Related papers: An Inverse Stefan Problem Relevant to Boilover: He…
We present an approach to theoretical assessment of the mean specific interface area $(\delta{S}/\delta{V})$ for a well-stirred system of two immiscible liquids experiencing interfacial boiling. The assessment is based on the balance of…
We develop a mathematical model for a three-phase free boundary problem in one dimension that involves the interactions between gas, water and ice. The dynamics are driven by melting of the ice layer, while the pressurized gas also…
An accurate and comprehensive numerical solution to the parabolic free boundary problem arising from thin film flow with both velocity and temperature distribution at large Reynolds numbers is obtained using a modified Keller box method. A…
We investigate the heat transport in a nonequilibrium spin-boson model, where a two level system bridging two harmonic reservoirs at different temperatures, by employing a unitary transformation along with a resolvent operator expansion…
We consider local solutions of the two-phase Stefan problem with a "mushy" region. We show that if a (distributional) solution u is locally square integrable then the temperature is continuous.
We consider the inverse Stefan type free boundary problem, where information on the boundary heat flux and density of the sources are missing and must be found along with the temperature and the free boundary. We pursue optimal control…
In this paper, the energy non-conservation problem of the hybrid thermal LB phase change model is emphasized. To solve this problem, an infinite volume discrete scheme is introduced to deal with the diffusion term in the energy equation.…
We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation…
In a recent letter [1], Zaitsev et al. report observations of evaporating water micro-droplets over a heated solid substrate and suggest a model for the mechanisms of both droplet levitation and inter-droplet interaction. According to their…
By expanding the Dirac delta function in terms of the eigenfunctions of the corresponding Sturm-Liouville problem, we construct some new (oscillating) integral transforms. These transforms are then used to solve various finance, physics,…
Here classes of moving boundary problems of Stefan-type for both an established non-linear evolution equation of cuspon theory and novel reciprocally linked solitonic equations are shown to be solvable via Painleve' II symmetry reduction.
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…
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…
We generalize time-evolving matrix product operators method to nonequilibrium quantum transport problems. The nonequilibrium current is obtained via numerical differentiation of the generating functional which is represented as a tensor…
In this paper, an inverse initial-boundary value problem for the heat equation in three dimensions is studied. Assume that a three-dimensional heat conductive body contains several cavities of strictly convex. In the outside boundary of…
We develop an enthalpy-based modeling and computational framework to quantify uncertainty in Stefan problems with an injection boundary. Inspired by airfoil icing studies, we consider a system featuring an injection boundary inducing domain…
We consider approximations of the Stefan-type condition by imbalances of volume closely around the inner interface and study convergence of the solutions of the corresponding semilinear stochastic moving boundary problems. After a…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…
Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…