| Course Unit Code | 635-3040/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| PYS30 | prof. Dr. Ing. René Pyszko |
| MAC589 | Ing. Mario Machů, Ph.D. |
| Summary |
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| The course focuses on theoretical and practical approaches to modelling of heat transport. Attention is paid to the application of the theory of similarity, the use of dimensional analysis for the description of physical phenomena, the numerical modelling of heat conduction in Cartesian and cylindrical coordinates using the method of elementary balances, respectively, finite volume methods, boundary conditions determination, heat conduction with phase change modelling, heat exchange by radiation between multiple surfaces in a diathermic environment. Knowledge is applied to the modelling of heat transfer in furnaces and in the continuous casting process, including the determination of boundary conditions. |
| Learning Outcomes of the Course Unit |
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Student will be able to:
- apply the theory of similarity in modelling,
- use dimensional analysis to describe physical processes, assemble a criteria equation,
- determine the boundary conditions of thermal problems,
- apply the stationary and non-stationary method of elementary balances, respectively, of the finite volumes to solve problems of heat conduction, convection, and radiation,
- determine the conditions of stability of an explicit method,
- solve numerical problems of heat conduction with phase change,
- solve problems of heat exchange by radiation between several surfaces,
- analyze and algorithmize heat transfer in furnaces and continuous casting machines and determine boundary conditions.
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| Course Contents |
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• 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.
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| Recommended or Required Reading |
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| Required Reading: |
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[1] LIENHARD IV, J. H., LIENHARD V, J. H. A Heat Transfer Textbook. 4th ed. Cambridge: Phlogiston Press, 2012. http://web.mit.edu/lienhard/www/ahtt.html
[2] BEJAN, A., KRAUS, A. D. Heat Transfer Handbook. John Wiley & Sons, 2003. ISBN 978-0-471-39015-2.
[3] TAN, L. Digital signal processing: fundamentals and applications. Burlington: Elsevier/Academic Press, 2008. ISBN 978-0-12-374090-8.
[4] TALER, J., DUDA, P. Solving Direct and Inverse Heat Conduction Problems. Berlin: Springer, 2006. ISBN 978-3-540-33470-5. |
[1] STAŠA, P. Modelování a simulace. Ostrava: Vysoká škola báňská - Technická univerzita Ostrava, 2014. ISBN 978-80-248-3657-7.
[2] KUNEŠ, J. Modelování tepelných procesů. 1. vyd. Praha: SNTL, 1989. ISBN 80-03-00134-X.
[3] RÉDR, M., PŘÍHODA, M. Základy tepelné techniky. 1. vyd. Praha: SNTL, 1991. ISBN 80-03-00366-0.
[4] VDI Heat Atlas, Springer-Verlag, Berlin, Heidelberg (2010).
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| Recommended Reading: |
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[1] SERTH, R. W. Process heat transfer: principles and applications, Elsevier Academic Press (2007).
[2] KREITH., F., BLACK, W. Z. Basic heat transfer. New York: Harper and Row, 1980.
[3] VASEGHI, S. V. Advanced digital signal processing and noise reduction. 3rd ed. Chichester: Wiley, 2006. ISBN 0-470-09494-X. |
[1] KOZEL, K., FÜRST, J. Numerické metody řešení problémů proudění. Praha: Vydavatelství ČVUT, 2001.
[2] DOLEJŠÍ, Z. a kol. Plynulé odlévání oceli. Díl 1., Tepelně technické poměry při plynulém odlévání oceli. 2. vyd. Praha: Technickoekonomický výzkumný ústav hutního průmyslu, 1989.
[3] ENENKL, V., HLOUŠEK, J., JANOTKOVÁ, E. Termomechanika. 10. vyd. Brno: VUT, 1983.
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Experimental work in labs |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 | 20 |
| Examination | Examination | 70 | 31 |