Mathematical model of steel blanks cooling process

The mathematical model of steel blanks cooling process is given in work. A basis of mathematical model is the heat conductivity equation of Biot-Fourier in one-dimensional statement which is solved by a pro-race method under boundary conditions of the first and third kind. Direct and inverse problems of heat conductivity are solved. It is shown that the solution of blank cooling problem when using completely implicit scheme, in comparison with the obvious scheme and the scheme Crank-Nicholson, is the most preferable, both on accuracy, and on time. The mathematical model is verified by comparison of calculated values of temperatures and heat transfer coefficients with the experimental. On the example of blank from steel 40H at one and two cooling surfaces of temperatures on which the assessment of phase transitions in material is possible are defined.