# Ingegneria Alimentare - Food Engineering | MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

## Ingegneria Alimentare - Food Engineering MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

cod. 0622800009

#### MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

0622800009 | |

DIPARTIMENTO DI INGEGNERIA INDUSTRIALE | |

EQF7 | |

FOOD ENGINEERING | |

2018/2019 |

OBBLIGATORIO | |

YEAR OF COURSE 2 | |

YEAR OF DIDACTIC SYSTEM 2016 | |

PRIMO SEMESTRE |

SSD | CFU | HOURS | ACTIVITY | |
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ING-IND/26 | 6 | 60 | LESSONS |

Objectives | |
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Knowledge and understanding: The course aims to provide the basic knowledge, methods and software instruments in order to: 1) discriminate the complexity of the systems of process engineering and meet the possibilities of abstract representation; 2) classify the models, particularly the ones related to processes; 3) numerically solve the parabolic partial differential equations; 4) understand the main issues of engineering optimization and know Linear Programming (LP) methods; 5) handle the Matlab® software to develop or obtain some classes of models, and to solve LP problems. Applying knowledge and understanding – engineering analysis Ability to obtain and critically analyze data of engineering interest. Ability to choose and use mathematical models to predict the behavior of typical processes of chemical and food industry. To describe a linear optimization problem according to the formalism and the basic hypotheses for linear programming. Applying knowledge and understanding – engineering design Ability to choose and use mathematical models to design the most appropriate equipment and the most common plants in the chemical and food processing industry. Making judgments - engineering practice: Ability to classify mathematical models, recognize limits and difficulties associated with the use of specific computing software, and distinguish the level of complexity required for systematic description of process industry facilities. Ability to classify and solve optimization problems. Communication skills – transversal skills: Knowing how to prepare and manage an interactive pc session with software, featuring both alphanumeric and graphical interface, and specifically matlab® and muc®. Ability to present a topic related to Mathematical modelling. Learning skills – transversal skills: To know how to apply the acquired knowledge also to different environments with respect to those presented during the course. |

Prerequisites | |
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General knowledge of: -differential calculus, -mass and energy balances on closed systems and on open systems, under steady and unsteady-state conditions -transport phenomena |

Contents | |
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After a brief presentation of the course syllabus and the procedure for learning assessment, the course will focus on the following topics: • Introduction to Matlab® languages and technical uses (1h th, 0h ex, 2h lab). • Classifications of models in general, and of mathematical models in particular (2h th, 0h ex, 0h lab). • First-principle models: Basic models; Models involving transport phenomena; Models based on the “population balance approach”(8h th, 3h ex, 0h lab). • Empirical models and data fitting (3h th, 0h ex, 5h lab). • Dynamical models: dynamic models with “input-output representation”; state-space dynamic models; black box dynamic models (6h th, 0h ex, 0h lab). • Time series (2h th, 0h ex, 0h lab). . • Numerical methods for parabolic PDEs. Use of MUC 1.0 - PARABOLIC PDE SOLVER code in LabView® (6h th, 1h ex, 2h lab). . • Introduction to optimization (3h th, 0h ex, 0h lab). • Linear Programming: the graphical method and the one and two phases Simplex algorithm (9h th, 1hex, 6h lab). |

Teaching Methods | |
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TEACHING INCLUDES 60 HOURS OF LECTURES AND EXERCISES (6CFU). IN PARTICULAR, IT INCLUDES 40 HOURS OF THEORETICAL LESSONS, 5 HOURS OF CLASSROOM EXERCISES LED BY THE TEACHER ON THE BOARD AND 15 HOURS EXERCISES IN THE COMPUTER LAB CONDUCTED BY THE TEACHER IN AN INTERACTIVE WAY WITH THE STUDENTS, THROUGH THE USE OF APPROPRIATE DIDACTIC SOFTWARE. EACH STUDENT IS ASSIGNED A USERNAME AND A PASSWORD, AND THEN ACCESS TO A MATHEMATICS CLASSROOM WITH A MATLAB®¸ LICENSE WITH ITS CURVE FITTING TOOLBOX AND THE MUC® EXECUTABLE. THE MINIMUM FRACTION OF ATTENDED HOURS OF LECTURES REQUIRED TO TAKE THE EXAM IS 60%. THE ATTENDANCE CHECK WILL NOT BE CARRIED OUT. Students who do not reach the sufficient number of attended hours must submit a request to the Teaching Council, specifying the topics they could not attend and the reasons. The Council will establish the methods of making up missed lessons on a case-by-case basis |

Verification of learning | |
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The assessment of the achievement of the objectives will be done through a practical test and an oral interview. The practical test is preliminary to the oral colloquium. It consists in the resolution of two problems described in English to be answered in two hours. The first problem is a linear programming problem, while the second one is focused either on PDE resolution or the development of the best fitting model of a set of experimental data. The software-based test requires preparation of an elaborate directly on pc, in ms word ®, with the results obtained from the matlab ® and / or muc ®, while having all course materials available. The interview typically lasts about 30min. The student is required to discuss on at least two different mathematical modelling, among those dealt during the course. The final vote is expressed in a scale from 1 to 30, with a pass grade equal to 18. It is an average of the results obtained in each test. It will depend on the degree of maturity acquired on the content and the methodological tools explained in the course, taking into account also the quality of the written and oral exposition and the autonomy of judgment shown. It is an essential condition for passing the exam the proper use of the specific software and tools illustrate during the course, the correct classification of a given mathematical model, the proper description of a linear programming problem, the ability to critically analyze the data and, accordingly, choose the most appropriate mathematical model to describe the behavior of a typical process of the food industry, highlighting the main advantages and limitations. The student reaches the level of excellence once he/she proves to be able to apply the acquired knowledge to contexts different from those presented during the course. |

Texts | |
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Himmelblau d.m. and bischoff k.b., “process analysis and simulation”, john wiley & sons inc., 1967 2. Snieder r., “a guided tour of mathematical methods for the physical sciences”, 2nd edition, cambridge university press, isbn-13: 9780521834926, isbn-10: 0521834929, 2004 3. Teaching aids provided by the lecturers Reference web site for personal study and exam matters: • http://docenti.unisa.it/005515/risorse • further information can be requested via e-mail: gpataro@unisa.it |

BETA VERSION Data source

**ESSE3**[Ultima Sincronizzazione: 2019-10-21]