Thermal control

Draft

There is no air. Convection does not exist, conduction only moves heat within the structure, and the sole path out of the vehicle is radiation to deep space. That single constraint determines the entire subsystem.

The balance

At equilibrium, absorbed plus dissipated equals emitted:

Spacecraft heat balance

\alpha\left(Q_{\text{solar}} + Q_{\text{albedo}} + Q_{\text{IR}}\right) + Q_{\text{internal}} = \varepsilon\sigma T^4 A_{\text{rad}}

The external terms and the surface property ratio $\alpha/\varepsilon$ are covered in The space environment. What concerns the subsystem designer is the right-hand side, because that is the only term that removes heat.

Radiator sizing

Rearranging for the area needed to reject a given dissipation to deep space:

A = \frac{Q}{\varepsilon\sigma\left(T^4 - T_{\text{sink}}^4\right)}

The fourth power is the governing fact of the subsystem, and it cuts both ways.

Radiator temperature	Rejection at $\varepsilon = 0.85$	Area per kW
250 K (−23 °C)	188 W/m²	5.3 m²
300 K (27 °C)	390 W/m²	2.6 m²
350 K (77 °C)	723 W/m²	1.4 m²
400 K (127 °C)	1234 W/m²	0.8 m²

Raising the rejection temperature from 250 K to 350 K cuts radiator area by almost four. This is why running electronics warm is thermally advantageous and why cryogenic instruments are so expensive in area: rejecting heat at 80 K requires roughly a thousand times the area of rejecting it at 300 K, which is why nothing rejects heat at 80 K directly and cryogenic systems instead pump heat up to a higher temperature first.

The 2.6 m² per kW at room temperature is worth committing to memory. It is the number that bounds orbital data centres, where thermal rejection rather than power generation is the binding constraint.

Passive control

Passive means no moving parts and no power. It is always preferred where it suffices.

Surface finishes: The alpha over epsilon ratio is selected per surface. Second-surface silvered Teflon at 0.10 for radiators, white paint at 0.18, black paint at 1.09 for internal surfaces and optical baffles.
Multilayer insulation: Ten to twenty layers of aluminised polyimide separated by low-conductivity netting. Effective emittance falls to 0.01 to 0.03, so MLI is close to a thermal short circuit in reverse.
Thermal straps and doublers: Conductive paths, usually graphite fibre or copper, that move heat from a dissipating component to a radiator.
Radiator placement: Anti-sun-facing where possible, and never facing a hot planet. Placement is one of the earliest configuration constraints and competes directly with antenna and instrument fields of view.

MLI works because radiation between two surfaces scales with the number of intervening layers. Its performance is dominated not by the layer count but by edges, seams and penetrations, so a blanket that is thermally excellent in analysis can be mediocre as installed. Handling and installation quality is a real variable.

Active control

Device	Function	Cost
Heaters	Add heat to keep components above their lower limit	Electrical power, often a large fraction of the survival load
Thermostats and software control	Cycle heaters against a setpoint	Complexity, and a failure mode
Louvers	Bimetallic vanes vary effective emissivity, typically from 0.1 to 0.7	Mass, mechanism reliability
Heat pipes	Capillary wick and working fluid move heat isothermally along a path	Orientation sensitivity in ground test
Loop heat pipes	Capillary pumped loop, transports heat over metres, works against gravity	Complexity, start-up behaviour
Pumped fluid loops	Mechanically circulated coolant	Pump power, single-point failure, leaks

Heaters deserve emphasis because they are frequently underestimated. Keeping hydrazine above its 2 °C freezing point along every metre of propellant line, and keeping batteries within their narrow band, can consume a substantial fraction of the power budget in the cold case. Survival heater power is often what sizes the battery for a safe mode, not the avionics.

Heat pipes are the workhorse of medium-power spacecraft. A sealed tube with a capillary wick and a working fluid, usually ammonia, transports heat by evaporation at the hot end and condensation at the cold end with almost no temperature drop and no moving parts. The complication is that a heat pipe tested horizontally on the ground behaves differently in zero gravity, so ground test setups must be tilted or the performance must be argued by analysis.

Hot and cold cases

The subsystem is verified against two bounding scenarios, and constructing them honestly is most of the work.

	Hot case	Cold case
Solar flux	Maximum, at perihelion	Minimum, at aphelion
Orbit	Full sun, no eclipse	Maximum eclipse duration
Albedo and planetary IR	Maximum, over bright cloud	Minimum
Internal dissipation	All units on, peak mode	Safe mode, minimum dissipation
Surface properties	End of life, degraded and darkened	Beginning of life, clean
Result	Sets radiator area	Sets heater power

The surface property row is easy to overlook and important. Ultraviolet exposure and contamination raise solar absorptivity over the mission while emissivity changes little, so $\alpha/\varepsilon$ increases with age and the vehicle runs hotter at end of life. The hot case is therefore an end-of-life case and the cold case a beginning-of-life one, which is the opposite of the intuition that a degraded spacecraft performs worse in every respect.

In low Earth orbit the driving parameter is the beta angle, the angle between the orbital plane and the solar vector. At high beta the orbit is in continuous sunlight with no eclipse, giving the hot case; at low beta the eclipse is longest, giving the cold case. Beta cycles over tens of days as the orbit plane precesses under $J_2$ , so both extremes occur repeatedly. See Orbital perturbations.

Cryogenic instruments

Infrared detectors must be cold, because at any appreciable temperature the instrument’s own thermal emission swamps the signal. This is a different problem from bulk heat rejection and is solved differently.

Passive cooling uses shielding and radiators alone and can reach roughly 30 to 50 K if the geometry cooperates. JWST is the definitive example: its five-layer sunshield at Sun-Earth $L_2$ holds the sun-facing side near 350 K and the observatory side below 50 K with no active cooler at all, because the geometry at $L_2$ puts Sun, Earth and Moon on one side. See Lagrange points.

Active cooling is required below that. Stirling and pulse-tube coolers mechanically pump heat from the cold stage up to a temperature where it can be radiated. JWST’s mid-infrared instrument needs 6.7 K and uses a three-stage pulse tube with a Joule-Thomson final stage. Mechanical coolers introduce vibration, which competes directly with the pointing stability the instrument also needs.

Stored cryogen, a dewar of solid hydrogen or liquid helium, gives excellent performance and a hard mission life: when the cryogen is gone the instrument is finished. Spitzer’s cold mission ended exactly this way, after which it continued on a reduced warm-instrument set.

The final box matters. A thermal model is not trusted until it has been correlated against thermal vacuum test data, with model parameters adjusted until predictions match measured temperatures. An uncorrelated model is an estimate, and thermal predictions before correlation routinely miss by tens of degrees.

References

Gilmore, D. G. (ed.) Spacecraft Thermal Control Handbook, Volume I: Fundamental Technologies, 2nd ed., Aerospace Press, 2002. The standard reference.
Karam, R. D. Satellite Thermal Control for Systems Engineers, AIAA, 1998.
Meseguer, J., Pérez-Grande, I. and Sanz-Andrés, A. Spacecraft Thermal Control, Woodhead, 2012.
ECSS-E-ST-31C, Space engineering: Thermal control general requirements.
Wright, G. S. et al. “The Mid-Infrared Instrument for JWST and its in-flight performance”, Publications of the Astronomical Society of the Pacific, 135:048003, 2023.