In classical spacecraft design, the balance of radiation and internal dissipation is essentially the only issue, since there are no conductive or convective paths for heat transfer in free space. During a probe or lander's cruise through space to its target, this is also the case. Furthermore, in some environments such as the surface of the Moon or an asteroid (and even to a small extent, Mars), the radiative transfer pathways may be dominant and thus the surface radiative properties are crucial to maintaining acceptable temperatures.
The key properties for radiative balance are visible reflectance and thermal emissivity. For a given wavelength, the properties of emissivity and reflectivity are complementary, that is they sum to unity - any radiation that is not emitted or absorbed at the surface is reflected. However, usually the dominant illumination has a solar spectrum, peaking at around 0.5 mm, while the emission spectrum of a black body at typical spacecraft temperatures of 200 to 350 K has a peak at 10 mm. Thus, the 'thermal emissivity' and 'visible reflectivity' do not apply to the same wavelength and can therefore be considered approximately independent parameters.
These two parameters are usefully considered on a map (see Figure 8.1). Materials on the upper right part of the map (high emissivity, high reflectivity) will tend to be cold, since they efficiently reject heat in the infrared, while avoiding the absorption of sunlight. Similarly, materials near the origin will run hot.
In the thermal IR, the Earth's atmosphere has a brightness temperature of around 250 K, and this is the appropriate value for Tp, i.e. the temperature of the atmosphere at the altitude at which the thickening atmosphere becomes opaque, close to the tropopause (indeed the relatively uniform appearance of the planet at these wavelengths, independent of time of day, etc. is why Earth horizon sensors on satellites usually operate in the IR).
Thermal control of landers and entry probes 1
Blackened copper Black paint
Figure 8.1. Map of radiative properties of surface coatings.
On or near the surface of a planet with a thick atmosphere, the incident flux F may have to be reduced due to absorption and scattering in the atmosphere. If the thermal optical depth of the atmosphere below is small, then Tp should be the surface temperature. If the atmosphere is thick enough for heat radiating down from the atmosphere above the probe to be significant (which might be considered another term similar to the f1 term above) then it is likely that convective heat transfer will be even stronger.
Formally, the convective term has the form +4xr K(Ta — T) where K is a heat transfer coefficient between the atmosphere and the spacecraft, and Ta denotes the ambient temperature. The value of K will depend on the atmospheric density, and on windspeed and turbulence. This term is important on Mars, and can be difficult to predict (since the boundary layer on Mars is quite thick, so there is a strong windspeed and temperature gradient near the surface - thus the heat transfer will depend strongly on how much the vehicle projects above the surface). Coefficients of the order of 1Wm—2K—1 are not untypical of afternoon conditions. However, in thick atmospheres this term is so large that the probe surface may be considered to be the same as the ambient atmosphere, and the thermal design must focus on isolating the interior of the probe from its surface.
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