The model of metal speed convection heating for using in algorithms of the control system

A technological process of metal processing in space machinery contains such mandatory operation as the preparation of the raw material, its heating, rolling and finishing. Heating metal before rolling increases its ductility and improves physical and mechanical properties. Increased requirements apply to processing of titanium and aluminum alloys to temperature conditions of the initial, intermediate heating, annealing and artificial aging. Strict compliance with these requirements provides metal resistant to high and low temperatures, vibration loads and effects of radiation. One of the important ways to improve the process of heating metal mode is to introduce modern process control system of furnaces, which in turn requires energy-efficient and provides the specified requirements for the heating control algorithms. To correctly predict such algorithms it is necessary to use mathematical models of processes. The purpose of our work is to create a model for using in algorithms of process control system, which enables you to control speed convective heating of metal ingots. For testing and determination of the boundaries of the application of calculations on the model developed in ordinary differential equations were compared by us with the calculations for a reference model based on unsteady heat conduction equation. In this work materials with high heat and low thermal conductivity were examined. We use analytical and numerical methods for solving ordinary differential equations; analytical and finite difference solution of the third boundary value problem for the heat equation. A simplified model of heating materials in the furnace high-speed convection heating, built on ordinary differential equations and allowing at work as part of process control system to calculate speed and the heating mode, to assess of uniformity of heating of ingots to provide these data to the operator or to automatic decision to change the power input, or change the time heating, is offered.