Simulation of the Thermal State of the Infinite Body with Dinamically Changing Boundary Conditions of the Third Kind

The paper contains a mathematical model to describe the thermal object of cooling in the aggregates of zone type. Imposed by the assumptions for the mathematical model allowed to perform an abstracting of a real object to a simplifed form in the shape as an infinite rectangular parallelepiped with a dynamically variable boundary conditions of the third kind. Distinctive features of the model is to describe the speed components of the movement of a fixed cross-section at a given time and the function that sets the value of the coefficient of heat transfer from the surface of the body in the form of time series with a variable structure. Presents the functional diagram of the developed software for computer simulation based on the constructed mathematical models to research the behavior of the temperature field of the body. It was revealed that the change in speed components associated with the choice of modes of cooling leads to temperature fluctuations in the layers of the body, lying at a depth of not more than 1 cm from the surface. The proposed mathematical model can be used in automated systems control of production continuously cast billets in adjusting the control in the local circuit rate of withdrawal for a given quality of the production.

Keywords

heat state of the infinite body, boundary conditions of the third kind, time series with a variable structure, dynamically changing boundary conditions.

References

1. Shestakov A.L., Sviridyuk G.A. A New Approach to Measuring Dynamically Distorted Signals. Vestnik Yuzhno-Ural'skogo gosudarstvennogo universiteta. Seriya "Matematicheskoe modelirovanie i programmirovanie" - Bulletin of South Ural State University. Seria 'Mathematical Modelling, Programming & Computer Software', 2010, no. 16(192), issue 5, pp. 116-120. (in Russian)
2. Belousov M.D., Shestakov A.L. Method of Self Resistance Thermometer in the Process of Operation Vestnik Yuzhno-Ural'skogo gosudarstvennogo universiteta. Seriya "Matematicheskoe modelirovanie i programmirovanie" - Bulletin of South Ural State University. Seria "Computer technology, management, electronics", 2009, no. 3, pp. 17-19. (in Russian)
3. Shestakov A.L., Sviridyuk G.A., Zakharova E.V. Dynamic Measurements as an Optimal Control. Obozrenie prikladnoy i promyshlennoy matematiki - Review of Industrial and Applied Mathematics, 2009, vol. 16, no. 4, pp. 732-733. (in Russian)
4. Logunova O.S., Devyatov D.H., Yachikov I.M. Mathematical Modeling of the Macroscopic Parameters of Continuous Ingot Solidification. News of higher educational institutions. Ferrous metallurgy, 1997, no. 1, pp. 49. (in Russian)
5. Logunova O.S. The Study of Quality Dependencies Formation of Internal Defects and Thermal State of the Billet. Steel, 2008, no. 10, pp. 60-63. (in Russian)
6. Takhautdinov R.S., Bodean J.A., Sarychev A.F., Gorostkin S.V., Filippova V.P., Nosov S.V. Improvement of Crack Formation of Secondary Cooling Mode Low-alloy Steel. Papers of the VIII Congress of Steelmakers, Moscow, 2005, pp. 452-456. (in Russian)