Numerical modeling of the single-phase Stefan problem in a layer with transparent and semitransparent boundaries

Numerical modeling of the single-phase Stefan problem in a semitransparent layer with transparent, nonabsorbing, and partially radiation-absorbing boundaries is performed. It is shown that at low temperatures of the medium, convection is a determining factor on the boundary of the irradiated sample, and at high temperatures, radiation is predominant. The absence of absorption on the boundaries of the layer leads to acceleration of the heating of the plate and considerable deceleration of melting processes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 84–91, May–June, 2006.     

Effect of radiation scattering on the melting and solidification of a flat layer of a translucent medium

The paper considers the effect of isotropic and anisotropic scattering of radiation on the melting (solidification) of a flat layer of a semitransparent medium between opaque surfaces. The mathematical model of the phase transition is the classical formulation of the Stefan problem. From results of numerical calculations it follows that radiation scattering has a significant effect on the rate of propagation of the phase transition front and formation of a temperature profile during melting (solidification) of a semitransparent medium.     

Single-phase Stefan problem in selectively absorbing medium

The thermal state of a translucent selectively absorbing medium was studied by the methods of numerical simulation at different values of the optical properties of boundaries and heat transfer from the left surface in approximation of one-phase Stefan problem. The temperature fields and densities of resultant radiation fluxes as well as the thermal state of the left boundary and dynamics of layer reduction in the melting process were analyzed. The processes of phase transition in a flat layer of selective and gray absorbing media and emitting media were compared, and their fundamental differences were shown.     

Modeling of ice heating and melting in approximation of the Stefan problem considering radiation

The problem of radiation-conductive heating and subsequent melting of ice in a climatic chamber in a single-phase approximation of the Stefan problem was posed and solved by mathematical modeling methods taking into account a thin water film formed on the irradiated surface. The fields of temperature and density of the resulting radiation flux are obtained, as well as the rate of melting and heating of the non-irradiated ice surface. Comparison of results with experimental data showed satisfactory agreement.     

NUMERICAL STUDY OF THE THERMAL STATE OF AN ICE LAYER CONTAINING AIR BUBBLES

Journal of Applied Mechanics and Technical Physics - The melting of an ice layer with air bubbles on exposure to an artificial thermal radiation source is studied by mathematical modeling within...