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

3.6.23 · Physics › Spacecraft Structures & Systems Engineering

Overview

Space sabse bada thermal challenge hai: spacecraft ka ek side Sun ki taraf +120°C par hota hai, doosra side 3 K void mein -270°C par stare karta hai, aur heat convect karne ke liye koi air nahi hoti. Thermal control systems electronics, propellant, aur payloads ko survivable limits ke andar rakhte hain (typically -20°C to +50°C) — passive insulation (MLI), active heating (resistive heaters), heat transport (heat pipes), aur heat rejection (radiators) ka use karke.

1. Multi-Layer Insulation (MLI)

MLI Kaise Kaam Karta Hai (First Principles)

Do parallel surfaces ke beech radiative heat transfer: $Q=\sigma A(T_1^4-T_2^4)\cdot {\epsilon }_{\text{eff}}$

jahan $\sigma =5.67\times 10^{-8}{\text{W/m}}^2{\text{K}}^4$ (Stefan-Boltzmann constant) hai, ${\epsilon }_{\text{eff}}$ effective emissivity hai.

Single layer: Agar surface 1 (hot) ki emissivity ${\epsilon }_1$ hai, surface 2 (cold) ki ${\epsilon }_2$ hai, aur woh directly ek doosre ko "dekhte" hain: $\frac{1}{{\epsilon }_{\text{eff}}}=\frac{1}{{\epsilon }_1}+\frac{1}{{\epsilon }_2}-1$

Aluminized Mylar ke liye ($\epsilon \approx 0.03$ per side), ${\epsilon }_{\text{eff}}\approx 0.015$.

N-layer MLI: Series mein layers add karne par, har layer re-radiate karti hai. N layers ke liye effective emissivity: ${\epsilon }_{\text{MLI}}\approx \frac{\epsilon }{N-1}\text{(radiation shield network)}$

Yeh step kyun? Har layer absorb karke re-emit karti hai, ek temperature gradient cascade create karti hai. 20 layers aur $\epsilon =0.03$ ke saath: ${\epsilon }_{\text{MLI}}\approx \frac{0.03}{19}\approx 0.0016$

Yeh heat leak ko single layer ke comparison mein ~10 factor se reduce karta hai, bare surface ($\epsilon \sim 0.9$ black paint ke liye) ke comparison mein ~100 factor se.

${\epsilon }_{\text{MLI}}=\frac{0.03}{29}\approx 0.001$

$Q=5.67\times 10^{-8}\cdot 2\cdot (293^4-100^4)\cdot 0.001$

$293^4=7.36\times 10^9,100^4=10^8$

$Q\approx 5.67\times 10^{-8}\cdot 2\cdot (7.36\times 10^9)\cdot 0.001=0.83\text{W}$

Yeh step kyun? MLI ke bina ($\epsilon =0.9$): $Q\approx 750\text{W}$. MLI heat loss ko ~900 factor se cut kar deta hai.

Fix: ~30 layers ke baad, blanket ke weight, handling, aur launch vibration se compression hoti hai jis se layers touch karti hain, conduction shorts enable ho jaate hain. Saath hi, mass penalty badhti hai. Diminishing returns shuru ho jaate hain. Typically: zyaatar missions ke liye 10–30 layers.

2. Heaters (Active Thermal Control)

Heaters Kyun Zaroori Hain

Eclipse ya deep-space cruise mein, components heat radiate karte hain lekin receive nahi karte. Batteries, propellant tanks, aur sensors operational limits se neeche chale jaate hain. Heaters controlled power add karte hain: $P_{\text{heater}}=I^{2}R=\frac{V^2}{R}$

Thermostatic control setpoint ke around on/off cycle karta hai (jaise, 10°C ± 2°C).

Heat capacity: $C=mc=5\times 1000=5000\text{J/K}$.

Cooling rate (heater ke bina): $\frac{dT}{dt}=-\frac{Q_{\text{loss}}}{C}=-\frac{5}{5000}=-0.001\text{K/s}=-0.06\text{K/min}$

90 min mein, $\Delta T=-5.4\text{K}$, toh $T$ 14.6°C tak girta hai (safe). Lekin agar eclipse longer ho ya external temp zyada thandi ho, toh heater zaroori hai.

10°C maintain karne ke liye heater power jab ambient 3 K space mein radiate kare: $P_{\text{heater}}=Q_{\text{loss}}=\sigma A{T}^4\epsilon \approx 5\text{W}$

Margin ke liye 50% duty cycle ke saath 10 W heater use karo.

3. Heat Pipes (Passive Heat Transport)

Heat Pipe Capacity ka Derivation

Har unit time mein transport kiya gaya heat: $Q=\dot{m}{L}_v$

jahan $\dot{m}$ vapor mass flow rate hai, $L_v$ latent heat of vaporization hai.

Vapor flow evaporator aur condenser ke beech pressure difference $\Delta P$ se drive hota hai. Tube mein incompressible flow ke liye: $\Delta P=\frac{8\mu L_{\text{pipe}}\dot{m}}{\rho \pi r^4}$

Capillary limit: Wick ko gravity/acceleration ke against liquid pump karna hota hai. Maximum capillary pressure: $\Delta P_{\text{cap}}=\frac{2\sigma \cos \theta }{r_{\text{pore}}}$

jahan $\sigma$ surface tension hai, $\theta$ contact angle hai, $r_{\text{pore}}$ wick pore radius hai.

Yeh step kyun? Heat pipe fail hota hai agar vapor pressure drop capillary pumping se zyada ho jaaye. Maximum heat: $Q_{\text{max}}=\frac{\Delta P_{\text{cap}}\cdot A_{\text{wick}}\cdot K\cdot L_v}{\mu L_{\text{pipe}}}$

jahan $K$ wick permeability hai.

$Q=0.001\times 1.37\times 10^6=1370\text{W}$

Ek single 1 cm diameter ammonia heat pipe ~1 kW 1 meter tak zero power input ke saath transport kar sakta hai. Compare karo copper rod se (conductivity $k=400\text{W/m⋅K}$, area $A=7.85\times 10^{-5}{\text{m}}^2$, length $L=1\text{m}$, $\Delta T=10\text{K}$): $Q_{\text{copper}}=\frac{kA\Delta T}{L}=\frac{400\cdot 7.85\times 10^{-5}\cdot 10}{1}=0.31\text{W}$

Heat pipe unit cross-section per 400× zyada effective hai.

Fix: Gravity enemy hai. Agar Earth par condenser evaporator se neeche ho, toh liquid gravity ke against upar wapas nahi aa sakta (wick capillary pressure ~ 1 kPa, gravity head ~ 10 kPa per meter). Microgravity mein (spacecraft), heat pipes sabhi orientations mein kaam karte hain kyunki capillary forces dominate karte hain. Ground testing mein, orientation matter karta hai!

4. Radiators (Heat Rejection)

Stefan-Boltzmann Law (Derivation)

Blackbody power per unit area emit karta hai: $j=\sigma T^4$

Kyun? Planck's law se, spectral radiance ko saare wavelengths aur solid angles par integrate karne par: ${\int }_0^{\infty }B(\lambda ,T)d\lambda =\frac{\sigma }{\pi }{T}^4$

$\pi$ steradians (hemisphere) se multiply karo, $\sigma T^4$ milta hai.

Real surface ke liye emissivity $\epsilon$ ke saath (blackbody emission ka fraction): $Q_{\text{rad}}=\epsilon \sigma A{T}^4$

Net heat rejection jab radiator $T_r$ par ho aur space $T_s\approx 3\text{K}$ ko dekhe: $Q_{\text{net}}=\epsilon \sigma A(T_r^4-T_s^4)\approx \epsilon \sigma A{T}_r^4(T_s\ll T_r)$

$A=\frac{Q}{\epsilon \sigma T^4}=\frac{500}{0.85\cdot 5.67\times 10^{-8}\cdot 313^4}$

$313^4=9.61\times 10^9$

$A=\frac{500}{0.85\cdot 5.67\times 10^{-8}\cdot 9.61\times 10^9}=\frac{500}{463}\approx 1.08{\text{m}}^2$

Yeh step kyun? Radiator itna bada hona chahiye ki uska $T^4$ emission waste heat se match kare. 313 K par, har m² ~463 W radiate karta hai. 500 W ke liye 1.08 m² chahiye.

Trade-off: Zyada $T$ se chota radiator allow hota hai ($Q\propto T^4$), lekin components ki max temp limits hoti hain. Hotter chalana = chota radiator lekin thermal transport mein zyada mass (bade heat pipes).

Active Recall Questions

#flashcards/physics

N-layer MLI ke liye effective emissivity formula kya hai? :: ${\epsilon }_{\text{MLI}}\approx \frac{\epsilon }{N-1}$, jahan $\epsilon$ single-layer emissivity hai. Har layer re-radiate karti hai, ek cascade create karti hai.

Temperature T par heat rejection Q ke liye radiator area derive karo :: $Q=\epsilon \sigma A{T}^4⟹A=\frac{Q}{\epsilon \sigma T^4}$. Zyada T se chota radiator allow hota hai (fourth-power scaling).

Connections

• Stefan-Boltzmann Law — radiator design aur MLI analysis ki foundation
• Heat Transfer in Vacuum — convection absent kyun hai, radiation dominate kyun karta hai
• Phase Change Heat Transfer — latent heat heat pipe operation enable karta hai
• Capillary Action — wick physics heat pipe performance limit karta hai
• Spacecraft Power Systems — heaters solar/battery bus se draw karte hain
• Orbital Thermal Environment — eclipse/Sun cycles heating/cooling drive karte hain
• Materials Science — Kapton & Mylar — MLI aur heater substrate properties
• Cryogenics — infrared sensors, propellant ke liye extreme thermal control

MLI (multi-layer insulation) matlab apne ghar ko 20 shiny space blankets mein wrap karna. Har blanket heat wapas reflect karta hai, toh andar jaldi hot ya cold nahi hota.

Heaters andar electric blankets ki tarah hain. Jab bahut thanda ho (jaise Earth ki shadow mein), tum unhe on karte ho taaki tumhari batteries aur computers freeze na hon.

Heat pipes magic straws hain. Hot paani (actually ammonia) hot end par boil hoti hai, steam cold end ki taraf zoom karta hai, liquid mein wapas badalta hai, aur sponge se wapas flow karta hai. Yeh ek self-running heat delivery system hai jisme koi battery nahi chahiye!

Radiators bade kaale panels hain. Woh invisible light (infrared) se glow karte hain taaki heat space mein phenk sakein, jaise campfire tumhara chehra warm karta hai lekin ulta — heat door bhejta hai.

Milke, yeh sab tumhare spacecraft ko cozy rakhte hain, bhale hi bahar temperature ka ek wild roller coaster ho!

Concept Map