MATHEMATICAL MODEL  OF CYLINDRICAL BLANK COOLING  BY ONE-DIMENSIONAL NON-STATIONARY WATER STREAM

The paper represents the mathematical model of cooling a cylindrical solid metal blank made of construction steel by the non-stationary water stream. Parametric study of cooling process is carried out. The basis of mathematical model is a system of differential equations such as: equation of continuity, equation of momentum, equation of energy for water steam and heat equation for blank. The model neglects the possibility of vaporization. The water steam is single-phase medium. The equation of two-dimensional non-stationary task of thermal conductivity is solved by double-sweep method. Boundary conditions are those of the third kind. In terms of blank of 30HGSA steel we have determined: reduced heat-transfer coefficient during the time of cooling process, reduced velocity, reduced pressure and temperature of water stream throughout of cooled blank surface. The article shows the evaluation possibility of phase change in the metal according to cooling rate over the entire blank volume. The mathematical model of cooling process and results obtained can be applied for solving engineering and metallurgic problems.