Knowledge and understanding:
The course aims to provide students with the tools required to understand and to mathematically model the phenomena involved in mass, energy and momentum transport (Mathematical Models and Related Statistics, Mass, Energy and Momentum balances). Particular attention is given to the use of the above-mentioned balances in biomedical applications such as, for instance, controlled release pharmaceutical systems (Biological Engineering).
Applying knowledge and understanding:
The student will acquire the ability to use/adapt the theoretical tools presented in the course (mass balance, energy and amount of motion) for the practical solution of several examples in order to get the necessary physical sensitivity towards the physical quantities involved.
Making judgements:
Being able to select the most appropriate mathematical model, among those presented in the course, in order to solve problems connected to mass, heat and momentum transport. Being able to evaluate the physical soundness of the results coming from the adopted mathematical models.
Communication skills:
Being able to expose, by means of a written, oral and graphical exposition, the results coming from the theoretical approach to a problem dealing with mass, heat and momentum transport. Learning skills:
Being able to get from scientific literature, manuals, textbooks and internet, the information (such as materials properties) required to correctly set up the solution of problems dealing with mass, heat and momentum transport.

Basic knowledge: integro-differential calculus, concept of scalar, vector and tensor
Didattic: Those required by the Three Years Course on Industrial Engineering, process/materials curricula

The course, starting from the concept of mathematical model, illustrates the microscopic/macroscopic Mass, Energy and Momentum balances in order to derive their equations in Cartesian, cylindrical and spherical coordinates. Based on these equations, several problems regarding mass transport, heat transmission, and momentum transport are considered. Particular attention is given to the emerging biomedical aspects that increasingly see the involvement of chemical and materials engineers. The course material is given to the student at the beginning of the course

1) R.B. Bird, W.E. Stewart, E.N. Lightfoot, Introductory Transport Phneomena, John Wiley & Sons, 1960.
2) R.B. Bird, W.E. Stewart, E.N. Lightfoot, Fenomeni di Trasporto, casa Editrice Ambrosiana Milano, 1979.
3) M. Grassi, G. Grassi, R. Lapasin, I. Colombo. “Understanding drug release and absorption mechanisms: a physical and mathematical approach”. 2007. CRC Press, Boca Raton, London, New York
4) F. Kreith. Principi di Trasmissione del Calore. Liguori Editore, 1975.
5) S.V. Patankar, Numerical Heat Transfer and Fluid Flow Hemisphere Publishing, New York, 1990
6) S. C. Chapra, R. P. Canale, “Numerical methods for Engineers”, McGraw-Hill, Boston (USA), terza edizione, 1998.
7) D. Manca “Calcolo numerico applicato”, Pitagora Editrice, Bologna 2007.
8) Course slides (pptx), lessons recordings and course notes (pdf).

0) Introduction to the Course
0.1 University
0.2 Transport Phenomena origins
1) Biological Engineering
1.1 Evolution of Chemical Engineering
1.2 Bio-pharmaceuticals
1.3 Common Points and New Challenges
2) Mathematical Models and Statistics
2.1 Definition and examples
2.2 Model Fitting on Experimental Data: Statistics
2.3 Comparison of two models
2.4 Correlation between two variables
3) Materia Balance
3.1 Definitions
3.2 Microscopic material balance
3.2.1 Expression of material flow
3.2.2 Generative term (reaction, from other phase)
3.2.3 Cylindrical and spherical coordinates
3.3 Macroscopic material balance
3.4 The Diffusion Coefficient
4) Energy Balance
4.1 Definitions
4.2 Microscopic energy balance
4.2.1 Balance Terms
4.2.2 Stress tensor
4.2.3 Cylindrical and spherical coordinates
4.2.4 Temperature dependence
4.2.5 Reynolds, Brinkman and Prandtl dimensionless numbers
4.3 Macroscopic Energy Balance
4.4 Thermal conductivity
5) Momentum Balance
5.1. Definitions.
5.2 Balance of microscopic motion quantity.
5.2.1 Balance Terms
5.2.2 Tensorial Newton Law
5.2.3 Cylindrical and spherical coordinates
5.2.4 Froude and Grashof dimensionless numbers
5.3 Forced and natural convection
5.3 Macroscopic momentum balance.
5.5 Viscosity
6) Examples and Applications
6.1. Mass Balance.
6.1.1 Release from matrices: different boundary and initial conditions, perforated septum
6.1.2 Reactions: homogeneous, catalytic
6.1.3 Diffusion and convection
6.1.4 Packed column
6.1.5 Resistance to mass transfer
6.2 Energy balance.
6.2.1 Conduction: overall heat transfer coefficient, electric wire, cooling fin, viscous dissipation
6.2.2 Convection: heterogeneous, forced, natural catalytic reaction,
6.2.3 Non-stationary: infinite and finite slab, sphere cooling
6.2.4 Energy transfer resistance
6.3 Momentum Balance
6.3.1 Flow through an annulus
6.3.2 Flow of not newtonian fluids
6.3.3 Slim Slit Flow (One or Two Immiscible Fluids)
6.3.4 Flow around a sphere
6.3.5 Rotating fluid shape
6.3.6 Not-stationary balance
6.3.7 Turbulent flow
6.3.8 Friction factor
7) Numerical solution of the discussed models
7.1. Programming
7.2 Solution of linear and not linear equation systems
7.3 Solution of ordinary differential equations
7.4 Solution of partial differential equations
7.5 Examples

Frontal Lesson.
After the explanation of the physics of the illustrated phenomenon, it follows its translation according to the mathematical language for the realization of a model. Finally, students are provided with digital tools (typically software written by the teacher, but not only) which allow the mathematical model to be operational, i.e. they allow the simulation of the described phenomenon in order to realize a close connection between the theoretical and the practical aspects. Many case studies referring to the teacher research and industrial work are presented and discussed to stimulate student sand confer them the so called "forma mentis" typical of engineers.

The final examination comprehends an oral test dealing with all the topics discussed in the course. The student will have to demonstrate that she/he is able to know the physics of the topics covered and their mathematical modeling.
The score of the exam is attributed by means of a vote expressed out of thirty. To pass the exam (18/30) the student must demonstrate that she/he has understood the physical aspects of the topics covered by correctly answering 3 questions using technically and scientifically sound language. To achieve the maximum score (30/30 cum laude), the student must also be able to give a correct mathematical translation of all the physical phenomena requested.

This course can be related to targets 3 and 9