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First Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)


Principles governing mass, momentum, and energy transfer in chemical engineering applications are tackled in this course. Students will learn how to apply local balances to solve problems in systems where spatial (up to three dimensional) and temporal changes of concentration, velocity/pressure and/or temperature are involved. Analytical methods are used, when possible, to quantify heat, mass and momentum fluxes.

Acquiring knowledge and understanding
During this course students will acquire knowledge and understanding which make them able to:
- apply the principles governing mass, momentum and energy transfer for a wide variety of chemical engineering applications
- identify the boundary conditions to be associated to the differential equations deriving from the application of local balances
- evaluate the relevant spatial (multidimensional) and temporal dependence of concentration, velocity/pressure and/or temperature as well as the related fluxes
- analyze critically the obtained concentration, temperature, and velocity/pressure as well as related fluxes spatial and temporal profiles

Applying knowledge and understanding
The course is organized to have theoretical aspects always coupled with numerous practical problems, characterized by progressively increasing complexity, that have to be solved in class. This fact prompt students to participate actively in the identification of the problems solution.

Making informed judgments and choices
The study of transport phenomena during the “Principle of Chemical Engineering and Processes” course helps students to develop their capability to evaluate critically the obtained results, to highlight the most relevant outcomes and to make appropriate approximations in complex problems.

Communicating knowledge and understanding
During the practical written tests foreseen in the course as well as the final examination (oral test), students have the chance to demonstrate their capability to communicate the obtained results and underline the encountered problems.

Capacities to continue learning
The basic knowledge provided during the “Principle of Chemical Engineering and Processes” course makes students able to handle autonomously new problems that are not examined in class.


Knowledge of chemistry, physics, thermodynamics, calculus and fundamentals of transport phenomena (bachelor level).


Consolidations of elements of Transport phenomena acquired at the bachelor level (6h Lecture + 3h Practical):
Molecular transport of mass, heat and momentum. Mass, heat and momentum macroscopic balances.

Transport in laminar flow or in solids, in one dimension (3h Lecture + 3h Practical):
Velocity distribution in laminar flow:
Shell momentum balances; boundary conditions; flow in a falling film; flow through a circular tube. Flow through an annulus. Adjacent flow of two immiscible fluids. Creeping flow around a solid sphere.

Temperature distributions in solids and in laminar flow (6h Lecture + 3h Practical):
Shell energy balances; boundary conditions; heat conduction with an electric heat source; heat conduction with a nuclear heat source; heat conduction with a viscous heat source; heat conduction with a chemical heat source; heat conduction in a cooling fin; forced convection; free convection.

Concentration distributions in solids and in laminar flow (6h Lecture + 4h Practical):
Shell mass balances. Boundary conditions. Diffusion through a stagnant gas film; Diffusion with homogeneous or heterogeneous chemical reaction. Diffusion into a falling liquid film: forced convection mass transport.
Transport in an arbitrary continuum
The equation of change for isothermal systems (3h Lecture):
The equation of continuity. The equation of motion. The equation of mechanical energy.

The equation of change for non-isothermal systems (4h Lecture + 2h Practical):
The equation of energy. The equations of motion for forced and free convection in non-isothermal flow.

The equation of change for multicomponent systems (6h Lecture + 3h Practical):
The equation of continuity for a binary mixture. The multicomponent equations of change in terms of the fluxes. The multicomponent fluxes in terms of transport properties.

Transport in laminar flow or in solids, with two independent variables
Velocity distributions with more than one independent variable (3h Lecture + 2h Practical):
Unsteady viscous flow. Boundary-layer theory: flow near a wall suddenly set in motion; flow near a leading edge of a flat plate.

Temperature distribution with more than one independent variable (2h Lecture):
Unsteady heat conduction in solids. Steady heat conduction in laminar flow of a viscous fluid. Boundary layer theory: heat transfer in forced convection along a heated flat plate.

Concentration distributions with more than one independent variable (6h Lecture + 3h Practical):
Unsteady diffusion. Boundary-layer theory for mass transfer.

Transport in turbulent flows
Velocity distributions in turbulent flow (6h Lecture + 2h Practical):
Fluctuations and time-smoothed quantities. Time-smoothing of the equations of change for an incompressible fluid. Semi-empirical expressions for the Reynolds stresses. Prandtl mixing length. Logarithmic distribution law for tube flow.

Temperature distribution in turbulent flow (1h Lecture):
Temperature fluctuations and time-smoothed temperature. Time –smoothing of the energy equation.

Concentration distribution in turbulent flow (2h Lecture):
Concentration fluctuations and time-smoothed concentration. Time –smoothing of the equation of continuity for one component.

Energy transport by radiation (6h Lecture + 5h Practical)
The spectrum of electromagnetic radiation. Absorption and emission at solid surfaces. Planck’s distribution, Wien’s displacement and Stefan-Boltzmann laws. Radiation between black bodies at different temperatures. View factors. Radiation between non-black bodies at different temperatures.

Teaching Methods

The course (90 hours) is shared in lectures (60 hours) and practical classes (30 hours). The theory related to the development of mass, energy and momentum equation balances will be considered during lectures. In addition, the solution of practical problems will be also associated to the theoretical part. During this stage, the lecturer will involve the students in the examination of practical problems, to verify the level of their acquired knowledge and understanding relative to the subject under discussion. The latter one will be better evaluated during practical classes, to be performed either in group or singularly, to stimulate students to collaborate or handle autonomously, respectively.

Verification of learning

The examination consists of an oral test during which students have to solve problems involving mass, energy and momentum transport phenomena, which are often combined. Students have to demonstrate to be able to apply the required, generally multidimensional, local balance equations as well as to identify the corresponding boundary conditions.
This feature represents the mandatory requirement to pass the exam.
Depending upon the problem, the latter one have to be solved analytically after appropriate approximations are taken into account.
The student ability to analyze critically the obtained results will be considered as the key parameter to gain scores progressively higher than the minimum required to pass the exam. In particular, the maximum score (30/30 cum laude) will be achieved by students that, relatively to the specific problems faced during the exam, will demonstrated to have acquired an excellent knowledge of the main topics tackled during the course.


Suggested textbook:
“Fenomeni di Trasporto”, R. Byron Bird, Warren E. Stewart and Edwin N. Lightfoot, Casa Editrice Ambrosiana, Milano.

Additional textbooks for integrations and further informations
-"Elementi di fenomeni di trasporto" R. Mauri, Plus- Pisa University Press
-“I Principi delle Operazioni Unitarie”A.S. Foust, L.A. Wenzel, C.W. Clump, L. Maus, L.B. Andersen, Ambrosiana - Milano.

More Information

Other than the suggested bibliography reported above, additional textbooks and other bibliography will be provided to the students relative to some of the aspects examined and discussed during the course.

Questionnaire and social

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