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Lecturer(s)
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Pecha Jiří, doc. Ing. Ph.D.
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Janáčová Dagmar, prof. Ing. CSc.
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Kolomazník Karel, prof. Ing. DrSc.
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Course content
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Energy balance, approximate balance. Mathematical modeling of diffusion processes. Modeling of extraction processes - extraction of unbound and bound components - model with distributed parameters - dynamic model of bath extraction. Heat and mass sharing: Drying - process modeling. Heat balance of a flow mixer - general procedure - model, linearization, dimensional conversion and image transfer. Control valve model. Liquid reservoir model Concentration liquid mixer model. Modeling of fermentation processes, application of automatic control.
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Learning activities and teaching methods
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Individual work of students
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| prerequisite |
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| Knowledge |
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| Knowledge from areas: Mathematics I, II Physics Processes in Building Technique Process Engineering |
| Knowledge from areas: Mathematics I, II Physics Processes in Building Technique Process Engineering |
| Knowledge from areas: Mathematics I, II Physics Thermal processes Fluid mechanics, |
| Knowledge from areas: Mathematics I, II Physics Thermal processes Fluid mechanics, |
| Skills |
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| Independent solution of numerical problems from Mathematics I, II Physics Thermal processes Fluid Mechanics |
| Independent solution of numerical problems from Mathematics I, II Physics Thermal processes Fluid Mechanics |
| learning outcomes |
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| Knowledge |
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| Knowledge of methods of mathematical modeling of technological processes concerning mass and energy balances Energy balance, approximate balance Heat and mass sharing: Drying - process modeling, Drying - enthalpy and mass balance of a convective dryer Control valve model General procedure - model, linearization, conversion to dimensionless form and image transfer Modeling of washing processes - washing of unbound and bound components The model with distributed parameters - the dynamic model of spa washing Modeling of fermentation processes, application of automatic control |
| Knowledge of methods of mathematical modeling of technological processes concerning mass and energy balances Energy balance, approximate balance Heat and mass sharing: Drying - process modeling, Drying - enthalpy and mass balance of a convective dryer Control valve model General procedure - model, linearization, conversion to dimensionless form and image transfer Modeling of washing processes - washing of unbound and bound components The model with distributed parameters - the dynamic model of spa washing Modeling of fermentation processes, application of automatic control |
| The student has knowledge about mathematic modelling on the base of mass and energy, is able successfully to solve suggested models. Is well informed in needed literature and uses needed thermodynamic data and realize so calculations for optimization and automatic control of technological processes. |
| The student has knowledge about mathematic modelling on the base of mass and energy, is able successfully to solve suggested models. Is well informed in needed literature and uses needed thermodynamic data and realize so calculations for optimization and automatic control of technological processes. |
| Skills |
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| orientation in the necessary literature design and solve a mathematical model of the discussed tasks the ability to linearize the model and determine the visual transmission of the event to control it the ability to find the necessary data the ability to solve optimization problems |
| orientation in the necessary literature design and solve a mathematical model of the discussed tasks the ability to linearize the model and determine the visual transmission of the event to control it the ability to find the necessary data the ability to solve optimization problems |
| Based on theoretical knowledge, perform the necessary calculations for the purpose of optimization and automatic control of technological processes and practical skills, - the ability to find the necessary data important for calculations. |
| Based on theoretical knowledge, perform the necessary calculations for the purpose of optimization and automatic control of technological processes and practical skills, - the ability to find the necessary data important for calculations. |
| teaching methods |
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| Knowledge |
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| Individual work of students |
| Individual work of students |
| assessment methods |
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| Analysis of the student's performance |
| Analysis of the student's performance |
| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
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Recommended literature
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CORRIOU J., P. Process Control, Theory and Applications. London, Springer, 2010. ISBN 978-1-84996.
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Crank, J. Mathematic of Diffusion, Oxford University. London, 1956.
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Ingham, J., Dunn, I.J., Heinzle, E., Prenosil, I.E. Chemical Engineering Dynamics. An Introduction to Modelling and Computer Simulation. Germany, 2000. ISBN 978-3-527-31678-6.
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INGHAM, J., DUNN, I.,J., HEINZLE, E., PRENOSIL J. Chemical Engineering Dynamics: Modelling with PC Simulation. Wiley-VCH, 2000. ISBN 3-527-29776-6.
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VíTEČEK, A., CEDRO, L., FARANA, R., VÍTEČKOVÁ, M. The fundamentals of mathematical modelling. Politechnika Swietokrzyska. Kielce, 2018. ISBN 978-8365719-35-5.
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