Thermodynamics and Heat Transfer

Thermodynamics and Heat Transfer
2 YEAR 2 semester 9 CREDITS
Prof. Paolo Coppa 2019-20
Michela Gefulsa – 

2021-22 to 2023-24

  Code: 8039146


LEARNING OUTCOMES: The course aims to provide students with the basic principles, physical laws, and applications of thermodynamics, thermo-fluid dynamics, and heat transfer, with the dual purpose of preparing them to afford more applicative courses and using the acquired knowledge for design and sizing simple components and thermal systems.


Students will have to understand the physical laws of applied thermodynamics and heat transfer, and understand the structure and operation of the simplest components and systems. They will also demonstrate that they have acquired the basic methodologies for verifying and designing the studied devices.


Students must be able to afford courses for which this course is preparatory (for example Thermotechnique, or Machines) and to size or verify simple components and systems, topics covered by the course, such as air conditioning systems, engine systems, fins and heat exchangers.


Students must assume the autonomous capacity to face the subsequent studies for which this course is preparatory and to draw up simple projects of thermal systems that use the studied components. They will also need to be able to evaluate projects written by other parties, checking that the project requirements are satisfied.


Students must be able to illustrate in a complete and exhaustive way the acquired information, the results of their study and of their project activity, also through the normally used means of communication (discussion of the results obtained, report on the performed activity, PowerPoint presentations, etc.).


Students must be able to apply the physical laws underlying the studied phenomena, and to face further studies that use the acquired knowledge. They will have to be able to expand the already owned information through the analysis of technical-scientific literature and to modify their curricula choosing future knowledge to be acquired on the base of their knowledge and tendency.


  • Fundamental laws of thermodynamics: zeroth law, first law for open and closed systems, second law, entropy definition and Clausius integral, Maxwell equations, Claperyron equation
  • Thermodynamic diagrams: P-v, T-s, H-s, P-h
  • Thermodynamic cycles for close and open systems: engine cycles: Otto Cycle, Diesel cycle, Joule Brighton cycle, Rankine and Hirn cycle, refrigeration cycle
  • Air and steam mixtures, design of conditioning air systems
  • Basic laws of fluid dynamics: Bernoulli equation, the motion of fluids in ducts, major and minor pressure drops, dimensional analysis for turbulent flow friction factor.
  • Heat transfer mechanisms. Conduction: Fourier law, basic conduction heat transfer equation, solution for simple geometries with and without heat generation, lumped parameter problems, cooling fins. Convection: dimension analysis for forced and free convection. Radiation heat transfer: basic laws of radiation, radiation exchanges between black bodies and grey bodies, configuration factors, electric analogy. Heat exchangers: types, size problem and rate problem.

Mechanics of Materials and Structures

Mechanics of Materials and Structures
2 YEAR 2 semester 9 CREDITS
Prof. Micheletti Andrea
Prof. Artioli Edoardo

2019-20 to 2022-23

  Code: 8037955


LEARNING OUTCOMES: The goal of this course is to provide the student with basic knowledge of the mechanics of linearly elastic structures and of the strength of materials. By completing this class successfully, the student will be able to compute simple structural elements and reasonably complex structures.

KNOWLEDGE AND UNDERSTANDING: At the end of this course, the student will be able to:

  • compute constraint reactions and internal actions in rigid-body systems and beams subjected to point/distributed forces and couples
  • compute centroid position and central principal second-order moments of area distributions
  • understand the formal structure of the theory of linear elasticity for both discrete and continuous systems (beams and 3D bodies)
  • analyze strain and stress states in 3D bodies
  • compute the stress state in beams subjected to uniaxial bending, biaxial bending, eccentric axial force
  • understand the behavior of beams subjected to shear with bending and torsion
  • understand how to compute displacements/rotations in isostatic beam systems, how to solve statically underdetermined systems, how to apply yield criteria, and how to design beams against buckling

APPLYING KNOWLEDGE AND UNDERSTANDING: The student will apply the knowledge and understanding skills developed during the course to the analysis of practical problems. This includes the analysis of linearly elastic structures and structural members in terms of strength and stiffness.

MAKING JUDGEMENTS: The student will have to demonstrate his awareness of the modeling assumptions useful to describe and calculate structural elements, as well as his critical judgment on the static response of elastic structures under loads, in terms of stresses, strains, and displacements.

COMMUNICATION SKILLS: The student will demonstrate, mostly during the oral test, his capacity of analyzing and computing the static response of linearly elastic structures, as well as his knowledge of the underlying theoretical models.

LEARNING SKILLS: The student will get familiar with the modeling of structures and structural elements in practical problems, mostly during the development of his skills for the written test. This mainly concerns discrete systems, beams, and three-dimensional bodies.


  • Review of basic notions of vector and tensor algebra and calculus.
  • Kinematics and statics of rigid-body systems.
  • Geometry of area distributions.
  • Discrete linearly elastic systems, static-kinematic duality, solution methods.
  • Strain and stress in 3D continuous bodies and beam-like bodies.
  • Virtual power and virtual work equation for discrete systems, beams, and 3D bodies.
  • One-dimensional beam models: Bernoulli-Navier model, Timoshenko model, constitutive equations, governing differential equations.
  • Constitutive equation for linearly elastic and isotropic bodies, material moduli.
  • Hypothesis in linear elasticity, equilibrium problem for linearly elastic discrete systems, beams, and 3D bodies.
  • Three-dimensional beam model: the Saint-Venant problem, uniaxial and biaxial bending, eccentric axial force, shear and bending, torsion.
  • Elastic energy of beams and 3D bodies, work-energy theorem, Betti’s reciprocal theorem, Castigliano’s theorem.
  • Yield criteria (maximum normal stress, maximum tangential stress, maximum elastic energy, maximum distortion energy).
  • Buckling instability, bifurcation diagrams, load and geometry imperfections, Euler buckling load, design against buckling.
  • Basic notions on the finite element method and structural analysis software.

Feedback Control Systems

Feedback Control Systems
2 YEAR 2 semester 9 CREDITS
Prof. Cristiano Maria Verrelli 2019-20 to 2023-24
  Code: 8037953


The theory of differential equations is successfully used to gain profound insight into the fundamental mathematical control design techniques for linear and nonlinear dynamical systems.

Students should be able to understand and use the theory of differential equations and systems theory, along with related mathematical control techniques.

Students should be able to design feedback controllers for linear (and even nonlinear) dynamical systems.

Students should be able to identify the specific design scenario and to apply the most suitable techniques. Students should be able to compare the effectiveness of different controls, while analyzing theoretical/experimental advantages and drawbacks.

COMMUNICATION SKILLS: Students are expected to be able to read and capture the main results of a technical paper concerning the topics of the course, as well as to effectively communicate in a precise and clear way the content of the course. Tutor-guided individual projects (including Maple and Matlab-Simulink computer simulations as well as visits to labs) invite intensive participation and ideas exchange.

Being skilled enough in the specific field to undertake following studies characterized by a high degree of autonomy.


Linear systems
The matrix exponential; the variation of constants formula. Computation of the matrix exponential via eigenvalues and eigenvectors and via residual matrices. Necessary and sufficient conditions for exponential stability: Routh-Hurwitz criterion. Invariant subspaces. Impulse responses, step responses and steady state responses to sinusoidal inputs. Transient behaviors. Modal analysis: mode excitation by initial conditions and by impulsive inputs; modal observability from output measurements; modes which are both excitable and observable. Popov conditions for modal excitability and observability. Autoregressive moving average (ARMA) models and transfer functions.
Kalman reachability conditions, gramian reachability matrices and the computation of input signals to drive the system between two given states. Kalman observability conditions, gramian observability matrices and the computation of initial conditions given input and output signals. Equivalence between Kalman and Popov conditions. Kalman decomposition for non-reachable and non-observable systems.
Eigenvalues assignment by state feedback for reachable systems. Design of asymptotic observers and Kalman filters for state estimation of observable systems. Design of dynamic compensators to stabilize any reachable and observable system. Design of regulators to reject disturbances generated by linear exosystems.
Introduction to adaptive control. Introduction to tracking control. Minimum phase systems and Proportional Integral Derivative (PID) control.
Bode plots. Static gain, system gain and high-frequency gain. Zero-pole cancellation. Nyquist plot and Nyquist criterion. Root locus analysis. Stability margins. Frequency domain design. Realization theory.

Introduction to nonlinear systems Nonlinear models and nonlinear phenomena. Fundamental properties. Lyapunov stability. Linear systems and linearization. Center manifold theorem. Stabilization by linearization.

Analogue Electronics

Analogue Electronics
2 YEAR 2 semester 9 CREDITS



Paolo Colantonio


Code: 8037954




  • Classification of electrical systems and requirements.
  • Analysis of transitory and frequency behavior.
  • Distortion in electronic systems and Bode diagrams.
  • Diode semiconductor devices and circuit applications: clipper, clamper, peak detector, etc. Bipolar Junction and Field-Effect Transistors.
  • Biasing techniques for Transistors. Amplifiers classification, analysis and circuit design.
  • Frequency response of single and cascaded amplifiers.
  • Differential amplifiers and Cascode.
  • Current mirrors.
  • Feedback amplifiers and stability issues. Power amplifiers.
  • Operational amplifiers and related applications.
  • Oscillator circuits. Integrated circuits and voltage waveform generators.

Physics II

Physics II
2 YEAR 1 semester 9 CREDITS
Prof. Vittorio Foglietti

2019-20 to 2022-23

Vittorio Foglietti (1cfu)

Simone Sanna (4cfu)

Daniele di Castro (4cfu)

  Code: 8037952


LEARNING OUTCOMES: Learning the basic elements of Electromagnetism and fundamental physical principles of quantum mechanics.

Knowledge of the basic principles of electromagnetism and quantum mechanics useful for the own field of study. Understanding of advanced books on the arguments treated during the course.

Capacity to develop autonomously basic conceptual ideas using arguments treated during the course.

Capacity to evaluate autonomously ideas or project using the knowledge acquired in the course.

Capacity to share informations and ideas on the basis of knwoledge acquired in the course.
Comprehension of specific problems and relative solutions proposed.

The knowledge acquired in the course must be of help for the student in future courses, improving the capacity of autonomous learning.


1) Electric Charge and Electric Field : Conductors, Insulators, and Induced Charges.
Coulomb’s Law. Electric Field and Electric Forces. Electric Field Lines. Charge and Electric Flux, Gauss’’ s Law. Charges on Conductors.
2) Electric Potential: Electric Potential Energy, Electric Potential, Equipotential Surfaces, Potential Gradient. Definition of electric dipole. Approximated formula for the electric potential of a dipole at large distances.
3) Capacitors and Capacitance. Capacitors in series and parallel configuration. Electrostatic Potential Energy of a Capacitor. Polarization in Dielectrics. Induced Dipoles. Alignment of Polar Molecules. Electric Field inside a dielectric material. Relative dielectric constant. Capacitors with dielectric materials.
4) Electric current, Vector current density J, Resistivity (ρ) and conductivity ( σ) of materials, Ohm’s law in vector and scalar form, Resistors and resistance, Microscopic theory of electric transport in metals (Drude model). Differences between thermal velocity and drift velocity of charge carriers. Thermal coefficient of resistivity for metal and semiconductors. Resistors in parallel. Kirchhoff current law and the conservation of charge. Resistors in series. Kirchhoff voltage law ( KVL) and the conservative nature of electric field. Resistor and capacitor in series. Charging a capacitor. Solving the equation for current and voltage in RC circuits, time constant.
5) Introduction to magnetism, historical notes. Magnetic Force on a moving charged particle in a Magnetic Field. Definition of the vector ( cross ) product. Vector product expressed by the formal determinant and calculated by Sarrus Rule. Thomson’s q/m experiment and the discovery of the electron. Magnetic force on a current carrying conductor. Local equation for the magnetic force, the second formula of Laplace. Introduction to current loops, the torque. Force and Torque on a current loop in presence of a constant magnetic field. The magnetic dipole moment. Torque in vector form. Stable and unstable equilibrium states. Equivalence between a magnetic dipole of a current loop and the dipole of a magnet. Potential energy of a dipole moment in a magnetic field. Force exerted on a magnetic dipole in a non-uniform magnetic field. Working principle of a dc motor. Generalization of a magnetic dipole to current loops with irregular area. Magnetic dipole of a coil consisting of n loops in series. The Hall effect.
6) Historical introduction to the Biot Savart Laplace equation. Electric current as sources of magnetic field, the current element. The Biot Savat Laplace (BSL) equation. BSL equation for an infinitely long wire with an electric current flow. The flux of the magnetic field B. The Gauss Law for the magnetic field. Forces acting on wires with electric current flow. Magnetic field on the axis of a current loop and a coil. Ampere Circuital Law. Definition of a Solenoid. Magnetic field from a long cylindrical conductor. Magnetic field from a toroidal coil. The Bohr magneton. Magnetic materials. Paramagnetism, Diamagnetism, Ferromagnetism.
7) Magnetic induction experiments. Faraday Law. Lenz Law. Flux swept by a coil and Motional Electromotive Force. Induced Electric Field. Displacement current. The four Maxwell equations in integral form. Symmetry of the Maxwell equation. Self induction. Inductors. Inductor as circuit element.Self inductance of a coil. Magnetic Field Energy. The R-L circuit. The LC circuit. The RLC series circuit.
8) The electromagnetic waves. Derivation of EM waves from Maxwell Equation. The electromagnetic spectrum. Electromagnetic energy flow and the Poynting vector. Energy in a sinusoidal wave. Electromagnetic momentum flow. Standing Electromagnetic waves.
9) Light waves behaving as particles. The photocurrent experiment. Threshold frequency and Stopping Potential. Einstein’s explanation of Light absorbed as “Photons”. Light Emitted as Photons: X-Ray Production. Light Scattered as Photons: Compton Scattering.
10) Interference and diffraction of waves. The Wave Particle Duality. De Broglie wavelength. The x-ray diffraction from a crystal lattice, the Bragg’s Law. The electron diffraction experiment of Davisson and Germer. The double slit experiment with electrons. Waves in one dimension: Particle Waves, the one-dimensional Schrödinger equation. Physical interpretation of the Wave Function. Wave Packets. Uncertainty principle. Particle in a box. Energy-levels and wave functions for a particle in a box. The tunneling effect.