Geodesic
Simulation of the Thermal State of the Infinite Body with Dinamically Changing Boundary Conditions of the Third Kind
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 13 (2012), pp. 74-85
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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. 
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     title = {Simulation of the {Thermal} {State} of the {Infinite} {Body} with {Dinamically} {Changing} {Boundary} {Conditions} of the {Third} {Kind}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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O. S. Logunova; I. I. Matsko; D. S. Safonov. Simulation of the Thermal State of the Infinite Body with Dinamically Changing Boundary Conditions of the Third Kind. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 13 (2012), pp. 74-85. http://geodesic.mathdoc.fr/item/VYURU_2012_13_a7/

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