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# Heat Transfer and Thermal Analysis

Synthetic program:il corso fornisce le conoscenze specifiche e gli strumenti operativi per affrontare problemi di scambio termico di media complessità nel campo della propulsione e del controllo termico di componenti e sistemi di interesse aeronautico e spaziale. Per la soluzione di problemi realistici di raffreddamento verrà introdotto l'uso di software specifici.

1. Heat conduction

Fourier law and thermal conductivity. Heat diffusion equation; initial conditions, boundary conditions and interface conditions. Steady-state conduction: one-dimensional solutions in Cartesian, cylindrical and spherical coordinate systems; thermal resistances and equivalent circuits. Transient conduction: lumped parameter method with convection and radiation boundary conditions, also in presence of a heat source; simplified one-dimensional cases.

2. Convective heat transfer

Governing equations, dimensionless version of the thermo-fluid dynamics equations and dimensionless groups of interest for convection. Free and forced convection in external flow: laminar and turbulent boundary layers, micro- and macro- scales, velocity profiles; some relevant heat transfer correlations for different geometries. Forced convection inside ducts: bulk temperature, logarithmic mean temperature difference, fully developed region and Graetz problem; some relevant heat transfer correlations. Boiling and condensation: vaporization; introduction to capillary and interface phenomena; metastable states; pool boiling, the boiling curve, critical and minimum heat fluxes, factors affecting the boiling curve; introduction to two-phase flow, forced-convection boiling inside tubes; film condensation on vertical flat plates and inside/outside tubes, dropwise condensation.

3. Radiative transfer

Introductory concepts about radiation and interactions between radiation and matter. Thermal radiation, radiation intensity, directional, spectral and total quantities, irradiation and radiosity. Blackbody radiation: Planck distribution, Stefan-Boltzmann law, Wien displacement law, band emission. Emission, absorption, reflection, transmission for real, diffuse and gray emitters; selective surfaces; Kirchhoff law. Radiation exchange between gray surfaces, view factors and their relationships, exchange between gray surfaces in an enclosure. Radiation in gases: emission, absorption, scattering. Solar and environmental radiation.

4. Thermal analysis

4.1 Thermal modeling

Multi-node lumped parameter approach: nodes, networks, resistances. Finite difference and finite volume methods: overview about the methods, mesh types, boundary conditions, discretization schemes and solution strategies, examples of application using commercial or open source software. Ray-tracing/radiosity algorithms and Monte Carlo methods for radiation. Design of heat exchangers and extended surfaces.

4.2 Thermal control

Temperature and heat transfer control. Operating, storage and survival limits. Internal and external exchanges and thermal sources for the different mission/spacecraft types; major issues; modeling and design strategies to implement a thermal control system; description of the most used devices: coatings/clothings/MLI, radiators, first/second surface mirrors, shields, thermal fillers/doublers/washers, cold plates, vapour chambers, heat pipes, heaters, other devices and systems.

## Lecture Notes

### Complete course:

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## Exercises

### Complete course:

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Digital notes | Collection of exercises | 2014/2015 |

Digital notes | Collection of exercises | 2013/2014 |

### Divided by topic:

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Digital notes | Conduction | 2018/2019 |

Digital notes | Convection | 2018/2019 |

Digital notes | Radiation | 2018/2019 |

### Other:

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## Exams

### First partial exam:

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### Second partial exam:

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### Full exam:

### Oral exam:

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### Multiple choice test:

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Text | 14/01/2022 |

Solution | 14/01/2022 |

Text | 26/08/2021 |

Solution | 26/08/2021 |

Solution | 22/07/2021 |

Text | 22/07/2021 |

Text | 02/07/2021 |

Solution | 02/07/2021 |

### Other:

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## Other

### Laboratory:

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### Projects:

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### Presentations:

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### Collections of notes, exercises or exams:

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Raccolta domande teoriche |

### Tables:

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Esempio parte a crocette |

## Live

Quick daily notes, exercises and audio recordings. Files will be approved on priority but deleted after 365 days. 2 points will be assigned by default.

### Quick contents:

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