Transpiration cooling — Hinglish notes

3.3.31 · Physics › Rocket Propulsion

Transpiration cooling KYA hai?

Yeh do related ideas ka "active" cousin hai:

Film cooling — coolant discrete slots/holes se inject kiya jaata hai (kuch bade holes).
Transpiration cooling — coolant uniformly bahut saare microscopic pores se "sweated" hota hai (ek porous solid).

Rockets mein WHY zaroori hai: combustion-chamber aur nozzle-throat gas temperatures ( $T_{g} \sim 3000 - 3500 K$ ) kisi bhi wall material ke melting point se zyada hain. Aap sirf material se survive nahi kar sakte; aapko actively heat remove karni hogi. Transpiration cooling common schemes mein sabse kam coolant per unit mein sabse low wall temperature deta hai, isliye yeh sabse extreme heat-load regions (throats, re-entry noses, turbine blades) pe use hota hai.

HOW kaam karta hai — physics chain

Blowing boundary layer ko mota karta hai. Injected coolant hot boundary layer ko wall se door push karta hai. Wall pe temperature gradient $(\frac{\partial T}{\partial y})_{w a l l}$ drop hoti hai, toh wall mein conduction drop hoti hai.
Coolant ek heat sink hai. Coolant $T_{c}$ pe thanda enter karta hai aur wall temperature $T_{w}$ ke paas leave karta hai, $\overset{m}{˙}_{c} c_{p} (T_{w} - T_{c})$ energy soak up karta hai.
Result: wall ek temperature $T_{w}$ pe baith ti hai jo gas temperature $T_{g}$ se bahut neeche hai.

DERIVATION — wall energy balance (scratch se)

Setup. Area $A$ ka ek chhota wall patch lo. Maano coolant mass flow usse $\overset{m}{˙}_{c}$ hai specific heat $c_{p}$ ke saath, $T_{c}$ pe enter karke aur wall temperature $T_{w}$ pe leave karke.

Step 1 — Blowing ke BINA gas se heat. Newton-style convection un-blown heat flux deta hai $q_{0} = h_{0} (T_{g} - T_{w})$ jahan $h_{0}$ bare hot boundary layer ka heat-transfer coefficient hai. Yeh step kyun? Convection heat flux driving temperature difference $(T_{g} - T_{w})$ ke proportional hai; $h_{0}$ saari boundary-layer fluid mechanics ko ek number mein package karta hai.

Step 2 — Blowing flux ko reduce karta hai. Coolant inject karne se effective coefficient $h < h_{0}$ ho jaata hai. Blowing reduction factor define karo $η = \frac{q}{q _{0}} = \frac{h}{h _{0}} (0 < η \leq 1),$ toh actual flux jo wall tak pahunchti hai $q = η h_{0} (T_{g} - T_{w}) .$ Yeh step kyun? Blowing directly $(T_{g} - T_{w})$ nahi badalta; yeh badalta hai ki gas kitni effectively heat deliver karta hai, yaani coefficient.

Step 3 — Woh heat kahan jaati hai. Coolant ise absorb karta hai $T_{c}$ se $T_{w}$ tak heat hote waqt: $q A = \overset{m}{˙}_{c} c_{p} (T_{w} - T_{c}) .$ Yeh step kyun? Energy in (gas se) = energy out (coolant stream mein). Pure conservation.

Step 4 — Wall temperature solve karo. Step 2 substitute karo: $η h_{0} (T_{g} - T_{w}) A = \overset{m}{˙}_{c} c_{p} (T_{w} - T_{c}) .$ Maano $G = \overset{m}{˙}_{c} / A$ coolant mass flux hai (kg m⁻² s⁻¹). $A$ se divide karo: $η h_{0} (T_{g} - T_{w}) = G c_{p} (T_{w} - T_{c}) .$ $T_{w}$ collect karo: $T_{w} = \frac{η h _{0} T _{g} + G c _{p} T _{c}}{η h _{0} + G c _{p}}$

Non-dimensional form. Cooling effectiveness define karo $ϕ \equiv \frac{T _{g} - T _{w}}{T _{g} - T _{c}} .$ Boxed result se ( $T_{g}$ se har side subtract karke aur simplify karke): $ϕ = \frac{G c _{p}}{η h _{0} + G c _{p}} = \frac{1}{1 + \frac{η h _{0}}{G c _{p}}}$ Padhne ka tarika: $ϕ = 0$ matlab wall gas jitni hot hai (koi cooling nahi); $ϕ = 1$ matlab wall coolant jitni cold hai (perfect). Ratio $\frac{G c _{p}}{η h _{0}}$ "coolant-to-gas" conductance ratio hai — woh single knob jo sab kuch control karta hai.

Worked examples

Common mistakes

Active recall

Recall Answers cover karo. Reveal karne se pehle har ek aloud explain karo.

Transpiration cooling mein heat load kaun se do mechanisms reduce karte hain? ➜ Coolant dwara heat-sink absorption + boundary-layer thickening (lower effective $h$ ).
$η < 1$ physically kya matlab hai? ➜ Blowing effective heat-transfer coefficient ko bare value $h_{0}$ se neeche le jaata hai.
$T_{w}$ kin do temperatures ke beech mein hona chahiye? ➜ $T_{c} < T_{w} < T_{g}$ .
Effectiveness control karne wala single ratio kya hai? ➜ $G c_{p} / (η h_{0})$ .
Coolant double karne se wall temperature half kyun nahi hoti? ➜ $T_{w}$ $T_{c}$ pe floored hai; returns diminish hote hain.

Transpiration cooling — definition

Coolant ek porous wall se hot boundary layer mein force kiya jaata hai, jo heat absorb bhi karta hai aur ek protective film banata hai jo effective heat-transfer coefficient kam karta hai.

Difference: film vs transpiration cooling

Film kuch discrete slots/holes use karta hai; transpiration coolant ko uniformly bahut saare microscopic pores se "sweats" karta hai.

Wall energy balance equation

η h_{0} (T_{g} - T_{w}) = G c_{p} (T_{w} - T_{c})

(gas-side flux = coolant absorption per area).

Wall temperature formula

T_{w} = \frac{η h _{0} T _{g} + G c _{p} T _{c}}{η h _{0} + G c _{p}}

Cooling effectiveness

ϕ

ϕ = \frac{T _{g} - T _{w}}{T _{g} - T _{c}} = \frac{G c _{p}}{η h _{0} + G c _{p}} = \frac{1}{1 + η h _{0} / ( G c _{p} )}

Blowing reduction factor

η

η = h / h_{0}

, blown aur un-blown heat-transfer coefficient ka ratio;

0 < η \leq 1

Coolant mass flux

G

G = \overset{m}{˙}_{c} / A

, coolant mass per unit wall area per second (kg m⁻² s⁻¹).

Transpiration film cooling se per unit coolant kyun beat karta hai

Bada

G

heat-sink capacity badhata hai AUR

η

kam karta hai (mota blanket) — double benefit.

Limit

ϕ \to 1

ka matlab

Wall coolant temperature ke paas pahunchti hai; near-perfect cooling.

Rocket mein heat load sabse zyada kahan hota hai

Nozzle throat pe (max

h_{0}

), isliye cooling wahan sabse critical hai.

Recall Feynman: 12-year-old ko explain karo

Socho tum ek bonfire ke paas khade ho aur tumhari skin hot ho rahi hai. Ab socho tumhari skin mein tiny holes hain jo hamesha thanda paani bahar nikaalte rehte hain. Do achhi cheezein hoti hain: paani heat ko ek sponge ki tarah soak karta hai, aur paani-mist ki layer hot air ko tumhari skin se thoda door push karti hai. Toh tumhari skin cool rehti hai chahe seedha aag ke paas ho. Ek rocket bilkul wahi trick karta hai: uski wall mein millions of tiny holes hain aur woh unse thanda fuel "sweats" karta hai, toh metal nahi pighalti chahe uske paas gas lava se bhi zyada hot ho. Jitna zyada sweats, utna cooler rehta hai — lekin woh kabhi paani se zyada thanda nahi ho sakta.

Connections

Regenerative Cooling — coolant wall ke peeche se chalta hai phir burn hota hai; heat paths compare karo.
Film Cooling — discrete-hole cousin; same $ϕ$ language.
Ablative Cooling — passive alternative jo material sacrifice karta hai.
Convective Heat Transfer — $q = h (T_{g} - T_{w})$ aur $h_{0}$ ka source.
Boundary Layer Theory — blowing $h$ kyun kam karta hai.
Nozzle Throat Heat Flux — jahan transpiration sabse zyada zaroori hai.
Specific Impulse — coolant mass ek thrust cost hai; $G$ ko performance se jodata hai.