Question bank — Regenerative cooling — heat flux, coolant flow, pressure drop

False. Thickness $t_w$ wall resistance $R_w=t_w/k_w$ badhata hai, aur bada resistance matlab metal ke across bada temperature drop, toh gas-side face $T_{wg}$ aur zyada garam ho jaata hai. Fix hai patli, high-$k$ copper.

True. Steady state mein wahi heat flux $q$ teeno layers se ek ke baad ek guzarta hai, bilkul series resistors mein current ki tarah, isliye unke per-area resistances sum hote hain.

False. Darcy–Weisbach deta hai $\Delta p\propto v^2$, toh $v$ double karne se $\Delta p$ chaar guna ho jaata hai. Velocity ek mehenga knob hai.

True. Zyada flow ${\dot{m}}_c$ badhata hai (heat zyada tezi se le jaata hai, $Q={\dot{m}}_c{c}_p\Delta T_c$) aur $h_c$ bhi badhata hai via Dittus–Boelter ($h_c\propto {\text{Re}}^{0.8}$), wall temperature giraata hai.

False. Coolant hi propellant hai; jo heat usne soak ki wo combustion chamber mein wapas jaati hai uske saath. Yahi recycling hai jo "regenerative" ka matlab banaati hai.

False (is design mein). Vapour film wall ko insulate kar deta hai (film boiling), $h_c$ collapse kar deta hai aur $T_{wg}$ burnout ki taraf spike karta hai. Isliye $\Delta T_c$ boiling/coking limit se neeche rakha jaata hai.

True ($M>0$ ke liye). Friction near-wall gas ko sirf aadha stagnation tak wapas garam karta hai, aur gases ke liye recovery factor $r={\text{Pr}}^{1/3}<1$ hota hai, isliye $T_{aw}<T_c$. Dekho Adiabatic Wall Temperature and Recovery Factor.

False. $q$ ek density hai (W/m²) — heat per unit wall area. $Q=qA$ total power (W) hai wetted area $A$ ke upar. Inhe confuse karna coolant flow calculation ko bigaad deta hai.

Error: driving temperature recovery temperature $T_{aw}$ hai, $T_c$ nahi. Gas tezi se chalti hai, isliye sirf $T_{aw}<T_c$ hi actually wall mein heat push karta hai; $T_c$ use karne se $q$ overestimate hota hai aur coolant waste hota hai.

Error: high conductivity $R_w=t_w/k_w$ ko tiny banata hai, isliye ye sabse chhoti resistance hai. Gas-side convection $R_g=1/h_g$ usually sabse badi hoti hai aur flux control karti hai.

Error: energy balance temperature rise $\Delta T_c=T_{out}-T_{in}$ use karta hai, sirf $T_{out}$ nahi. Coolant pehle se $T_{in}$ par garm enter karta hai; sirf rise hi absorbed heat store karta hai.

Error: short channels $\Delta p$ giraate hain lekin wetted area $A$ kam karte hain, heat dump karne ki jagah kam hoti hai, aur $v$ zyada force ho sakta hai (jo $\Delta p$ ko $v^2$ ki tarah wapas badhata hai). Ye trade-off hai, free win nahi.

Correct, error nahi hai — drops telescope karte hain: $(T_{aw}-T_{wg})+(T_{wg}-T_{wc})+(T_{wc}-T_{co})=T_{aw}-T_{co}$. (Trap: check karo ki tumne blink nahi kiya aur isse galat nahi keh diya.)

Error: $\Delta p\propto 1/d_h$, isliye bada $d_h$ $\Delta p$ giraata hai. Bade channels pump ke liye gentle hote hain — lekin flow slow karte hain aur $h_c$ weak karte hain, trade ka doosra side.

Error: resistances add karte hain, phir invert karte hain: $U=(1/h_g+t_w/k_w+1/h_c{)}^{-1}$. Conductances seedha add karna dimensionally aur physically galat hai.

Turbulent wall friction ko fluid ka momentum flux destroy karna hota hai, jo dynamic pressure $\frac{1}{2}\rho v^2$ ke saath scale karta hai. Dimensionless $f$ messy geometry/turbulence ko ek measured number mein package karta hai.

Alag coolant dead mass hoga jo tumhe carry karna hoga aur jala nahi sakte. Propellant use karne ka matlab hai heat flame mein recycle hoti hai aur koi extra tank nahi chahiye — rockets mein mass efficiency sab kuch hai.

Iska per-area resistance $R_g=1/h_g$ typically sabse bada hota hai (gas convection dense liquid coolant ke comparison mein heat ka ghata mover hai). Series mein, sabse badi resistance total dominate karti hai, isliye ye flux set karti hai.

Regen cooling tabhi kaam karta hai jab tumhare paas itna propellant ho jo stream ho sake. Agar cooling ki demand engine ke burn se zyada mass flow maange, toh wall ko regen se cool nahi kiya ja sakta — tumhe help ke liye Film Cooling ya Ablative Cooling chahiye hoga.

Chhota $d_h$ velocity badhata hai, $h_c$ boost karta hai (better cooling), lekin $\Delta p\propto v^2/d_h$ explode karta hai (worse pump cost). Cooling aur pumping channel size par opposite directions mein pull karte hain.

Steady state ka matlab hai koi bhi heat kahin accumulate nahi karti; har layer par energy in equals energy out. Agar flux layers ke beech alag hota, toh temperature change hoti rehti — steady nahi. Yahi conservation hai jo resistances ko telescope karne deta hai.

Coolant resistance $R_c=1/h_c\to 0$ drop ho jaata hai. Flux phir bache hue gas aur wall resistances se cap ho jaata hai — chahe coolant kitna bhi achcha ho, tum un do se neeche cool nahi kar sakte.

Tab $R_w=t_w/k_w\to 0$ aur $T_{wg}=T_{wc}$ — metal ke across koi temperature drop nahi. Flux poori tarah do convection resistances $R_g$ aur $R_c$ se set hota hai.

Coolant-side driving difference $T_{wc}-T_{co}\to 0$, isliye wo stage koi heat carry nahi karta — coolant ab energy absorb nahi kar sakta aur wall overheat ho jaati hai. Cool inlet temperature essential hai.

$\Delta p\to 0$ — vanishingly short channel ke paas rub karne ke liye koi wall nahi. Lekin wetted area $A\to 0$ bhi ho jaata hai, isliye koi heat remove nahi hoti; zero-pressure "win" useless hai.

Velocity-recovery correction vanish ho jaata hai aur $T_{aw}\to T_c$: bina motion ke koi slowdown-reheating distinction nahi, isliye recovery temperature flame temperature par collapse kar jaata hai.

Full stagnation temperature — near-wall gas ki saari kinetic energy heat ke roop mein recover ho jaati hai. Real gases mein $r={\text{Pr}}^{1/3}<1$ hota hai, isliye $T_{aw}$ stagnation se thoda neeche rehta hai.