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

3.6.23 · D5 · Physics › Spacecraft Structures & Systems Engineering › Thermal control — multi-layer insulation (MLI), heaters, hea

Yeh page tumhari intuition ki workout hai, calculator ki nahi. Neeche har item ek aisi jagah ko target karta hai jahan thermal control ka "common sense" quietly tumhe galat rasta dikha deta hai — temperature difference ka sign, vacuum mein kya kar sakte ho, aur kyun gravity tumhare lab bench par heat pipe ko barbad kar deti hai. Question padho, apna jawab zor se bolke decide karo, phir reveal karo.

Agar koi bhi word naya lage, toh parent topic har tool ko scratch se banata hai. Prerequisite pictures Stefan-Boltzmann Law, Heat Transfer in Vacuum, Phase Change Heat Transfer, aur Capillary Action mein milenge.

Definition Is page par use kiya gaya har symbol (ek baar padho, refer karte raho)

$T$ , $T_{1}$ , $T_{2}$ — kisi surface ya do facing surfaces ki absolute temperatures kelvin (K) mein.
$T_{r}$ — ek radiator surface ka temperature (K); $T_{s}$ — jis space sink ko woh face karta hai uska temperature (K) (~3 K).
$σ_{SB} = 5.67 \times 1 0^{- 8} W/m^{2} K^{4}$ — Stefan–Boltzmann constant (prakriti ka ek fixed number).
$σ_{γ}$ — kisi liquid ki surface tension, units N/m. (Yeh $σ_{SB}$ se alag quantity hai — humne inhe alag subscripts diye hain taaki yeh kabhi blur na hon.)
$ε$ — emissivity, 0 se 1 tak ka ek dimensionless fraction: koi surface ek perfect blackbody ( $ε = 1$ ) ke comparison mein kitna achha radiate karta hai.
$ε_{eff}$ — heat exchange karne wali do facing surfaces ki combined emissivity; $ε_{MLI}$ — $N$ shields ki poori blanket ki whole-blanket effective emissivity.
$A$ — radiating/exchanging area, m². $N$ — MLI shield layers ki sankhya.
$\overset{m}{˙}$ — heat pipe mein vapor ka mass flow rate, kg/s. $L_{v}$ — latent heat of vaporization, J/kg (1 kg ubaalane ki energy).
$r_{pore}$ — wick ka pore radius, m; $θ$ — liquid–wall contact angle.
$F_{12}$ — view factor: surface 1 se nikli radiation ka woh fraction jo actually surface 2 par girti hai (sirf geometry, 0 se 1 tak).

Formula Teen MLI/radiator formulas kahan se aate hain

Two-surface exchange. Ek blackbody $σ_{SB} T^{4}$ per unit area emit karta hai. Do facing surfaces ek doosre ki taraf emit karti hain aur jo aata hai uska kuch part absorb karti hain; reflected radiation ke endless back-and-forth ko track karna aur geometric series ko sum karna net flow deta hai $Q = ε_{eff} σ_{SB} A F_{12} (T_{1}^{4} - T_{2}^{4}), \frac{1}{ε _{eff}} = \frac{1}{ε _{1}} + \frac{1}{ε _{2}} - 1.$ $- 1$ isliye aata hai kyunki surface 1 se nikla ek photon tabhi finally lost hota hai jab woh reflect hokar wapas aane mein fail ho jaata hai — resistances $1/ ε_{1}$ aur $1/ ε_{2}$ ek common "gap" share karte hain, isliye double-counting se bachne ke liye ek minus karte hain. Bade parallel plates ke liye $F_{12} = 1$ .

N-shield stack. $N$ floating foils daalo, sab ke dono faces par same emissivity $ε$ ho, aur har ek itna well-spaced ho ki koi bhi do touch na karein. Har foil radiation ka ek aur "resistor" series mein add karta hai; $N$ shields enclosing walls ke beech $N - 1$ equal gaps create karte hain, isliye total resistance ek gap ki $(N - 1)$ guna hoti hai, jo deta hai $ε_{MLI} \approx \frac{ε}{N - 1} .$ Domain: yeh sirf identical, non-touching foils ke liye hold karta hai jinmein negligible edge aur conduction effects hon; seams aur compression wali real blankets isse worse karti hain.

True or false — justify karo

TF1. "MLI spacecraft ko utne hi tarike se warm rakhta hai jaise oon ka blanket tumhe warm rakhta hai."

False. Ek blanket hawa ko trap karta hai convection block karne ke liye; vacuum mein hawa nahi hoti, isliye MLI bajaye uske radiation block karta hai mirror-jaise reflective (low-

ε

) layers stack karke, har ek infrared ka ~95% wapas bounce karta hai. Dekho Heat Transfer in Vacuum.

TF2. "Zyada MLI layers add karne se hamesha heat leak kam hoti hai."

False. Formula

ε_{MLI} \approx ε / (N - 1)

aisa suggest karta hai, lekin ~30 layers ke baad blanket ka apna weight aur launch vibration layers ko press karte hain ek saath, conduction shorts create karte hain jo heat wapas add karte hain, aur mass penalty bhi lagti hai.

TF3. "Ek radiator tabhi radiate karta hai jab spacecraft hot hoti hai; jab woh cool hoti hai toh band ho jaata hai."

False. Ek radiator kisi bhi

T > 0

ke liye

ε σ_{SB} A T^{4}

emit karta hai; yeh kabhi switch off nahi hota. Yehi exact wajah hai ki cold-side components ko heaters ki zaroorat hoti hai — woh 3 K space mein radiate karte rehte hain jab bhi tum unhe warm rakhna chahte ho.

TF4. "Kyunki space 3 K par hai, radiator ka net rejection space temperature par strongly depend karta hai."

False.

T_{r} \sim 300 K

aur

T_{s} = 3 K

ke saath ratio

(300/3)^{4} = 1 0^{8}

hai, isliye

T_{s}^{4}

T_{r}^{4}

ka lagbhag ek-sau-millionths hissa hai — bilkul negligible, aur radiator aisa behave karta hai jaise space absolute zero par ho.

TF5. "Heat pipes ko heat move karne ke liye electrical power chahiye."

False. Ek heat pipe fully passive hoti hai: yeh hot end par evaporation aur wick se capillary return par chalti hai, bina pump aur bina power ke. Dekho Phase Change Heat Transfer.

TF6. "Ek heat pipe kisi bhi orientation mein equally well kaam karta hai."

Ground par False. Capillary pressure (~1 kPa) gravity ke head (~10 kPa per metre) ko nahi hara sakta agar condenser evaporator ke neeche ho. Microgravity mein capillary forces dominate karte hain aur orientation truly matter karna band kar deta hai.

TF7. "Same temperature par do surfaces ab bhi net radiative heat exchange karti hain."

False.

Q \propto (T_{1}^{4} - T_{2}^{4})

; equal temperatures ise zero kar dete hain. Radiation dono taraf chalti rehti hai, lekin net flow zero hota hai — thermal equilibrium.

TF8. "Radiator ke liye high emissivity achha hai, isliye yeh spacecraft mein har jagah achha hona chahiye."

False. High

ε

sirf wahan chahiye jahan tum heat dump karna chahte ho. Insulated surfaces par tum opposite chahte ho — bahut low

ε

(MLI ka aluminized Mylar) taaki heat wahan rahe.

TF9. "Ek heater aur ek radiator opposite hain, isliye ek achhi tarah se design ki gayi spacecraft koi ek use karti hai."

False. Real spacecraft dono simultaneously use karte hain — radiators hot case ke liye sized hote hain, heaters eclipse ke dauran fill-in karte hain — kyunki environment sun-facing

+ 120° C

aur shadowed

- 270° C

ke beech swing karta hai. Dekho Orbital Thermal Environment.

Spot the error

SE1. "Kyunki

Q = ε_{eff} σ_{SB} A (T_{1}^{4} - T_{2}^{4})

hai, dono surface temperatures ko double karne se heat flow double ho jaati hai."

Galat — flow

T^{4}

par depend karta hai,

T

par nahi. Dono temperatures double karne se har

T^{4}

term 16 guna ho jaata hai, isliye difference 16 guna scale hota hai, 2 nahi.

SE2. "Do surfaces ke beech ek single MLI layer ke liye main emissivities add karta hoon:

ε_{eff} = ε_{1} + ε_{2}

Galat. Tum resistances combine karte ho:

1/ ε_{eff} = 1/ ε_{1} + 1/ ε_{2} - 1

. Series mein do poor emitters ek aur chhoti effective emissivity dete hain, sum nahi.

SE3. "Ek copper rod aur equal cross-section ki ammonia heat pipe similar heat move karti hai kyunki copper itna achha conduct karta hai."

Galat. Heat pipe ek boiling/condensing fluid ki latent heat carry karta hai, jo solid copper conduction se same length par hundreds of times zyada heat per unit area move karta hai. Dekho Phase Change Heat Transfer.

SE4. "Ek pipe jo heat carry karta hai

Q = \overset{m}{˙} L_{v}

hai, isliye

\overset{m}{˙}

ko arbitrarily bada karne se unlimited transport milta hai."

Galat. Jaise

\overset{m}{˙}

badhta hai, vapor pressure drop

Δ P

bhi badhta hai, aur jab yeh wick ki capillary pressure

2 σ_{γ} cos θ / r_{pore}

se zyada ho jaata hai toh liquid wapas nahi aa sakta — pipe "dry out" ho jaata hai (capillary limit).

SE5. "Ek blackbody radiator per unit area

j = σ_{SB} T

emit karta hai."

Galat. Stefan-Boltzmann

j = σ_{SB} T^{4}

hai; fourth power hi wajah hai ki chhoti temperature increases vastly zyada heat dump karti hain. Dekho Stefan-Boltzmann Law.

SE6. "Zyada waste heat ke liye radiator size karne ke liye, bas ise thanda karo — lower

T

matlab kam leftover heat."

Galat, ulta hai. Kyunki

Q = ε σ_{SB} A T^{4}

hai, ek thanda radiator kam heat reject karta hai, jis wajah se bada area chahiye. Zyada allowed temperature matlab chhota radiator.

SE7. "MLI ki effective emissivity

N

shields ke liye

ε_{MLI} = εN

hai."

Galat. Har added shield leak ko reduce karta hai:

ε_{MLI} \approx ε / (N - 1)

. Zyada layers number ko chhota banate hain, bada nahi.

SE8. "5,\text{W} $a v er a g e k e l i y es i z e d e k h e a t er k oe k$ 5,\text{W} $e l e m e n t k er oo p m e in co n t in u o u s l y r u nk i y aj aana c hahi y e ." ::: P r a c t i ce m e in g a l a t . T h er m os t a t i c h e a t er scy c l eo n / o f f k a r t e hain, i s l i y e t u m e x t r a c a p a c i t y in s t a l l k a r t e h o (j ai se 50% d u t y p a r$ 10,\text{W}$) taaki colder-than-expected cases mein margin ke saath setpoint hold ho sake. Dekho Spacecraft Power Systems.

SE9. "Do facing radiators

ε_{eff} σ_{SB} A (T_{1}^{4} - T_{2}^{4})

heat exchange karte hain chahe woh kaise bhi aimed hon."

Galat. Exchange ek view factor

F_{12}

bhi carry karta hai — agar surfaces ek doosre se door face kar rahi hain toh emitted radiation ka zyada hissa miss ho jaata hai, aur net exchange zero ki taraf shrink ho jaata hai.

Why questions

WHY1. Kyun ek spacecraft heat ko conduction se space mein dump nahi kar sakti jaise ek hot pan countertop par thanda hota hai?

Kyunki space near-vacuum hai jisme essentially koi matter nahi hai jo touch kare; conduction aur convection dono ko medium chahiye, sirf radiation hi ek path bachta hai. Dekho Heat Transfer in Vacuum.

WHY2. Kyun Stefan-Boltzmann law temperature ki fourth power use karta hai first power ki jagah?

Yeh Planck ke spectral curve ko saare wavelengths par integrate karne se aata hai; hotter bodies dono zyada photons emit karti hain aur higher-energy (shorter-wavelength) wale, aur yeh effects compound hokar

T^{4}

dependence dete hain. Dekho Stefan-Boltzmann Law.

WHY3. Kyun ek heat pipe itni zyada heat move karta hai jitni raw temperature difference suggest karta hai?

Kyunki fluid boil hone par ek badi latent heat absorb karta hai aur condense hone par sab release kar deta hai; temperature end-to-end almost change nahi hota, phir bhi enormous energy per kilogram shuttle hoti hai. Dekho Phase Change Heat Transfer.

WHY4. Kyun heat pipe mein returning liquid bina kisi pump ke wick se climb karta hai?

Fine wick pores mein surface tension (

σ_{γ}

) ek pressure difference (capillary action) create karta hai jo literally cold condenser se hot evaporator tak liquid suck karta hai. Dekho Capillary Action.

WHY5. MLI ke liye aluminized Mylar kyun choose kiya jaata hai, maan lo thick foam ki jagah?

MLI radiation se ladhta hai, isliye ise kai thin, highly reflective (low-emissivity,

ε \approx 0.03

) mirror layers chahiye; foam mass aur conduction paths add karta bina reflective shielding ke. Dekho Materials Science — Kapton & Mylar.

WHY6. Batteries aur propellant tanks ko specifically dedicated heaters kyun milte hain?

Unki hard lower temperature limits hoti hain — ek thandi battery current deliver nahi kar sakti aur propellant freeze ho sakta hai — isliye long eclipse periods ke dauran heaters woh heat replace karte hain jo yeh masses steadily radiate karte hain. Dekho Spacecraft Power Systems.

WHY7. Lab mein measure ki gayi MLI performance often real vehicle par performance se better kyun hoti hai?

Lab blankets pristine aur uncompressed hote hain; real spacecraft par, seams, cable penetrations, aur clamped edges conduction shorts create karte hain jo effective emissivity ko ideal

ε / (N - 1)

se oopar raise kar dete hain.

WHY8. Radiator ko hotter run karna attractive kyun hai despite tighter component limits?

Kyunki

Q \propto T^{4}

hai, ek moderate temperature rise required area aur mass ko sharply shrink karta hai — lekin tum iske liye bade heat pipes aur stricter component derating ke saath pay karte ho zyada temperature survive karne ke liye.

WHY9. Do-surface exchange formula mein view factor

F_{12}

aakhir hai kyun?

Kyunki radiation seedhi rays mein travel karta hai; sirf woh fraction of rays jo ek surface se nikal kar actually doosri par girte hain woh heat transfer karte hain, aur woh fraction poori tarah unki shape, size, aur orientation par depend karta hai. Dekho Heat Transfer in Vacuum.

Edge cases

EC1. Jis exact moment do facing surfaces identical temperature tak pahunch jaati hain, net radiative exchange kya hota hai?

Exactly zero net flow, kyunki

T_{1}^{4} - T_{2}^{4} = 0

hai; dono surfaces ab bhi emit karti hain, lekin incoming aur outgoing streams cancel ho jaate hain.

EC2. Jaise

N \to \infty

layers, MLI formula kya predict karta hai, aur yeh unphysical kyun hai?

Yeh predict karta hai

ε_{MLI} \to 0

(perfect insulation), jo kabhi nahi hota kyunki compression, mass, aur conduction shorts ~30 layers ke aas-paas real limits impose karte hain.

EC3. Agar heat pipe ka poora hissa working fluid ke freezing point se neeche ho startup par, toh kya hota hai?

Fluid frozen hai, isliye koi vapor nahi banta aur koi heat nahi chalti jab tak ek external heater evaporator ko thaw na kare — yeh cryogenic-range pipes ke liye ek real "startup from frozen" hazard hai. Dekho Cryogenics.

EC4. Radiator equation

Q_{net} = ε σ_{SB} A (T_{r}^{4} - T_{s}^{4})

mein

T_{s} \to 0

karne se kya hota hai?

Almost kuch nahi — kyunki

T_{s} \approx 3 K

already

T_{s}^{4}

ko negligible bana deta hai, deep-space sink absolute zero jaisa behave karta hai aur

Q_{net} \approx ε σ_{SB} A T_{r}^{4}

EC5. Agar satellite ka eclipse period achanak lamba ho jaaye toh heater demand kya hota hai?

Components bina kisi solar input ke zyada der tak radiate karte hain, isliye unka temperature aur neeche girta hai; heater energy demand (aur use supply karne ke liye battery drain) badhti hai, potentially power budget exceed karke. Dekho Orbital Thermal Environment.

EC6. Ground par, heat pipe test karne ke liye sabse worst orientation kaunsa hai, aur kyun?

Condenser evaporator ke neeche mounted hona, liquid ko gravity ke against climb karne par majboor karta hai; ~1 kPa capillary pressure ~10 kPa/m gravity head se haar jaata hai aur pipe fail ho jaati hai.

EC7. Kya cheez radiator ki usefulness ko limit karti hai jab spacecraft surface Sun ki taraf face kar rahi ho?

Absorbed solar flux emitted heat se zyada ho sakta hai, isliye radiator net heat gain karta hai reject karne ki jagah — designers radiators ko deep space ki taraf point karte hain ya optical solar reflectors use karte hain jo IR emit karte hain sunlight reflect karte hue. Dekho Orbital Thermal Environment.

EC8. Agar MLI mein ek chhota sa hole ya unblanket ed cable penetration ho toh MLI ke benefit ka kya hoga?

Woh gap ek high-emissivity "leak" ban jaata hai jiska heat flow many square metres achhe MLI ki rival kar sakta hai, kyunki surrounding blanket itna achha hai — sabse kamzor patch total dominate karta hai.

EC9. Do radiators side by side mostly ek doosre ki taraf face kar rahe hain bajaye space ke — kya trap hai?

Unka view factor deep space mein kam ho jaata hai aur ek doosre mein badhta hai, isliye har ek doosre ki heat ka kuch part re-absorb karta hai; net rejection akele area se kahi kam hoti hai. Dekho Heat Transfer in Vacuum.

EC10. Kya "vacuum convection ko completely rokta hai" ek partial vacuum mein exactly true hai?

Nahi — low-pressure (rarefied) gas mein, residual molecules ab bhi chhote gaps mein heat conduct kar sakte hain, jo exact wajah hai ki compressed MLI ya poorly evacuated blanket pure-radiation model ke predict se zyada leak karta hai.

Recall Jaane se pehle ek-line self-test

Kyun is page par almost har trap ek hi fact par trace back karta hai? ::: Kyunki vacuum mein sirf radiation ( $\propto T^{4}$ ) heat transfer karta hai, aur yeh kabhi band nahi hota aur hamesha dono taraf flow karta hai — yeh bhool jaao aur intuition toot jaati hai.