The non-local in space two-phase Stefan problem (a prototype phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits unique weak solution. This formulation makes to part of the General Filtration Problems; class includes Porous Medium Equation. In this work, we prove that solutions both and Media problems are continuous.

We reduce the two phase Stefan problem with kinetic to a system of nonlinear Volterra integral equations of second kind and apply Newton's method to linearize it. We found product integration solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

in this present study, volume of fluid method in openfoam open source cfd package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. this model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. both phases (liqu...

Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...

One proves that the moving interface of a two-phase Stefan problem on Ω⊂Rd, d=1,2,3, is controllable at end time T by Neumann boundary controller u. The phase-transition region mushy {σtu;0≤t≤T} modified and main result amounts to saying that, for each Lebesgue measurable set Ω∗ with positive measure, there u∈L2((0,T)×∂Ω) such Ω∗⊂σTu. To this aim, one uses an optimal control approach combined C...