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MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

International Teaching MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

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0622800009
DEPARTMENT OF INDUSTRIAL ENGINEERING
EQF7
FOOD ENGINEERING
2025/2026

OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2024
AUTUMN SEMESTER
CFUHOURSACTIVITY
660LESSONS
- T
Objectives
Knowledge and understanding
Students will acquire basic knowledge, methodologies and some software tools to deal with the abstract representation of systems in process engineering, in particular for cases of interest in industrial food production.
In particular, students will know and understand the following concepts:
the formalism and abstract representation tools, the classification criteria and the development techniques of mathematical models, the minimum ability to discern the level of complexity appropriate for the systemic description of the plants of the food industry;
numerical resolution of mathematical models consisting of partial differential equations of the parabolic type;
solving linear programming problems.

Applying knowledge and understanding
Being able to obtain, select, re-elaborate and critically analyze engineering data. Knowing how to classify mathematical models.
The student will be able to: select and use mathematical models predictive of the behavior of typical processes of the food and process industry; describe a linear optimization problem according to the formalism and the basic hypotheses for linear programming; recognize the specific characteristics and the most frequent connotations in the mathematical models representative of processes in the food industry.; recognize phenomena and processes that are best described by a mathematical model based on the concept of population balance, and possess the foundations for developing it; solve a dynamic model described through a partial differential equation (PDE) of parabolic type through the method of finite differences, consciously using software; describe a linear optimization problem according to the formalism and the basic hypotheses for linear
programming and solve it with standard algorithms; knowingly using software.

Making judgments
The student will be able to: -knowing how to classify mathematical models.
-distinguish the differences in behavior, conceptual and practical, under steady-state or dynamic conditions, between linear and non-linear systems.
-knowing how to recognize limits and difficulties related to the use of specific calculation software.
-knowing how to distinguish the level of complexity appropriate for the system description of the process industry plants.
-knowing how to classify and solve optimization problems.

Communication skills
The student will be able to: Understand the terminology used in English in the development and applications of mathematical models. learn to deal with mastery and enhancement of a software, the solution of a problem and the effective representation of the results.
The student will acquire the ability to present, with language properties, a simple case study typical of the food industry capable of being modeled and, using dedicated software (such as MATLAB® and MUC®), to discuss the results of the mathematical resolution, even in a time of limited exposure.

Learning skills
Knowing how to apply the knowledge acquired to contexts other than those presented during the course, and to deepen the topics covered using study materials other than those proposed.
Distinguish the differences in behavior, conceptual and practical, under steady-state or dynamic conditions, between linear and non-linear systems.
Distinguishing the implications of a nonlinear optimum problem presents with respect to a linear one.


Prerequisites
Propedeutics: none
TO PROFITABLELY ACHIEVE THE SET OBJECTIVES, BASIC MATHEMATICAL KNOWLEDGE IS REQUIRED, IN PARTICULAR FOR ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, MASTERY OF MATTER AND ENERGY BALANCES IN NON-STATIONARY CONDITIONS AND THE FUNDAMENTALS OF TRANSPORT PHENOMENA.
Contents
AFTER A BRIEF PRESENTATION OF THE COURSE AND THE METHODS OF LEARNING ASSESSMENT, THE COURSE WILL FOCUS ON THE FOLLOWING TOPICS:

• INTRODUCTION TO MATLAB® (1H THEORY, 0H EXERCISING, 2H LAB).
• CLASSIFICATION OF MODELS IN GENERAL AND OF MATHEMATICAL ONES IN PARTICULAR (2H THEORY, 0H EXERCISING, 0H LAB).
• FIRST PRINCIPLES MODELS: EX. PREDATOR-PREDATOR MODEL; MODELS BASED ON TRANSPORT PHENOMENA; GENERAL CASES OF MODELS BASED ON ACCOUNTING POPULATION BALANCES (8H THEORY, 3H EXERCISING, 0H LAB).
• EMPIRICAL MODELS AND DATA FITTING (3H THEORY, 0H EXERCISING, 5H LAB).
• DYNAMIC MODELS: INPUT-OUTPUT MODELS AND STATE SPACE MODELS. (6H THEORY, 0H EXERCISE, 0H LAB)
• TIME SERIES WITH BOTH BASIC AND ADVANCED DATA ANALYSIS (2H THEORY, 0H EXERCISE, 2H LAB).
• NUMERICAL SOLUTION OF PARABOLIC PDEs: EULER, LAASONEN AND CRANK-NICHOLSON METHODS. STABILITY, CONSISTENCY AND CONVERGENCE. MUC CODE 1.0 - PARABOLIC PDE SOLVER WRITTEN IN LABVIEW® (6H THEORY, 1 HOUR EXERCISE, 2H LAB).
• INTRODUCTION TO OPTIMIZATION: CLASSIFICATIONS OF OPTIMIZATION PROBLEMS: CONSTRAINTED AND UNCONTRESTED, LINEAR AND NONLINEAR (3H THEORY, 0H PRACTICE, 0H LAB).
• LINEAR PROGRAMMING: THEORY; THE GRAPHICAL METHOD; THE SIMPLEX ALGORITHM IN ONE AND TWO STAGES (9H THEORY, 1H PRACTICE, 6H LAB).
Teaching Methods
THE COURSE INCLUDES A TOTAL OF 60H DIVIDED INTO 44H OF THEORY, 6H OF EXERCISES AND 10H OF LABORATORY WITH INTERACTIVE SOFTWARE.
THE COURSE IS DELIVERED “IN PERSON” AND IN ENGLISH.
ATTENDANCE IN THE TEACHING COURSES IS STRONGLY RECOMMENDED.
THE COURSE INCLUDES THEORETICAL LESSONS CONDUCTED BY THE TEACHER WITH EXTENSIVE USE OF SLIDES AND COMPUTER ANIMATIONS, CLASSROOM EXERCISES CONDUCTED BY THE TEACHER ALSO WITH IT SUPPORT AND ACTIVITIES IN THE COMPUTER LABORATORY CONDUCTED BY THE TEACHER INTERACTIVELY WITH THE STUDENTS, THROUGH THE USE OF APPROPRIATE EDUCATIONAL SOFTWARE. EACH STUDENT IS ASSIGNED A USER NAME AND A PASSWORD, AND THEREFORE ALLOWED ACCESS TO THEIR OWN LAPTOP OR NETWORKED PCS, EQUIPPED WITH THE MATLAB® LICENSE WITH THE NECESSARY TOOLBOXES (CURVE FITTING, ECONOMETRIC) AND THE MUC® EXECUTABLE.
EACH STUDENT CAN INSTALL AND USE THE LICENSE OF THE UPDATED VERSION OF MATLAB® OF THE UNIVERSITY, DOWNLOADING IT FROM HTTPS://WEB.UNISA.IT/SERVIZI-ON-LINE/MATLAB-X-UNISA. IN ADDITION, EACH STUDENT WILL BE GIVEN THE FREEWARE CODE MUC 1.0 - PARABOLIC PDE SOLVER AND SOME MATLAB® SCRIPTS.
ALL COURSE PRESENTATIONS, OTHER NOTES AND TEXTS FROM PREVIOUS WRITTEN EXAMS ARE MADE AVAILABLE BY THE TEACHER ON THE UNIVERSITY PLATFORM MS TEAMS®.
Verification of learning
THE EVALUATION OF THE ACHIEVEMENT OF THE SET OBJECTIVES IS MADE BY MEANS OF A WRITTEN TEST LASTING 2H. IT INCLUDES AN "APPLICATION AND PRACTICAL" PART BASED ON THE USE OF MATLAB® AND MUC®, CONSISTING OF THE SOLVING OF LINEAR PROGRAMMING PROBLEMS DESCRIBED IN ENGLISH, RESOLUTION OF FINITE DIFFERENCE PDEs, CONSTRUCTION OF A DATA FITTING MODEL, SIMPLIFIED ANALYSIS OF A TIME SERIES,
FOLLOWED BY A THEORETICAL PART WITH OPEN-ENDED QUESTIONS OR QUIZZES ON MATHEMATICAL MODELING.
THE TEST INVOLVES THE COMPLETION OF A PROJECT DIRECTLY ON A PC IN MS WORD® AND WITH THE RESULTS OBTAINED FROM MATLAB® AND/OR MUC®, KEEPING ALL THE COURSE EDUCATIONAL MATERIAL AVAILABLE.
THE TEST IS CONSIDERED PASSED WITH THE MINIMUM SCORE (18/30) IF THE STUDENT HAS COMPLETED AT LEAST TWO OF THE FOUR CALCULATIVE PROBLEMS, AND AT THE SAME TIME HAS PROVIDED VALID ANSWERS TO 60% OF THE QUESTIONS. IF THE STUDENT DEMONSTRATES THE COMPARATIVE KNOWLEDGE, THE APPLIED ABILITY TO UNDERSTAND AND THE CRITICAL AUTONOMY OF JUDGMENT AND REASONING, DESCRIBED IN THE PREVIOUS PARAGRAPHS, HE/SHE ACHIEVES THE MAXIMUM SCORE (30/30). FOR THE PURPOSE OF HONOURS, THE QUANTITY (EXHAUSTIVE AND NUMERICALLY CORRECT ANSWER TO APPROXIMATELY 90% OF THE QUESTIONS) AND THE QUALITY (APPROPRIATE SCIENTIFIC LANGUAGE AND MASTERY OF THE SUBJECT) OF THE PRESENTATION WILL BE TAKEN INTO ACCOUNT.
Texts
1. SNIEDER R., “A GUIDED TOUR OF MATHEMATICAL METHODS FOR THE PHYSICAL SCIENCES”, 2ND EDITION, CAMBRIDGE UNIVERSITY PRESS, ISBN-13: 9780521834926, ISBN-10: 0521834929, 2004
2. HIMMELBLAU D.M. E BISCHOFF K.B., “PROCESS ANALYSIS AND SIMULATION”, WILEY,1967
3. ZONDERVAN E., A NUMERICAL PRIMER FOR THE CHEMICAL ENGINEER, SECOND EDITION, TAYLOR & FRANCIS, 2020
4. PRESENTATIONS AND HANDOUTS PROVIDED BY THE TEACHER
More Information
THE COURSE IS DELIVERED IN ENGLISH.

REFERENCE WEBSITE FOR PERSONAL STUDY AND EXAMS:
HTTP://COMET.ENG.UNIPR.IT/~MICCIO/

UNIVERSITY PLATFORM MS TEAMS® FOR REGISTERED STUDENTS:
“MATHEMATICAL MODELING OF FOOD INDUSTRY PROCESSES – 0622800009”
Lessons Timetable

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