5.4.8
Ek spacecraft jab atmosphere mein re-entry karta hai, toh itni tezi se hawa ko compress karta hai ki shock layer hazaaron kelvin tak superheated ho jaati hai. Vehicle ko sirf "strong" material ki zaroorat nahi hoti — usse ek aisi skin chahiye jo ya toh insulate kare (heat bahar rakhe, jaise Shuttle ke silica tiles) ya survive kare roasting ko (jaise sharp leading edges pe UHTCs). Ye do opposite design philosophies hain: heat ko block karo vs heat ko jhelo .
Definition Re-entry heatingRe-entry ke dauran, vehicle ki kinetic energy shock-heated gas ki thermal energy mein convert hoti hai. Peak stagnation-point heat flux q q ∝ R n 1 ρ 1/2 V 3 R n ρ V
Ye form kyun hai? (first principles se derive karo):
Vehicle kinetic energy ko us rate pe dissipate karta hai jo shock mein air mass flux se set hoti hai, m ˙ ∝ ρ V ∝ V 2 ∝ ρ V ⋅ V 2 = ρ V 3 V 3
ρ 1/2 R n − 1/2
Intuition Do consequences jo tumhe FEEL karni chahiye
Velocity dominate karta hai (V 3 Sharp = hot : q ∝ R n − 1/2 sharp AND survivable edges dene dete hain.
Definition Shuttle silica tile (LI-900)Ek rigid, highly porous (~94% air) block jo almost pure amorphous silica (SiO₂) fibres ka bana hota hai, density ~144 kg/m³ (= 9 lb/ft³, isliye "LI-900"), emissivity ke liye black borosilicate RCG glaze se coated.
Silica kyun?
Amorphous SiO₂ mein bahut low thermal conductivity k
Iska coefficient of thermal expansion low hota hai, toh rapid heating/cooling mein crack nahi karta.
High melting/softening point (~1700 °C) — Shuttle ke windward surfaces (~1260 °C) ke liye kaafi hai.
Intuition Emissivity bhi bahut bada kaam karti haiBlack glaze high emissivity ε ≈ 0.9 q rad = ε σ T 4 bada fraction space mein radiate kar deti hai (T 4 nahi dump kar sakti . Ye hai radiative cooling : hot ho, glow karo, survive karo.
Definition Ultra-High-Temperature CeramicsRefractory borides/carbides — mainly ZrB₂ aur HfB₂ , aksar SiC ke saath — melting points 3000 °C se upar , use hote hain sharp leading edges & nose tips pe jahaan temperatures silica ki capability se zyada ho jaati hai.
Material
Melting point
Role
ZrB₂
~3245 °C
sharp-edge structural ceramic
HfB₂
~3380 °C
highest-T leading edges
SiC (additive)
~2700 °C
protective glass banata hai, neeche dekho
Diborides itne high melt kyun karte hain?
Strong covalent + metallic mixed bonding : Zr/Hf metal sublattice (metallic, conductivity deta hai) strong covalent B–B sheets ke saath interleaved. Is network ko todne mein enormous energy lagti hai ⇒ high melting point aur high hardness.
High thermal conductivity (silica ke unlike!) sharp tip se heat spread karta hai, local hotspots avoid karta hai.
Intuition "Heat ko jhelo" kyun, "heat ko block karo" nahinEk sharp leading edge (R n → q ek maatra class hain jo teeno kaam karte hain.
Worked example 1 — Silica tile ki back-face temperatureTile: k = 0.05 W m − 1 K − 1 L = 0.06 m q = 12 , 000 W/ m 2 Δ T = k q L = 0.05 12000 × 0.06 = 14 , 400 K Ye step kyun? Δ T = q L / k q actually conducted q Δ T / L
Worked example 2 — Radiative equilibrium surface temperatureEk leading edge q = 1.0 × 1 0 6 W/ m 2 ε = 0.85 T q = ε σ T 4 σ = 5.67 × 1 0 − 8 T = ( ε σ q ) 1/4 = ( 0.85 × 5.67 × 1 0 − 8 1 0 6 ) 1/4 = ( 2.07 × 1 0 13 ) 1/4 ≈ 2135 K ( ≈ 1860 ∘ C ) Ye step kyun? Balance isliye justified hai kyunki steady state mein heat ke liye single escape route radiation hi hai. T ≈ 2135 UHTC chahiye . Ye ek calculation batati hai ki kaunsi philosophy use karo.
Worked example 3 — Velocity scaling (Forecast-then-Verify)Forecast: lunar return 11 km/s pe vs LEO return 7.8 km/s pe — heating kitna bura hoga?
q LEO q moon = ( 7.8 11 ) 3 = ( 1.41 ) 3 ≈ 2.8 Verify: ~3× higher peak flux — match karta hai us jaani-maani baat se ki Apollo ko ablative shield chahiye thi, reusable tiles nahi. Ye step kyun? Agar ρ , R n V 3 ( V 2 / V 1 ) 3
Common mistake "Higher melting point hamesha better thermal protection matlab hai."Kyun sahi lagta hai: survive karna = na pighalna, toh highest T m Fix: Shuttle ke broad surfaces ke liye winner silica hai — ek low melting point material — kyunki wahan kaam hai insulation + re-radiation , 3000 °C survive karna nahi. Melting point sirf sharp edges pe dominate karta hai jahaan insulate nahi kar sakte. Material ko match karo — heat block karna hai ya jhhelna hai.
Common mistake "UHTCs oxidise nahi karte kyunki ceramics inert hote hain."Kyun sahi lagta hai: ceramics chemically stable lagte hain. Fix: ZrB₂/HfB₂ hot air mein readily oxidise karte hain; protection aati hai oxide products se jo khud glass banate hain — khaaskar SiC se borosilicate . SiC ke bina, B₂O₃ evaporate ho jaata hai aur part degrade ho jaata hai. Stability kinetic hai (glass ke through slow O₂ diffusion), thermodynamic inertness nahi.
Common mistake "Conductivity saare heat shields ke liye low honi chahiye."Kyun sahi lagta hai: low k Fix: UHTC leading edges high k
Recall Quick self-test (answers cover karo)
Silica tiles aur UHTCs kaun si do opposite philosophies represent karte hain? → block/insulate vs take/survive.
q V 3 ρ V V 2 ZrB₂ mein SiC kyun add karte hain? → protective self-healing SiO₂/borosilicate glass banata hai.
Sharp noses hot kyun hote hain? → q ∝ R n − 1/2
Black glaze kya role play karta hai? → high ε q rad = ε σ T 4
Recall Feynman: ek 12-saal ke bachche ko explain karoSpace se wapas aana aise hai jaise ek giant slide pe itni tezi se utaro ki aage ki hawa aag ban jaaye. Jalne se bachne ke liye tumhare paas do tricks hain. Trick one: ek fluffy fireproof sweater pahno jo zyaadatar hawa hi hai (Shuttle ke white-and-black tiles) — heat fluff mein se nahi ghus sakti, aur bahar ki side glow karke heat wapas space mein phenkti hai jaise mirror. Trick two: nose-cone ki pointy tip ke liye sweater kaam nahi karta kyunki wahan bahut patla hai, toh tip ko ek super-ceramic se banao jo simply 3000 degree pe koi problem nahi feel karta aur jab hawa use rust karne ki koshish kare toh apna khud ka glassy band-aid bana leta hai. Bade flat hisson ke liye fluffy blanket, sharp points ke liye tough magic ceramic.
"TILES InSulate, BORIDES Bear it." — silica = blocking se cool karo ; diborides = hot but unbeaten . Aur chemistry ke liye: "SiC makes the glass that lasts."
Why does stagnation heat flux scale as V 3 Shock mein air ka mass flux ∝ ρ V ∝ V 2 ∝ ρ V 3
What is LI-900? Shuttle reusable surface insulation: ~94% porous amorphous silica fibre tile, density 144 kg/m³, RCG black glaze.
Amorphous silica achha insulator kyun hai? Random disordered network + huge porosity → bahut low thermal conductivity k
Black glaze kyun help karta hai? High emissivity ε ≈ 0.9 q rad = ε σ T 4
Do example UHTCs aur unke melting points? ZrB₂ (~3245 °C) aur HfB₂ (~3380 °C).
Diborides itna high melt kyun karte hain? Mixed strong covalent (B–B) + metallic (Zr/Hf) bonding network todne mein huge energy chahiye.
ZrB₂ mein SiC kyun add karte hain? Ye SiO₂ mein oxidise hota hai jo ek self-healing borosilicate glass banata hai jo O₂ diffusion ke against seal karta hai.
Akele B₂O₃ pe protection ke liye rely karne mein kya problem hai? B₂O₃ volatile hai aur ~1100 °C ke upar evaporate ho jaata hai, porous ZrO₂ chhodta hai; stability ke liye SiC-derived glass chahiye.
Tile ki back-face temperature ka formula? T cold = T hot − q L / k
Tiles ki jagah sharp leading edges pe UHTCs kyun? q ∝ R n − 1/2
Radiation balance se equilibrium surface temperature? T = ( q / ε σ ) 1/4
Fourier's Law of Heat Conduction Stefan-Boltzmann Radiation Law Covalent vs Metallic Bonding Oxidation Kinetics and Protective Oxide Layers Ablative Heat Shields (Apollo, PICA) Amorphous vs Crystalline Solids Refractory Ceramics and Carbides Re-entry Aerodynamics & Boundary Layers
scales as q ~ rho^0.5 V^3 / sqrt Rn
V^3 term: velocity dominates
amorphous SiO2, ~94% porous
Fourier: T_cold = T_hot - qL/k
needs sharp AND survivable
Fast re-entry = huge heat
Sharp edges concentrate heat
High emissivity radiates heat
Withstands thousands of K
