Related papers: The one-dimensional Stefan problem with non-Fourie…
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…
In this article we consider two different heat conducting fluids each modelled by the incompressible Navier-Stokes-Fourier system separated by a non-linear elastic Koiter shell. The motion of the shell changes the domain of definition of…
A brief review of the Stefan problem of solidification from a mixture, and its main numerical solution methods is given. Simulation of this problem in 2D or 3D is most practically done on a regular grid, where a sharp solid-liquid interface…
This article is concerned with the shape of small devices used to control the heat flowing between a solid and a fluid phase, usually called \textsl{fin}. The temperature along a fin in stationary regime is modeled by a one-dimensional…
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)…
We study heat conduction in a system of hard disks confined to a narrow two dimensional channel. The system is initially in a high density solid-like phase. We study, through nonequilibrium molecular dynamics simulations, the dependence of…
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal,…
We study heat conduction in one dimensional lattice dynamical systems far from equilibrium. The Fermi-Pasta-Ulam model and the $\phi^4$ model are numerically compared to elucidate differences between momentum-conserving and nonconserving…
We use nonequilibrium molecular dynamics (NEMD) to explore the effect of shear flow on heat flux. By simulating a simple fluid in a channel bounded by tethered atoms, the heat flux is computed for two systems: a temperature driven one with…
In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…
It is difficult to derive the solid--fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for…
Although ubiquitous in nature and industrial processes, transport processes at the interface during evaporation and condensation are still poorly understood. Experiments have shown temperature discontinuities at the interface during…
We investigate directed thermal heat flux across 1D homogenous nonlinear lattices when no net thermal bias is present on average. A nonlinear lattice of Fermi-Pasta-Ulam-type or Lennard-Jones-type system is connected at both ends to thermal…
We study the non-equilibrium dynamics of a symmetry restoring phase transition in a scalar field theory, the ``system'', linearly coupled to another scalar field taken as a ``heat bath''. The ``system'' is initially in an ordered low…
Thermal transport in solids changes its nature from phonon propagation that suffers from perturbative scattering to thermally activated hops between localized vibrational modes as the level of disorder increases. Models have been proposed…
Results of direct numerical simulations (DNS) of porous-wall turbulent flows in open channels with conjugate heat transfer are reported in this work. For the conductive porous walls considered here, the change in heat transfer is not…
The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the…
We consider a situation where an $N$-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general…
We study the transport of heat in a three dimensional harmonic crystal of slab geometry whose boundaries and the intermediate surfaces are connected to stochastic, white noise heat baths at different temperatures. Heat baths at the…
A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of three basic state variables: the {\it absolute temperature} $\teta$, the {\it velocity field} $\ub$, and the {\it director…