Year of erogation: 
Disciplinary Sector: 
Technical Physics
Second semester
Year of study: 
Language of instruction: 


Learning outcomes of the course unit

Knowledge and ability to understand: through the frontal lessons carried out during the course, the student will be able to learn the methods and the knowledge necessary to understand and describe the basis of numerical analysis applied to the phenomena of transport of energy, mass and momentum of engineering and industrial interest. The student will learn the different methodologies of numerical solution of the conservation equations of energy, mass and momentum; the student will acquire the theoretical and practical fundamentals required for the realization, validation and critical and conscious use of the numerical methods.

Ability to apply knowledge and understanding: through practical exercises carried out with the help of the computer, the student will acquire practical abilities related to the phenomena of transport of energy, mass and momentum that regards engineering processes. Through the analysis and the use of numerical simulation codes the student must be able to consciously apply the acquired knowledge about the numerical methods discussed in class.

Self-judgement: the student must be able to understand and critically evaluate the main techniques of computational thermofluiddynamics. In particular, the student must have the background to face and evaluate the impact of design choices in the field of numerical modelling of devices of engineering interest. In addition, the student should be able to consciously read, through analysis and proof tools, the results obtained by the application of the described numerical solution methodologies.

Communication skills: through the theoretical and practical lessons the student will adopt the specific vocabulary regarding the numerical solution methods of typical thermofluiddynamics problems. The student must have the ability to clearly present, in oral and written form, not only the theoretical topics addressed during the course but also the results obtained from the practical application of one of the studied numerical methods, the relative design choices in the application of that technique, the problems faced, and the methods of solution identified.

Learning ability: the student who has attended the course will have the basic skills to deepen his knowledge with the aim of training a professional figure with theoretical, numerical and modelling skills and able to deal with work issues that also involve multidisciplinary contexts. Specifically, the student will have the tools for the understanding and analysis of scientific journals and specialized texts with the aim of increasing his knowledge by addressing topics that are not strictly covered during the course.


To follow the course with profit it is necessary the knowledge of the basic concepts of Thermofluid dynamics.

Course contents summary

The course aims to provide students with general knowledge about the phenomena of energy, mass and momentum transport and the numerical models necessary to describe them: the laws of fluid motion, the laws of conservation of energy, mass and momentum, the models of analysis of the finite differences, finite elements, finite volumes, turbulence and the models to describe its fundamental characteristics. In addition to the frontal lessons in which theoretical concepts will be illustrated, an exercise/practical activity will be dedicated to numerical exercises in order to apply theoretical notions acquired during the lessons. Part of the exercise activity is carried out in the computer lab and is dedicated to numerical analysis applied to problems of heat transfer and fluid motion. In order to acquire methodological and applicative knowledge, this part of the course adopts practical exercises in which the Matlab programming environment is used and utilizes specific softwares for the numerical modelling of thermofluid dynamic problems.

Course contents

- Introduction to the laws of fluid motion, mass conservation, energy conservation, and momentum conservation.
- Numerical method of finite differences: stationary finite differences, energy balance method, matrix notation, non-stationary finite differences with explicit and implicit method
- Finite element analysis, energy conservation, Navier Stokes laws, boundary conditions, numerical solution methodologies, SIMPLE scheme, weighed residues method, Assembly, spatial discretization, transient regime equations, integration over time, shape functions
- Turbulence and its models. General characteristics of turbulence, decomposition and fluctuations, Kolmogorov cascade, turbulence models based on temporal average: general aspects, turbulent viscosity models, the k-epsilon model and its variants, boundary conditions, k-omega models. Direct simulation of turbulence. Large Eddy simulation.
- Finite volume analysis: the basic concepts, spatial discretization, calculation grids, temporal integration, solution of thermofluid dynamic problems
- Solution accuracy, discretization errors, modelling errors, convergence errors
- Workshop exercises on the practical application of the topics explained during the course

Recommended readings

-Fondamenti di Termofluidodinamica Computazionale, Gianni Comini, Giulio Croce Enrico Nobile, SGE Editoriali
- Fundamentals of heat and mass transfer, T. L. Bergman, F. P. Incropera, D. P. DeWitt and A. S. Lavine, John Wiley & Sons.
- Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data, R. K. Shah and London A. L., Academic press.

Teaching methods

The teaching activity will be mainly organized in frontal lessons and practical exercises carried out in the computer lab. During the frontal lessons the theoretical topics of the subject will be dealt with the aim of promoting the understanding and assimilation of the concepts at the base of the course. In the computer-assisted exercises, the concepts illustrated in the frontal lessons will be applied in practice, tackling problems of engineering interest.

Assessment methods and criteria

The learning assessment is organized in two steps: a written/practical test carried out in the computer lab based on the resolution of a practical problem of thermofluid dynamics through one of the numerical solution methodologies faced during the course; an oral test based on open-answer questions in which there will be evaluated the knowledge of the issues presented during the course, the explanation attitude and the knowledge of the disciplinary vocabulary. The final mark is calculated by assigning each of the two tests a score from 0 to 30 and making the weighted average of the individual assessments, with final rounding up.