
The current study is a pioneering work in presenting the boundary layer equations for the two-dimensional flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of partial differential equations is turned…
The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed,…
In this paper we address the temperature patch problem of the 2D viscous Boussinesq system without heat diffusion term. The temperature satisfies the transport equation and the initial data of temperature is given in the form of…
A bio-heat transfer model for biological tissues in a micro-scale and periodical settings is investigated . It is assumed that the model is a two-component system consisting of solid particles representing tissue cells and interconnected…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
In Stochastic Thermodynamics, heat is a random variable with a probability distribution associated. Studies of the distribution of heat are mostly in the overdamped regime and in one dimension. Here we solve the heat distribution in the…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a surface cluster whose distributional solution was studied by…
Modeling phase change problems numerically is vital for understanding many natural (e.g., ice formation, steam generation) and engineering processes (e.g., casting, welding, additive manufacturing). Almost all phase change materials (PCMs)…
Schauder's fixed point theorem is used to derive the existence of solutions to a semilinear heat equation. The equation features a nonlinear term that depends on the time-integral of the unknown on the whole, a priori given, interval of…
In this paper we present a mathematical analysis of thin film flow and heat transfer to a laminar liquid film from a horizontal stretching sheet. The flow of thin liquid film and subsequent heat transfer from the stretching surface is…