Application of «Stefan Conditions» for Solving Heat Tasks in Objects of the Forest Complex

Abstract

A two-phase formulation of the problems of "thermal shock" is considered when two homogeneous half-spaces come into contact at an initial instant of time with different phases and temperatures different from the phase transition temperature. In the absence of convection and thermal sources for constant thermophysical parameters, which can be formulated as the problem of conjugation of two temperature fields on the moving solidification front with additional boundary conditions (Stefan conditions). From a practical point of view, this kind of problem can be the arrival of processes occurring in the objects of the forest complex: in the production of particle board, the processing of ponds and reservoirs, the freezing (thawing) of soils, etc. The solution was carried out using the Laplace integral transformation. The exact analytical dependence obtained in this way explicitly determines the law of interference in each phase. These functions are used for integral transformations. The resulting temperature field corresponds to the known Gaussian distribution, and the velocity of the interphase boundary movement is inversely proportional to the square root of the crystallization time. The data of the approximate numerical calculation carried out for the water-ice system corresponds to a freezing (thawing) rate of approximately 10-3 mm / s. The obtained results can be used for research work in the field of construction thermal physics, geophysics and metallurgy.