Foundations — Thermal control — multi-layer insulation (MLI), heaters, heat pipes, radiators

Before you can read a single formula in the parent note, you must own every letter in it. This page introduces each symbol once, in plain words, with a picture, and explains why the topic cannot live without it. Nothing below assumes anything above line one.

0. The stage: hot box in cold nothing

Look at the figure. There is a warm spacecraft (the yellow box) and, all around it, black space. On Earth, a hot cup of coffee cools three ways: conduction (heat crawls through touching solids), convection (moving air carries heat away), and radiation (glowing energy leaves as light). In the vacuum of space there is no air, so convection is gone, and the spacecraft is mounted on thin isolating struts, so conduction is nearly gone too.

1. Temperature — $T$

Plain words: how hot or cold something is, measured in kelvin (K).

The picture: a thermometer that starts at absolute zero — the coldest possible, where all jiggling of atoms stops. $0\text{K}$ is that floor; water freezes at $273\text{K}$ (which is $0°\text{C}$), room temperature is $293\text{K}$ ($20°\text{C}$).

Why the topic needs kelvin, not celsius: the amount of light a surface radiates depends on $T^4$ (you'll meet this in §5). Raising a number to the fourth power only makes physical sense if the number is measured from absolute zero — you can't have "twice as hot" if your zero is arbitrary. Kelvin has a real zero, so $T^4$ means something real.

2. Area — $A$

Plain words: the size of a surface, measured in square metres (${\text{m}}^2$).

The picture: unfold one wall of the spacecraft flat on a table and measure its length times its width. A $2{\text{m}}^2$ panel is about the size of a door.

Why the topic needs it: radiation leaves through a surface. A bigger window loses more heat, a smaller window loses less — everything scales with how much surface is doing the radiating. Doubling $A$ doubles the heat flow.

3. Heat flow — $Q$ and power $P$

Plain words: $Q$ is how much heat-energy crosses a boundary each second, measured in watts (W). One watt is one joule of energy per second.

The picture: imagine energy as water. $Q$ is the flow rate — litres per second — not the total amount in the tank. A $60\text{W}$ lightbulb pours out 60 joules of heat every second.

Why the topic needs it: thermal control is a balance of flows. Heat leaking in must equal heat pumped out, or the temperature drifts. $Q$ is the currency of every equation ahead.

4. Emissivity — $\epsilon$

Plain words: a number between $0$ and $1$ telling you how good a surface is at radiating compared to a perfect radiator.

The picture: two surfaces at the same temperature.

The black-painted panel (right) glows with almost all the heat it possibly could — $\epsilon \approx 0.9$. The shiny aluminium foil (left) barely glows at all — $\epsilon \approx 0.03$. Same temperature, wildly different radiated power, purely because of the surface finish.

Why the topic needs it — and why it's the master knob: every strategy in thermal control is really a choice of $\epsilon$:

• MLI wants $\epsilon$ as low as possible (trap heat in) → shiny aluminium.
• Radiators want $\epsilon$ as high as possible (dump heat out) → black paint.

One number, opposite goals. See Materials Science — Kapton & Mylar.

5. The Stefan–Boltzmann constant — $\sigma$

Plain words: a fixed number of nature that converts a temperature into a radiated power per square metre.

$\sigma =5.67\times 10^{-8}\frac{\text{W}}{{\text{m}}^2{\text{K}}^4}$

The picture: think of $\sigma$ as an exchange rate. You hand it a temperature (in K) and an area (in m²), and it tells you how many watts of light stream off.

Why the fourth power $T^4$, and not $T$ or $T^2$?

Look at the steep curve. Doubling the temperature multiplies the radiated power by $2^4=16$. This is the single most important fact in the whole topic:

The little ${\text{K}}^4$ in $\sigma$'s units is there precisely to cancel the $T^4$, leaving clean watts.

6. Net heat between two temperatures — $T_1^4-T_2^4$

Plain words: when a hot surface at $T_1$ faces a cold one at $T_2$, both radiate at each other. The net flow is what the hot one sends minus what the cold one sends back.

The picture: two campfires facing each other. Each throws light at the other; you only feel the difference. If both are equally hot, no net heat moves.

Why the topic needs it: MLI and radiators are always about the gap between an inside and an outside temperature. When the cold side is space ($T_2=3\text{K}$), $T_2^4$ is so tiny it vanishes, and $Q\approx \epsilon \sigma A{T}_1^4$ — the "one-way" radiator formula.

7. Effective emissivity — ${\epsilon }_{\text{eff}}$ and the layer trick

Plain words: when two shiny surfaces face each other, or when you stack many, the combined poorness-at-radiating is captured by one lumped number ${\epsilon }_{\text{eff}}$.

The picture: each shiny layer is a toll gate that bounces ~97% of heat back. Stack $N$ of them and the heat must pay every gate; the leak drops roughly as ${\epsilon }_{\text{MLI}}\approx \epsilon /(N-1)$.

Why the topic needs it: this is the entire secret of MLI — many cheap shiny sheets multiply into an enormous insulator. You must recognise ${\epsilon }_{\text{eff}}$ and ${\epsilon }_{\text{MLI}}$ as just a bookkeeping of many $\epsilon$'s in series, not new physics.

8. Electrical symbols for heaters — $V$, $I$, $R$, $P$

Plain words:

• $V$ = voltage, the electrical "push" (volts).
• $I$ = current, the flow of charge (amps).
• $R$ = resistance, how hard the wire fights the current (ohms).
• $P$ = electrical power turned into heat (watts).

The picture: push electricity through a stubborn wire and it warms up — exactly like a toaster coil. All the electrical energy becomes heat.

Why the topic needs it: heaters are the only active way to add heat when there's no sunlight. Powered by the bus, they convert precious electricity into warmth. Every joule a heater burns is a joule the batteries can't spend elsewhere — so sizing them (via $P$) matters.

9. Heat capacity — $c$, $C$ — and the rate of cooling $\frac{dT}{dt}$

Plain words:

• $c$ = specific heat: joules needed to warm $1\text{kg}$ by $1\text{K}$.
• $C=mc$ = heat capacity of the whole object (mass $m$ times $c$): joules per kelvin.
• $\frac{dT}{dt}$ = rate of temperature change: how fast the thermometer moves each second.

The picture: a big thermal mass (big $C$) is a heavy flywheel — it takes a long time to slow down (cool). The minus sign means losing heat lowers temperature.

Why the topic needs it: it tells you whether a battery will survive an eclipse before a heater is even needed. Big $C$ → slow drift → maybe no heater. Small $C$ → rapid drop → heater essential.

10. Symbols of the heat pipe — $L_v$, $\dot{m}$, $\Delta P$, ${\sigma }_s$, $\theta$, $r$

A heat pipe carries heat by boiling fluid at the hot end and condensing it at the cold end. Its symbols:

• $L_v$ = latent heat of vaporisation: joules to boil $1\text{kg}$ of liquid without changing its temperature. See Phase Change Heat Transfer.
• $\dot{m}$ = mass flow rate: kilograms of vapour moving per second (the dot means "per second").
• $Q=\dot{m}{L}_v$: the heat carried equals fluid boiled per second times energy per kilogram to boil it.
• $\Delta P$ = pressure difference driving vapour from hot to cold end (the $\Delta$ means "difference in").
• ${\sigma }_s$ = surface tension of the liquid; $\theta$ = contact angle; $r_{\text{pore}}$ = wick pore radius. Together these set the capillary suction $\Delta P_{\text{cap}}=\frac{2{\sigma }_s\cos \theta }{r_{\text{pore}}}$ that sucks liquid back through the wick. See Capillary Action.

Why the topic needs these: a heat pipe moves ~1000× more heat than a solid rod because latent heat $L_v$ is huge — boiling stores enormous energy. But it only works if the wick can pump liquid back, which is a race between $\Delta P_{\text{cap}}$ (suction) and $\Delta P$ (flow resistance). See Cryogenics for the very cold end of this world.

The prerequisite map

Read it top to bottom: every box is a symbol you now own, and the arrows show which combine into the four thermal-control tools.

Equipment checklist

Cover the right side and test yourself.