# Aerothermodynamic Heating

### The Heating Problem

The heating problem consists in evaluating all the relevant terms in the energy equations at the body surface, in order to establish the correct heat transfer rates.

### Stagnation Temperatures

Figure 1: Bow shock and heating process

Figure 2: Bow shock in front of wedge at M = 1.8

#### Temperature Limits

The current limit is above 1300 °K. The skin of the vehicle can be covered by material (for exemple, silicon), that melts and evaporates (ablation process), thus absorbing part of the heat.

1. Supersonic Vehicles
Thermodynamic heating in supersonic jet transport (Concorde, M=2.0÷2.4) is estimated at about 700 °K. Maximum heating rates are reported for ballistic missiles, because of their steep flight path toward the lower atmosphere.

2. Hypersonic Vehicles
The atmospheric entry of a spacecraft has instead the maximum total heat load because of its longer trajectory in the high temperature corridor. Some interesting data are the following: 1600 °K for the Space Shuttle in atmospheric re-entry; over 7000 °K for the Apollo capsule and intercontinental ballistic missiles (ICBM) in atmospheric re-entry.

See Table of Skin Temperatures for more data.

The temperature and the pressure field are useful to identify the similitude conditions at supersonic and hypersonic speeds for simulation in hyper-velocity tunnels.

### Cooling Requirements

In most of the cases listed in Table 1 the heating is so strong that cooling is made necessary to protect the structure. The maximum temperature that the skin of a space vehicle or ballistic missile can reach is a technological limit, which may move upward with further progress in material science and configuration design.

Blunt Nose. An important parameter is the geometry of the nose. A basic result of hypersonic theory shows that the heat transfer at the nose is inversely proportional to the radius of the nose, Fig. 1.

### Shooting Stars

Another case, though not technological, is the atmospheric penetration of meteors, which occurs as speeds estimated between 20 km/h and 70 Km/s. The meteors look as luminous objects (shooting stars) because of the high temperature reached. Their vaporization starts at temperatures around 3500 °K. Small meteors disintegrate before reaching the lower atmosphere.

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