During transient operation, the steel nozzle of a rocket engine must not exceed a maximum allowable operatingtemperature of 1500 K when exposed to combustion gases characterized by a temperature of 2300 K and a convectioncoefficient of 5000 W/m².K. To extend the duration of engine operation, it is proposed that a ceramic thermal barriercoating (k = 10 W/m-K, α = 6 × 106 m²/s) be applied to the interior surface of the nozzle.(a) If the ceramic coating is 10 mm thick and at an initial temperature of 300 K, obtain a conservative estimate of themaximum allowable duration of engine operation, in s. The nozzle radius is much larger than the combined wall andcoating thickness.(b) Determine the inner (x = 0) and outer(x = L) surface temperatures, in °C, of the coating at time t = 30 seconds.

Tmax.=1500kh=5000 w/m2.kk=10 W/m.K* The ceramic temperature at x=0, corresponds to the maximum wall…

During transient operation, the steel nozzle of a rocket engine must not exceed a maximum allowable operating temperature of 1500 K when exposed to combustion gases characterized by a temperature of 2300 K and a convection coefficient of 5000 W/m²K. To extend the duration of engine operation, it is proposed that a ceramic thermal barrier coating (k = 10 W/m-K, a = 6 x 10-6 m²/s) be applied to the interior surface of the nozzle. (a) If the ceramic coating is 10 mm thick and at an initial temperature of 300 K, obtain a conservative estimate of the maximum allowable duration of engine operation, in s. The nozzle radius is much larger than the combined wall and coating thickness. (b) Determine the inner (x = 0) and outer(x = L) surface temperatures, in °C, of the coating at time t = 30 seconds.

During transient operation, the steel nozzle of a rocket engine must not exceed a maximum allowable operating temperature of 1500 K when exposed to combustion gases characterized by a temperature of 2300 K and a convection coefficient of 5000 W/m²K. To extend the duration of engine operation, it is proposed that a ceramic thermal barrier coating (k = 10 W/m-K, a = 6 x 10-6 m²/s) be applied to the interior surface of the nozzle. (a) If the ceramic coating is 10 mm thick and at an initial temperature of 300 K, obtain a conservative estimate of the maximum allowable duration of engine operation, in s. The nozzle radius is much larger than the combined wall and coating thickness. (b) Determine the inner (x = 0) and outer(x = L) surface temperatures, in °C, of the coating at time t = 30 seconds.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

During transient operation, the steel nozzle of a rocket engine must not exceed a maximum allowable operating
temperature of 1500 K when exposed to combustion gases characterized by a temperature of 2300 K and a convection
coefficient of 5000 W/m².K. To extend the duration of engine operation, it is proposed that a ceramic thermal barrier
coating (k = 10 W/m-K, α = 6 × 106 m²/s) be applied to the interior surface of the nozzle.
(a) If the ceramic coating is 10 mm thick and at an initial temperature of 300 K, obtain a conservative estimate of the
maximum allowable duration of engine operation, in s. The nozzle radius is much larger than the combined wall and
coating thickness.
(b) Determine the inner (x = 0) and outer(x = L) surface temperatures, in °C, of the coating at time t = 30 seconds.

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