Kiselyov Alexandr Sergeyevich

    My work purpose is the development of the model of ingots nonsteady thernal field, which is warmed in the rate of impact heating.

   A three-dimensional differential equation of thermal conductivity is assumed as the models basis. Its soluction is realized by the method of variable direction:

   The approximation of thermal conductivitys differential equation has such an appearance:

    where Т -temperatures; , с, , а - therma-physical properties; - is the time step; x, y, z - coordinate pitch; к - is a number of time step, which is divided into three parts.

   The solution is carried out under boundary condition of the third sort. The heating mediums temperature is defermined from the equation of thermal balance over a period, which is equal to the time step. The ingot in the three-dimensional organization arrangement|position represents a parallele-piped with four side and one upper heat-transfer area.

    The surfaces variable temperature throughout the ingots height and variable temperature of the medium for every heat exchanges surface are taken into account in the model. The metals thermophysical properties are taken depending on the temperature on each time and coordinate step.

    The worked out model forms a part of the systems mathematical supplying of heating rates automatic regulation of the pit-type furnace with one upper impulse heating's burner.