Basics of Aerothermodynamics

Chapter 3: The Thermal State of the Surface

The "thermal state of a surface" was introduced in Section 1.4. It was shown that a distinction is appropriate between "thermal loads" and "thermal surface effects". In this chapter we discuss in detail the thermal state of a vehicle surface, which can be an external or an internal surface, past which a highspeed flow happens. External surfaces of hypersonic flight vehicles usually are radiation cooled. Basics of surface thermal radiation cooling are treated in Section 3.2. With simple approximations we try to obtain a basic understanding of the aerothermodynamics of radiation-cooled surfaces. Results of computations with numerical methods are used to illustrate the findings. A case study, Section 3.3, gives a detailed account. Thermo-chemical and especially viscous-flow thermal-surface effects as such are treated in Chapters 5, 7, 8, and 9. Thermal loads on structures are not a central topic of this book.

3.1 Definitions

The thermal state of a surface is governed by at least one temperature ( T), and at least one heat flux q (heat transported through an unit area per unit time). Hence both a surface temperature and a temperature gradient, respectively a heat flux, must be given to define it. Large heat fluxes can be present at low surface temperature levels, and vice versa. If a surface is radiation cooled, at least three different heat fluxes at the surface must be distinguished. In the slip-flow regime, which basically belongs to the continuum regime, two temperatures must be distinguished at the surface, Sections...

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