This paper presents approaches to the computational analysis of solidification and cooling processes of continuously cast billets in order to improve and develop technological modes in the conditions of modern continuous casting machines using FEM. The application of modern numerical methods for solidification and cooling of workpieces on continuous casting machines is considered. The use of the finite element method is justified when using computational and experimental data for the development and improvement of casting technology.

The technological, economic, and energy indices of high-technology modern metallurgical plants are analyzed.

The status of power engineering in the world and the main tendencies of its development are analyzed, the problems of energy saving in industrial complex of the Republic of Belarus, particularly in machine-building and metallurgical complex, are examined.

The results of mathematical modeling of the heat exchange processes in the furnaces with mechanized bottom (of mills 850, 320, 150 furnaces) of Belorussian metallurgical works are given in the present articles.

The carried out calculations showed that partial modernization of thermal furnaces of machine building production by means of replacement of chamotte by fibrous fettling is economically reasonable and has rather short period of payback.

Modern approaches at designing and building of metallurgical lines of factories of last generation are considered.

More that 30ty – years experience of the authors in the field of complex investigations of heating processing of metal in methodical pusher furnaces, carried out in conditions of major metallurgical enterprises of CIS, is summarized.

A physicomathematical model and a procedure of calculation of the basic indices of axial chemical inhomogeneity in continuously-cast steel billets have been developed. The influence of the processes of convective transfer in the two-phase zone of the alloy on the occurrence and development of axial chemical inhomogeneity has been shown.

The heating of cylindrical billet in annular furnaces in shaft and pipe rolling is investigated. The laws of billet heating and rough-shaft heat treatment are established, as a function of the state of the furnace hearth, the increment of billet supply, and the adjustment of the gas lines to regulate the heating process and ensure uniform heating. Improved conditions for billet heating and heat treatment and the cooling of rolled shafts have been introduced at the 250 shaft-rolling mill at Dneprovsk Metallurgical Works.

Based on the mathematical model, the analytical solution of the problem of formation of dendritic liquation for different configurations of a dendritic cell has been obtained; the use of this solution makes it possible to optimize melting processes from the viewpoint of the chemical inhomogeneity of ingots and billets.

The durability of support rollers of continuous slab-casting machines has been evaluated by determining the long-time ductility of steel as a function of the dimension of nonmetallic oxide-type inclusions contained in the metal.

An algorithm for selection of an energy efficient refractory lining has been developed on the basis of a ratio of summed-up capital expenditure and operating costs. A non-linear problem of thermal conductivity in a layer of the fiber refractory lining has been numerically solved in the paper. The paper determines an actuality of the fiber refractory lining application at the temperature level of 55–75 °C (on the average65 °C) on its external surface. A mathematical solution of a refractory layer selection has been executed in the paper. The paper gives several variants of the arrangement of three-layer fiber refractory lining.

A mathematical model has been developed and an algorithm of calculation of heat-and mass-transfer processes in heating and melting of metal scrap in an electric-arc steel-making furnace has been created. The results of numerical modeling of the dynamics of melting of metal scrap in this furnace have been given.