• Goals of modelling, types of models. Physical and mathematical modelling.
• Fundamentals of theory of similarity. Physical equation, conditions of unambiguity. Constant of similarity, similarity indicator, invariant. Derivation of the criteria equation by the method of analysis of the fundamental physical equation.
• Principle of dimensional analysis, application on practical problems.
• Physical modelling. Using analogies.
• Implementation of thermo-physical properties dependencies in numerical models. Regression analysis, interpolation. Practical tasks.
• Boundary conditions. Using criteria equations to define surface conditions.
• Modelling of heating and cooling of a heat-slim body with recrystallization. Implementation of the model in Matlab and Excel.
• Modelling of heat conduction in thick bodies. Fourier heat conduction equation, Laplace operator discretization. Finite volume methods and finite element methods.
• Numerical substitution of derivations in the Fourier heat conduction equation. Explicit, implicit and mixed solving methods.
• Method of elementary balance for stationary and non-stationary task in Cartesian and polar coordinates. Applications for specific tasks.
• Condition of stability of explicit method for internal and external element, fictive temperature. Choice of mesh density. Accuracy of numerical solution.
• Phase change modelling. Practical task of steel solidification modelling.
• Modelling of heat conduction with mass transfer. Model of continuous casting mould.
• Combined temperature model with electric current and Joule's heat.
• Modelling heat transfer by radiation. View factors. Radiative heat transfer between several surfaces in diathermic environment.
• Modelling of heat transfer in furnace workspace.
• Modelling of the continuous casting process, methods for determining unambiguous conditions in the casting machine. Determination of surface conditions in the crystallizer, in secondary and tertiary zones. Simulation of influence of parameters on heat removal and solid shell formation.
• Fundamentals of theory of similarity. Physical equation, conditions of unambiguity. Constant of similarity, similarity indicator, invariant. Derivation of the criteria equation by the method of analysis of the fundamental physical equation.
• Principle of dimensional analysis, application on practical problems.
• Physical modelling. Using analogies.
• Implementation of thermo-physical properties dependencies in numerical models. Regression analysis, interpolation. Practical tasks.
• Boundary conditions. Using criteria equations to define surface conditions.
• Modelling of heating and cooling of a heat-slim body with recrystallization. Implementation of the model in Matlab and Excel.
• Modelling of heat conduction in thick bodies. Fourier heat conduction equation, Laplace operator discretization. Finite volume methods and finite element methods.
• Numerical substitution of derivations in the Fourier heat conduction equation. Explicit, implicit and mixed solving methods.
• Method of elementary balance for stationary and non-stationary task in Cartesian and polar coordinates. Applications for specific tasks.
• Condition of stability of explicit method for internal and external element, fictive temperature. Choice of mesh density. Accuracy of numerical solution.
• Phase change modelling. Practical task of steel solidification modelling.
• Modelling of heat conduction with mass transfer. Model of continuous casting mould.
• Combined temperature model with electric current and Joule's heat.
• Modelling heat transfer by radiation. View factors. Radiative heat transfer between several surfaces in diathermic environment.
• Modelling of heat transfer in furnace workspace.
• Modelling of the continuous casting process, methods for determining unambiguous conditions in the casting machine. Determination of surface conditions in the crystallizer, in secondary and tertiary zones. Simulation of influence of parameters on heat removal and solid shell formation.