This course aims at providing a deep understanding of the foundations of transport phenomena, specifically involving heat and mass, together with a systematic methodology oriented to the solution of complex problems.

The student widens and deepens his knowledge about transport phenomena (mass, momentum and energy) related to diffusion, advection and radiation with respect to the basics learned during the first cycle.

The student becomes able to:

+ search and consult the relevant technical and scientific literature in order to find information (data, technical features) about processes whose specifications  are only partially assigned;

+ identify the transport phenomena relevant to real specific processes and/or apparatuses;

+ formulate the equations describing transport phenomena at global and local scale;

+ solve the governing equations by means of analytical/numerical methods;

+ analyse and design components and systems for heat and mass transfer (such as heat sinks, radiators, heat exchangers, burners, simple chemical reactors and apparatuses for process industry).

The course includes theoretical lessons and practical classes devoted to solve exercises on fundamental aspects of thermal design and control of equipment and systems.

1. Radiative transfer. Thermal radiation, radiation intensity and derived spectral and total radiation quantities. Blackbody radiation: the Planck’s distribution, the Stefan-Boltzmann’s law, Wien’s displacement laws, band emission. Emission, absorption, reflection and transmission from real surfaces; Kirchhoff’s law; grey surface and selective surface. Solar and environmental radiation; radiators, the greenhouse effect. Radiation exchange between grey surfaces: view factors and their relationships, evaluating radiation exchange between between opaque, diffuse and grey surfaces in an enclosure. Radiation shields. The reradiating surface. Multimode heat transfer. Radiation exchange with participating media. Volumetric absorption. Gaseous emission and absorption.

2. Heat conduction. The Fourier’s law, thermal conductivity. The heat diffusion equation; initial-, boundary- and interface- conditions. Steady-state, one-dimensional solutions; thermal resistances and equivalent circuits. Conduction with uniform and non-uniform, thermal energy generation. Heat transfer from extended surfaces. Approximate one dimensional conduction analysis. Multi-dimensional, steady-state conduction: the conduction shape factor. Transient conduction: lumped-capacity solutions, analytical solutions in one-dimensional slab, one-term approximation; analytical solutions in a semi-infinite medium with constant or periodic temperature boundary condition; thermal waves.

3. Mass diffusion. Fick’s law of diffusion, mass diffusivity. Mass transfer in nonstationary media. Absolute and diffusive species fluxes, evaporation in a column. The stationary medium approximation. The mass diffusion equation, boundary conditions and discontinuous concentrations at interfaces, evaporation and sublimation, solubility of gases in liquids and solids, catalytic surface reactions; mass diffusion with homogeneous chemical reactions. Transient diffusion.

4. Convective heat and mass transfer. The governing equations. Velocity, temperature and concentration boundary layers. The boundary layer (BL) equations for laminar flow; BL similarity parameters; functional form of the solutions. Introduction to turbulence; micro- and macro- scales. The time-smoothed boundary layer equations. Time-smoothed velocity profile near a wall. Eddy viscosity, the Prandtl’s mixing length theory, turbulence models. Forced convection in external flows: heat transfer over flat plate, cylinders, banks of tubes, spheres and bluff bodies. Forced convection inside ducts: the mean velocity and the bulk temperature, the fully developed region and the Graezt problem; laminar and turbulent flow in tubes and channels. Forced convection mass transfer: the Lewis analogy. Free convection: the governing equations for laminar boundary layers under the assumptions; similarity considerations; laminar free convection on a vertical surface; the effects of turbulence; empirical correlations for bodies of various shapes. Free convection within parallel plate channels and enclosures. Combined free and forced convection. Convection mass transfer. Free convection mass transfer. Similarity considerations.

5. Boiling and Condensation. Introduction to the phenomenology of pool/forced convective boiling, and film condensation.

No prerequisites.

Students’ evaluation consists of a written test at the end of the course (no intermediate tests are planned). Written test requires solving, with closed books, two numerical problems and answering three theoretical questions on fundamental aspects of the course; for each problem, score is equally assigned to both formal and numerical solution.

The numerical problems aim at verifying the ability to:

+ sketch the processes occurring in the case study identifying the relevant transport phenomena;

+ write the governing equations and solve them by means of suitable algorithms;

+ analyze and design the assigned components and systems possibly taking missing information from enclosed bibliographic material.

The questions aim at verifying the degree of understanding and depth about transport phenomena and related mechanisms.

After tests have been withdrawn, solution is handed out; after some minutes, the instructor asks each student if he requires the test correction (by default tests are not corrected). No penalization applies for scores lower than 18/30 but larger than or equal to 10/30. The student reporting less than 10/30 will not be allowed to take the following exam belonging to the same session.

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