01NMFQD

A.A. 2019/20

Course Language

Inglese

Course degree

Course structure

Teaching | Hours |
---|---|

Lezioni | 37,5 |

Esercitazioni in aula | 12 |

Esercitazioni in laboratorio | 1,5 |

Tutoraggio | 4 |

Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|

Teaching assistant

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

2018/19

The subject consists of two parts: the first one discusses some advanced topics in the field of engineering thermodynamics, the second one discusses the use of numerical methods for solving engineering problems. In particular, the modeling and numerical methods are applied to meaningful test cases relevant for engineering thermodynamics.
The module of Advanced Engineering Thermodynamics is designed to complete the student's preparation in the field of engineering thermodynamics, whose basics were provided in previous subjects. This teaching module completes the theoretical background required by the design of devices with regards to the specific problems involving heat transfer. In particular, the subject discusses the thermal performance of energy components and mechanical systems and it provides some basic concepts about numerical fluid dynamics, including modeling of heat transfer systems. Finally, the basic concepts of environmental acoustics and lighting are provided in order to characterize the interaction of the devices with the end users.
The module of Numerical Modelling is intended to provide the tools for the systematic and critical study of the main numerical models involving partial derivatives and used in various fields of engineering, which can be solved by appropriate numerical discretization methods. In particular, the module aims to provide the essential features for evaluating a numerical method in terms of the quality and the reliability of the numerical solution. Some test cases will be discussed in the field of advanced engineering thermodynamics.

The subject consists of two parts: the first one discusses some advanced topics in the field of engineering thermodynamics, the second one discusses the use of numerical methods for solving engineering problems. In particular, the modeling and numerical methods are applied to meaningful test cases relevant for engineering thermodynamics.
The module of Advanced Engineering Thermodynamics is designed to complete the student's preparation in the field of engineering thermodynamics, whose basics were provided in previous subjects. This teaching module completes the theoretical background required by the design of devices with regards to the specific problems involving heat transfer. In particular, the subject discusses the thermal performance of energy components and mechanical systems and it provides some basic concepts about numerical fluid dynamics, including modeling of heat transfer systems. Finally, the basic concepts of environmental acoustics and lighting are provided in order to characterize the interaction of the devices with the end users.
The module of Numerical Modelling is intended to provide the tools for the systematic and critical study of the main numerical models involving partial derivatives and used in various fields of engineering, which can be solved by appropriate numerical discretization methods. In particular, the module aims to provide the essential features for evaluating a numerical method in terms of the quality and the reliability of the numerical solution. Some test cases will be discussed in the field of advanced engineering thermodynamics.

The objective is to convey to the student in-depth knowledge of thermomechanical continuous media, thermodynamics and fluid dynamics, with particular emphasis on the concept of exergy, and, as regards the interaction with the end user, the basic elements of environmental acoustics and lighting.
Additionally, the student should acquire the basic knowledge about the discretization methods for initial and boundary value problems involving elliptic, parabolic and hyperbolic partial differential equations (PDEs). Some emphasis is put on the basic mathematical properties (such as consistency, stability and convergence) of numerical methods. Students should become able to transform numerical models into systems of algebraic equations, and to solve these systems.
The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and exergy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations.
Finally, the student is expected to learn the ability to implement in the MATLAB(r) software, or similar ones, some numerical models that describe engineering problems (particularly those relevant to engineering thermodynamics) and to relate their performances to the theoretical context. The student should also develop the ability of applying the numerical tools to the simulation of the behaviour of simple yet significant problems in applied thermodynamics.

The objective is to convey to the student in-depth knowledge of thermomechanical continuous media, thermodynamics and fluid dynamics, with particular emphasis on the concept of exergy, and, as regards the interaction with the end user, the basic elements of environmental acoustics and lighting.
Additionally, the student should acquire the basic knowledge about the discretization methods for initial and boundary value problems involving elliptic, parabolic and hyperbolic partial differential equations (PDEs). Some emphasis is put on the basic mathematical properties (such as consistency, stability and convergence) of numerical methods. Students should become able to transform numerical models into systems of algebraic equations, and to solve these systems.
The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and exergy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations.
Finally, the student is expected to learn the ability to implement in the MATLAB(r) software, or similar ones, some numerical models that describe engineering problems (particularly those relevant to engineering thermodynamics) and to relate their performances to the theoretical context. The student should also develop the ability of applying the numerical tools to the simulation of the behaviour of simple yet significant problems in applied thermodynamics.

Thermodynamics and heat transfer basics. Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in programming languages as C, C++, MATLAB(r) o Python.

Thermodynamics and heat transfer basics. Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in programming languages as C, C++, MATLAB(r) o Python.

Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters.
CLASSICAL MOLECULAR DYNAMICS and KINETIC THEORY. Introduction to classical molecular dynamics. Bond and non-bond interactions. Force fields. Elementary numerical schemes (Verlet integration). Elementary statistical ensembles: Thermostats and barostats. Practical examples. Large systems approaching the local equilibrium: Maxwellian distribution function. The distribution function dynamics. Linear relaxation towards the local equilibrium: Bhatnagar–Gross–Krook (BGK) model. Practical examples.
CONTINUUM THERMO-MECHANICS. Deduction of the equation of mass and momentum conservation by both kinetic local equilibrium and by elementary control volume. Deduction of the wave equation. Small deviations from the conditions of local equilibrium. Phenomenological relations in Navier-Stokes-Fourier equations: Stress tensor and thermal flux. Generalization of the results obtained by the ideal gas to other types of fluids. Dimensionless equations. Meaning of dimensionless numbers. Incompressible limit. Equation for kinetic energy and enthalpy. First principle of thermodynamics. Generalization of entropy for continuous body. Generalization of Gibbs’s correlation. The second principle of thermodynamics for a continuous body. Work, heat and the thermodynamics of irreversible processes.
THERMAL DESIGN. Deduction of the integral equations for closed systems and open systems. Technical formulation of integral equations. Physical meaning of irreversibility. Correct calculation of irreversibility by practical formulas. Turbulence and turbulent flows. Characteristic scales of the phenomenon, deduction of the equations for the average quantities and the closure problem. Artificial viscosity induced by turbulence and modeling. Exergy balance in a reversible system. Exergy and internal exergy for an ideal gas. The theorem of Guy-Stodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams.
ACOUSTICS. Deduction of the wave equation. Introduction, elastic, plane, longitudinal and progressive waves. Propagation speed of elastic waves; sound speed of air. Mechanical power transported by sound wave, wave intensity, resistance and effective pressure. Acoustic intensity and acoustic feeling: Law of Weber-Fechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Iso-phon curves. Frequency bands, level of pressure, interpolating weight curve A. Interaction between elastic waves and materials, factors of reflection, transmission, absorption, apparent absorption. Effect of frequency. Apparent absorption factor of several walls. Acoustics in open environments. Open field. Sound tail. Acoustic energy balance and reverberation, reverberation time by conventional formula of Sabine. Sound insulation; sound proofing; plain wall and law of mass and frequency; case study for a pipe.
LIGHTING. Deduction of the radiative transfer equation (RTE) from kinetic theory. The light, electromagnetic radiation, main features, diffuse radiation. Visual perception and photometric system. Definition of physical units of measured quantities. Point source. Light intensity. Indicator of emission. Light flux emitted from a point source with a given indicator of emission. The first formula of Lambert. Linear source, linear luminance, and lighting calculations on surface. Surface source, luminance, and lighting calculation on a surface. The second law of Lambert. Lambert emitter. Efficiency of a light bulb.
Concerning the model of numerical modelling, the program of class lessons is provided below.
INTRODUCTORY PART. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. Basic concepts of numerical methods.
STEADY-STATE PROBLEMS. Elliptic problems; the steady diffusion and the membrane equilibrium examples; discretization by centered finite differences; variational formulation; discretization by finite elements. Implementation of Dirichlet, Neumann and Robin boundary conditions. Reduction of the discrete problem to an algebraic problem; properties of the corresponding matrices; techniques for solving large systems of algebraic equations. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue problems.
TIME-DEPENDENT PROBLEMS. Formulation and discretization of evolutionary problems; parabolic and hyperbolic equations; the heat equation, the wave equation; mass lumping; time advancing techniques; asymptotic stability and choice of the time step; rate of convergence in space and time. Convection-diffusion problems; mesh Peclet number; centered versus upwind discretizations. Conservation and balance laws; characteristics; integral formulation; discretization by finite volumes; cell averages and numerical fluxes; review of the main classical methods; relation with finite differences; Courant number and CFL condition; numerical diffusion and dispersion; stability and convergence.

Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters.
CLASSICAL MOLECULAR DYNAMICS and KINETIC THEORY. Introduction to classical molecular dynamics. Bond and non-bond interactions. Force fields. Elementary numerical schemes (Verlet integration). Elementary statistical ensembles: Thermostats and barostats. Practical examples. Large systems approaching the local equilibrium: Maxwellian distribution function. The distribution function dynamics. Linear relaxation towards the local equilibrium: Bhatnagar–Gross–Krook (BGK) model. Practical examples.
CONTINUUM THERMO-MECHANICS. Deduction of the equation of mass and momentum conservation by both kinetic local equilibrium and by elementary control volume. Deduction of the wave equation. Small deviations from the conditions of local equilibrium. Phenomenological relations in Navier-Stokes-Fourier equations: Stress tensor and thermal flux. Generalization of the results obtained by the ideal gas to other types of fluids. Dimensionless equations. Meaning of dimensionless numbers. Incompressible limit. Equation for kinetic energy and enthalpy. First principle of thermodynamics. Generalization of entropy for continuous body. Generalization of Gibbs’s correlation. The second principle of thermodynamics for a continuous body. Work, heat and the thermodynamics of irreversible processes.
THERMAL DESIGN. Deduction of the integral equations for closed systems and open systems. Technical formulation of integral equations. Physical meaning of irreversibility. Correct calculation of irreversibility by practical formulas. Turbulence and turbulent flows. Characteristic scales of the phenomenon, deduction of the equations for the average quantities and the closure problem. Artificial viscosity induced by turbulence and modeling. Exergy balance in a reversible system. Exergy and internal exergy for an ideal gas. The theorem of Guy-Stodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams.
ACOUSTICS. Deduction of the wave equation. Introduction, elastic, plane, longitudinal and progressive waves. Propagation speed of elastic waves; sound speed of air. Mechanical power transported by sound wave, wave intensity, resistance and effective pressure. Acoustic intensity and acoustic feeling: Law of Weber-Fechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Iso-phon curves. Frequency bands, level of pressure, interpolating weight curve A. Interaction between elastic waves and materials, factors of reflection, transmission, absorption, apparent absorption. Effect of frequency. Apparent absorption factor of several walls. Acoustics in open environments. Open field. Sound tail. Acoustic energy balance and reverberation, reverberation time by conventional formula of Sabine. Sound insulation; sound proofing; plain wall and law of mass and frequency; case study for a pipe.
LIGHTING. Deduction of the radiative transfer equation (RTE) from kinetic theory. The light, electromagnetic radiation, main features, diffuse radiation. Visual perception and photometric system. Definition of physical units of measured quantities. Point source. Light intensity. Indicator of emission. Light flux emitted from a point source with a given indicator of emission. The first formula of Lambert. Linear source, linear luminance, and lighting calculations on surface. Surface source, luminance, and lighting calculation on a surface. The second law of Lambert. Lambert emitter. Efficiency of a light bulb.
Concerning the model of numerical modelling, the program of class lessons is provided below.
INTRODUCTORY PART. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. Basic concepts of numerical methods.
STEADY-STATE PROBLEMS. Elliptic problems; the steady diffusion and the membrane equilibrium examples; discretization by centered finite differences; variational formulation; discretization by finite elements. Implementation of Dirichlet, Neumann and Robin boundary conditions. Reduction of the discrete problem to an algebraic problem; properties of the corresponding matrices; techniques for solving large systems of algebraic equations. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue problems.
TIME-DEPENDENT PROBLEMS. Formulation and discretization of evolutionary problems; parabolic and hyperbolic equations; the heat equation, the wave equation; mass lumping; time advancing techniques; asymptotic stability and choice of the time step; rate of convergence in space and time. Convection-diffusion problems; mesh Peclet number; centered versus upwind discretizations. Conservation and balance laws; characteristics; integral formulation; discretization by finite volumes; cell averages and numerical fluxes; review of the main classical methods; relation with finite differences; Courant number and CFL condition; numerical diffusion and dispersion; stability and convergence.

In addition to lessons, the following activities are provided.
Concerning the first part of applied engineering thermodynamics, students are expected to develop a project. Students are divided into 5 teams, as many as the number of applications. For each theme, they must provide (a) calculation of an off-design condition, (b) exergetic analysis and (c) all the technical details related to the design performed. To develop the project, specific notes are made available on the “Portale della Didattica”. In addition, some lectures are focused on the presentation of the guidelines for the project developments and practical examples.
Concerning the part on applied acoustics, a practical application in class is developed, aiming at the evaluation of acoustic behavior of the room. In particular, three different analyses are performed: evaluation of the acoustic field, measurement of the reverberation time and measurements of the acoustic pressure.
Concerning the part on numerical modeling, the following exercises and laboratory activity is developed: Mesh generation; construction of mass and stiffness matrices in various situations; iterative solution of large algebraic systems with sparse matrices; computation of the equilibrium configuration of several physical problems; analysis of the behavior of the spatial discretization error. Implementation of eigenvalue problems and modal analysis. Implementation of time advancing techniques; investigation on the stability of the schemes and the behavior of the temporal error; computation of the evolution of the temperature of a conducting body, and of the propagation of waves in an elastic body. Implementation of numerical schemes for scalar conservation laws and experimental investigation on their behavior.

In addition to lessons, the following activities are provided.
Concerning the first part of applied engineering thermodynamics, students are expected to develop a project. Students are divided into 5 teams, as many as the number of applications. For each theme, they must provide (a) calculation of an off-design condition, (b) exergetic analysis and (c) all the technical details related to the design performed. To develop the project, specific notes are made available on the “Portale della Didattica”. In addition, some lectures are focused on the presentation of the guidelines for the project developments and practical examples.
Concerning the part on applied acoustics, a practical application in class is developed, aiming at the evaluation of acoustic behavior of the room. In particular, three different analyses are performed: evaluation of the acoustic field, measurement of the reverberation time and measurements of the acoustic pressure.
Concerning the part on numerical modeling, the following exercises and laboratory activity is developed: Mesh generation; construction of mass and stiffness matrices in various situations; iterative solution of large algebraic systems with sparse matrices; computation of the equilibrium configuration of several physical problems; analysis of the behavior of the spatial discretization error. Implementation of eigenvalue problems and modal analysis. Implementation of time advancing techniques; investigation on the stability of the schemes and the behavior of the temporal error; computation of the evolution of the temperature of a conducting body, and of the propagation of waves in an elastic body. Implementation of numerical schemes for scalar conservation laws and experimental investigation on their behavior.

- P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013.
- M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997.
- A. Bejan, "Advanced Engineering Thermodynamic" John Wiley & Sons 1997.
- G. Guglielmini, C. Pisoni, Introduzione alla trasmissione del calore, Casa Editrice Ambrosiana, 2002.
- G. Comini, G. Cortella, Fondamenti di trasmissione del calore, Servizi Grafici Editoriali, 2001.
- C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica.
- A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

- P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013.
- M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997.
- A. Bejan, "Advanced Engineering Thermodynamic" John Wiley & Sons 1997.
- G. Guglielmini, C. Pisoni, Introduzione alla trasmissione del calore, Casa Editrice Ambrosiana, 2002.
- G. Comini, G. Cortella, Fondamenti di trasmissione del calore, Servizi Grafici Editoriali, 2001.
- C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica.
- A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

...
The exam consists of both a written part, related to the module of Numerical Modelling, and an oral part, related to the module of Advanced Engineering Thermodynamics. The final evaluation of the exam consists of the arithmetic mean (rounded up) of the two partial scores obtained in the two modules.
With regards to the module on Numerical Modeling, the evaluation procedure is based on the following tests: a) solving some exercises on the main topics covered in the module (available time: 60n minutes), b) answering a series of multiple-choice questions with the help of MATLAB (available time: 45 minutes). No educational material is allowed in these tests.
The mark of the written part will also take into account c) the optional preparation of a computational project during the semester, carried out by small groups of students on a numerical topic related to the group project developed in the advanced engineering thermodynamics module, and evaluated on the basis of the individual contribution. Tests a) and b) have a relative weight of 2/3 and 1/3, and overall they allow the sudent to obtain up to 28 points, whereas the computational project allows the student to obtain a higher mark than 28, including the laude. The mark of the written part will be communicated to students through the Portale della Didattica, together with the indication of when and where they can meet the teacher and check the results of their tests.
Consistently with the expected learning outcomes, the written part of the exam aims to ensure the achievement of the following objectives:
1. In-depth knowledge of the main methods to numerically discretise a mathematical model and to translate it into a system of algebraic equations. This is accomplished by test a).
2. Ability to implement in MATLAB(r) the numerical models presented in class. This is mainly established through test b), but also through test c).
3. Ability to apply the numerical tools to the simulation of the behaviour of physical problems of simple thermodynamic interest. This is establishes through test c).
As for the module on advanced engineering thermodynamics, the exam is oral and is conducted as follows. Each student will have to answer a first question on a theoretical topic discussed during the semester. The answer to the first question is written and discussed immediately afterwards through a direct interaction with the examiner, so that it is possible to assess that the student has correctly learned the fundamentals of thermomechanical continuous media, thermodynamics, fluid dynamics as well as environmental acoustics and lighting. This part will last about fourty five minutes with no educational material allowed. Subsequently, the student will have to demonstrate that he/she has actively contributed to the group project, answering a second oral question by the examiner. Here, by focussing on a realistic energy conversion system, it is possible to assess if the student correctly developed sufficient skills for thermal, energy, exergy analysis of energy conversion devices. Alternatively, at the choice of the examiner, this second question may possibly focus on the applied acoustics part. About thirty minutes will be given to reply to the second question. During this part, it is allowed the use of educational material.
A partial score for the advanced engineering thermodynamics module only is established, which is given by the arithmetic mean of the marks assigned by the examiner to the first and second answers.
Consistently with the expected learning outcomes, the oral part of the exam aims to ensure the achievement of the following objectives:
1. In-depth knowledge of the theoretical notions on thermo-mechanics, continuum theory and thermodynamic. This is accomplished by the first theoretical question;
2. Ability to use the theoretical tools provided in the subject energy and exergetic design and analysis to study real/complex systems involving energy transformation processes. This is established both through the first theoretical question and through the implementation of the group project;
3. Ability to properly interpret the regulations and to perform estimates in the field of lighting and applied acoustic. This is mainly determined by the implementation of the group project and the report on applied acoustic.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The exam consists of both a written part, related to the module of Numerical Modelling, and an oral part, related to the module of Advanced Engineering Thermodynamics. The final evaluation of the exam consists of the arithmetic mean (rounded up) of the two partial scores obtained in the two modules.
With regards to the module on Numerical Modeling, the evaluation procedure is based on the following tests: a) solving some exercises on the main topics covered in the module (available time: 60n minutes), b) answering a series of multiple-choice questions with the help of MATLAB (available time: 45 minutes). No educational material is allowed in these tests.
The mark of the written part will also take into account c) the optional preparation of a computational project during the semester, carried out by small groups of students on a numerical topic related to the group project developed in the advanced engineering thermodynamics module, and evaluated on the basis of the individual contribution. Tests a) and b) have a relative weight of 2/3 and 1/3, and overall they allow the sudent to obtain up to 28 points, whereas the computational project allows the student to obtain a higher mark than 28, including the laude. The mark of the written part will be communicated to students through the Portale della Didattica, together with the indication of when and where they can meet the teacher and check the results of their tests.
Consistently with the expected learning outcomes, the written part of the exam aims to ensure the achievement of the following objectives:
1. In-depth knowledge of the main methods to numerically discretise a mathematical model and to translate it into a system of algebraic equations. This is accomplished by test a).
2. Ability to implement in MATLAB(r) the numerical models presented in class. This is mainly established through test b), but also through test c).
3. Ability to apply the numerical tools to the simulation of the behaviour of physical problems of simple thermodynamic interest. This is establishes through test c).
As for the module on advanced engineering thermodynamics, the exam is oral and is conducted as follows. Each student will have to answer a first question on a theoretical topic discussed during the semester. The answer to the first question is written and discussed immediately afterwards through a direct interaction with the examiner, so that it is possible to assess that the student has correctly learned the fundamentals of thermomechanical continuous media, thermodynamics, fluid dynamics as well as environmental acoustics and lighting. This part will last about fourty five minutes with no educational material allowed. Subsequently, the student will have to demonstrate that he/she has actively contributed to the group project, answering a second oral question by the examiner. Here, by focussing on a realistic energy conversion system, it is possible to assess if the student correctly developed sufficient skills for thermal, energy, exergy analysis of energy conversion devices. Alternatively, at the choice of the examiner, this second question may possibly focus on the applied acoustics part. About thirty minutes will be given to reply to the second question. During this part, it is allowed the use of educational material.
A partial score for the advanced engineering thermodynamics module only is established, which is given by the arithmetic mean of the marks assigned by the examiner to the first and second answers.
Consistently with the expected learning outcomes, the oral part of the exam aims to ensure the achievement of the following objectives:
1. In-depth knowledge of the theoretical notions on thermo-mechanics, continuum theory and thermodynamic. This is accomplished by the first theoretical question;
2. Ability to use the theoretical tools provided in the subject energy and exergetic design and analysis to study real/complex systems involving energy transformation processes. This is established both through the first theoretical question and through the implementation of the group project;
3. Ability to properly interpret the regulations and to perform estimates in the field of lighting and applied acoustic. This is mainly determined by the implementation of the group project and the report on applied acoustic.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

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