ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| TRANSPORT PHENOMENA IN MATERIALS | ING-IND/22 | LEZIONI | 48 |
|
The student will get the necessary knowledge of the fundamentals of transport of energy, mass, species and momentum according to chemical engineering perspective, seeking for unification of the different transport mechanisms. The student will learn the constitutive equations of convective and diffusive fluxes as well as the conservation equations in order to model physical systems and get the distribution of species, temperature and velocity fields. The class gives some practical examples and ready-to-use equations to grasp the ruling behaviours of transport phenomena and the relevant dimensionless quantities, building the fundamentals for more advanced applications. Specific tutorials will make use of spreadsheets and numerical codes to assist the computation and strengthen the numerical skills. The class is intended to homogenise the different backgrounds of the students.
During the final oral exam, the level of knowledge will be assessed through quantitative exercises to be set and solved by the candidate. The exercises will cover the key concepts of transport of heat and species, mimicking those presented during the course and going beyond them. The capability of the candidate of evidencing the unification of transport phenomena and the framework of the mathematical solutions, making parallelisms among different topics, is appreciated. The proper technical terminology and the capability to translate the concepts for different applications is assessed too.
At the end of the class the student:
During the final exam, practical exercises will be given to assess the student capability to set up their correct implementation. No specific projects or homeworks are required to be admitted to the final exam, although the candidate is free to present an application that she/he prepared.
The student will develop a proper insight and a unified viewpoint on the conservation of mass, species, energy and momentum, building an engineering and physics approach to the mathematical solution, even in applications not discussed during the class.
During the oral exam, the examiner will assess the insight gained by the student in her/his capability to apply the concepts beyond what discussed during the class. The mastery of the subject will be assessed by asking connections among different fields and by investigating the understanding of the physical fundamentals.
Derivatives and integrals, algebra and matrix operations, basic knowledge of ordinary and partial differential equations.
Delivery is via the on-line platform MS Teams. Attending lectures is adviced.
Meetings with the teacher must be organised directly via email and through the e-learning platform.
Learning activities:
attending lectures
attending and carrying out tutorials by actively participating to them
be involved in discussions in class
Teaching methods: lectures + class tutorials
INTRODUCTION. Local equilibrium, definition of convective and diffusive fluxes, materials transport properties, dimensionless numbers (Reynolds, Prandtl, Schmidt, Peclet, etc), origin of diffusive equations & random walk. MICROSCOPIC GOVERNING EQUATIONS. Derivation of microscopic balance equations (general, mass, species, internal energy, momentum), Eulerian and Lagrangian approaches, tensor notation and operators. STATIONARY HEAT CONDUCTION. Governing equation and boundary conditions, Newton law of cooling, Biot and Nusselt numbers, unidirectional heat conduction (linear, cylindrical and spherical coordinates), effective thermal conductive of composite materials, heat conduction with heat source. TIME-DEPENDENT HEAT CONDUCTION. Step response in a semi-infinite slab, self-similar solutions, response to heat pulse. FUNDAMENTALS OF MATERIAL TRANSPORT. Species fluxes and velocities, convection vs diffusion, mass vs molar basis, constitutive equations of diffusion (Fick law), balance equations and boundary conditions. STATIONARY MATERIAL TRANSPORT. Diffusion in a stagnant film, effective mass transport coefficient, Sheerwood number, simplifications in the dilute limit, diffusion with heterogeneous reaction, diffusion with homogeneous reaction, Thiele modulus and effectiveness factor, scaling of regimes (kinetic, internal and external). TIME-DEPENDENT MATERIAL TRANSPORT. Unidirectional diffusion in semi-infinite slab with Robin-type boundary condition (Crank’s solution). MOMENTUM TRANSPORT. Laminar and turbulent flows, velocity profiles in a pipe, non-Newtonian fluids, flow in porous media, Knudsen effects. TUTORIALS. Use of Microsoft Excel and codes in Comsol Multiphysics: isotope exchange, baking of a ceramic brick with phase transformation. SEMINARS. Transport phenomena in lithium-ion batteries.
Lecture notes provided by the teacher, which contain indications of specific textbooks (not strictly necessary), among which:
Mauri, Transport Phenomena in Multiphase Flows, Springer 2015, ISBN: 978-3-319-15792-4
R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena 2nd ed., Wiley 2002, ISBN: 0-471-41077-2
Crank, The Mathematics of diffusion 2nd ed., Clarendon Press 1975, ISBN: 0-19-853344-6
No variations for non-attending students
The global assessment of the learning outcomes is made with an oral exam (1h on avearge). The exam consists of 2-3 practical exercises to be implemented and solved by the candidate, covering the key subjects of the class (transport of species and heat, steady-state and transient solutions). Based on the exercises, the general knowledge of the meaning of dimensionless quantities, asymptotic behaviours, correlations among different fields, will be assessed. The correct implementation of the practical exercises is a necessary criterium to succeed in the exam.
Not required
MS Team: 727II - TRANSPORT PHENOMENA IN MATERIALS [WNT-LM] a.a.20/21
Code for MS Teams: l7pwo7k
