2013 1(12)

THE SINGLE-PHASE STEFAN PROBLEM IN A SEMITRANSPARENT MEDIUM IN THE MODIFIED CLASSICAL SOLUTION. THE PROBLEM STATEMENT AND ANALYZE.

Sleptsov S.D., Rubtsov N.A.

Institute of Thermophysics SB RAS, Novosibirsk, Russia

The single-phase Stefan problem is a particular case of the two-phase Stefan problem, where the temperature of one phase equals identically to the constant temperature of phase transition [1]. It is evident that in the framework of the similar classical solution the Stefan condition at the interface includes the zero heat flux from the phase with a constant temperature. Actually, there is heat energy transfer on either side of the interface, and the physical models of the single-phase Stefan problem do not meet the stated conditions. Here we can note the most typical works [2, 3], where heating and melting of uniform semitransparent plates due to one-sided external radiant-convective (conductive) heat supply are modeled numerically.

Developing ideas suggested in [3], the current work offers approximate consideration of the single-phase Stefan problem with the use of restrictions for the classical solution to this problem.

Using approximations of classical solutions to Stefan problem, which at the considered conditions is based on the assumption that heat energy flux formed at liquid phase evaporation in the ambient medium is balanced by the resultant radiation flux supplied from outside from the source of radiation, turns out to be efficient in a wide range of values ε₂ and physically justifiable. The physical explanation of solid phase superheating and respective instability of Stefan problem solution is apparently bound with the conditions of forced conjugation of non-equilibrium liquid phase with phase transformation front determined under equilibrium conditions. The effectiveness of classical solution approximation is determined by possible inversion of heat energy fluxes both by thermal conductivity (at ε₂ ≥0,3), and resultant radiation (at ε₂≥0,5) in liquid phase at the conditions of the considered problem.

Artificial maintaining of the equilibrium state of ambient medium adjacent to liquid phase at null value of energy flow accelerates melting process by an order, compared with the option of present non-equilibrium caused by supply of heat energy flux, and turns out to be comparable on time with the processes of solid phase melting having an absolutely black boundary of phase transition.

Thus, regardless of heat transfer conditions at the external plate boundary undergoing phase transition, it is possible to perform simulation of heat processes as applied to the development of both effective heat shield and perfect technology of melting (evaporation) of the layers of semitransparent materials. 

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