1. Objectives of modelling, types of models. Physical and mathematical modelling.
2. Basic theory of similarity. Complete physical equation, boundary conditions. Constant of similarity indicator of similarity criterion. Derivation of criteria equation using the analysis of the basic equations method.
3. The principle of dimensional analysis, application to practical problems.
4. Modelling of heat conduction. Heat conduction equation, Laplace operator for Cartesian, cylindrical and spherical coordinates.
5. Temperature profile and heat flow in the cylindrical wall. The critical radius of the cylindrical wall, the critical radius of the cylindrical wall insulation. Temperature profile and heat flux in spherical wall.
6. Temperature profile in the cylindrical wall with an internal volume heat source, an electric wire.
7. Heat conduction in rods (ribs) of finite and infinite length.
8. Modelling of heat radiation. View factors. Radiating heat exchange between several surfaces in diathermic environment.
9. Numerical models. Principle of finite difference and finite element methods. Numerical substitution of derivatives in the Fourier’s heat equation. Comparison of explicit, implicit and mixed networks.
10. The method of elementary balances for steady and unsteady problem in Cartesian and polar coordinates.
11. Stability condition for explicit methods of internal and external element, fictitious temperature. Accuracy of the numerical solution.
12. Modelling of phase change in temperature numerical models.
13. Modelling of continuous casting, methods of determining the boundary conditions. Influence of different parameters on heat transfer in the mould and in the secondary and tertiary zones of cooling.
2. Basic theory of similarity. Complete physical equation, boundary conditions. Constant of similarity indicator of similarity criterion. Derivation of criteria equation using the analysis of the basic equations method.
3. The principle of dimensional analysis, application to practical problems.
4. Modelling of heat conduction. Heat conduction equation, Laplace operator for Cartesian, cylindrical and spherical coordinates.
5. Temperature profile and heat flow in the cylindrical wall. The critical radius of the cylindrical wall, the critical radius of the cylindrical wall insulation. Temperature profile and heat flux in spherical wall.
6. Temperature profile in the cylindrical wall with an internal volume heat source, an electric wire.
7. Heat conduction in rods (ribs) of finite and infinite length.
8. Modelling of heat radiation. View factors. Radiating heat exchange between several surfaces in diathermic environment.
9. Numerical models. Principle of finite difference and finite element methods. Numerical substitution of derivatives in the Fourier’s heat equation. Comparison of explicit, implicit and mixed networks.
10. The method of elementary balances for steady and unsteady problem in Cartesian and polar coordinates.
11. Stability condition for explicit methods of internal and external element, fictitious temperature. Accuracy of the numerical solution.
12. Modelling of phase change in temperature numerical models.
13. Modelling of continuous casting, methods of determining the boundary conditions. Influence of different parameters on heat transfer in the mould and in the secondary and tertiary zones of cooling.