# Spacecraft thermal design

Because spacecraft operate in the vacuum of space, convection and conduction exchanges with the environment are not possible, and radiative exchange is the only available mechanism for energy transfer. Spacecraft are exposed to solar energy except when in the Earth's shadow, so they generally absorb solar energy through part of their orbit unless they are actively oriented to minimize solar absorption. Controlling the temperature of a satellite requires a careful balance between absorbed and emitted radiation.

Another application of radiative heat transfer for spacecraft is in the design of radiators to reject waste heat. The net rate of heat rejection per unit area, q", is the difference between the emitted and the absorbed radiative fluxes. To minimize the absorbed flux, the radiator can be oriented edge-on to the sun, so that the energy absorbed comes only from the Earth and from space. Space itself has an apparent background temperature of 4K, and radiation from this source can be neglected. The heat rejection rate from the space radiator is

$q = q''A = \left( {2\varepsilon \sigma T_{rad}^4 - {{q''}_{Earth}}} \right)A\qquad \qquad(1)$

Note that the factor of two enters the equation because both sides of the radiator emit energy, but only one side is exposed to the Earth's radiation. If the spacecraft is far from Earth or other planets so that q''Earth = 0, then the radiator area required to reject a certain rate of energy is

$A = \frac{q}{{2\varepsilon \sigma T_{rad}^4}}\qquad \qquad(2)$

For a given radiator temperature T, choosing a radiator coating with the largest possible value of emissivity, ε , will allow the smallest possible radiator area. Clearly, a higher heat rejection temperature can greatly reduce the required area for heat rejection because of the fourth-power relation.

## References

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.