Question

The nozzle of an experimental rocket motor is fabricated from 5 mm-thick alloy steel. The combustion gases are at 2100 K, and the effective heat transfer coefficient is 6000 W/m²K. If the nozzle is initially at 300 K and the maximum allowable operating temperature for the steel is specified as 1300 K, what is the allowable duration of firing? To obtain a conservative estimate, neglect the heat loss from the outer surface of the nozzle. Take $k = 43 \text{ W/mK}$, $\alpha = 12.0 \times 10^{-6} \text{ m²/s}$ for the steel.

          The nozzle of an experimental rocket motor is fabricated from 5 mm-thick alloy steel.
The combustion gases are at 2100 K, and the effective heat transfer coefficient is
6000 W/m²K. If the nozzle is initially at 300 K and the maximum allowable operating
temperature for the steel is specified as 1300 K, what is the allowable duration of
firing? To obtain a conservative estimate, neglect the heat loss from the outer surface
of the nozzle. Take $k = 43 \text{ W/mK}$, $\alpha = 12.0 \times 10^{-6} \text{ m²/s}$ for the steel.

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The nozzle of an experimental rocket motor is fabricated from 5 mm-thick alloy steel.
The combustion gases are at 2100 K, and the effective heat transfer coefficient is
6000 W/m²K. If the nozzle is initially at 300 K and the maximum allowable operating
temperature for the steel is specified as 1300 K, what is the allowable duration of
firing? To obtain a conservative estimate, neglect the heat loss from the outer surface
of the nozzle. Take k = 43 W/mK, α = 12.0 × 10^-6 m²/s for the steel.

Added by Steven H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Dwijendra Rao

Step 1

This can be done using the formula for transient heat conduction in a semi-infinite solid: T - Ti = (q / (sqrt(pi * k * a * t))) * exp(-x^2 / (4 * a * t)) where: T = final temperature (1300 K) Ti = initial temperature (300 K) q = heat flux (h * (Tg - Ti)) = 6000 Show more…

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The nozzle of an experimental rocket motor is fabricated from 5 mm-thick alloy steel. The combustion gases are at 210 K, and the effective heat transfer coefficient is 6000 W/m^2K. If the nozzle is initially at 300 K and the maximum allowable operating temperature for the steel is specified as 1300 K, what is the allowable duration of firing? To obtain a conservative estimate, neglect the heat loss from the outer surface of the nozzle. Take k = 43 W/mK, a = 12.0x10^-6 m^2/s for the steel.

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