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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter11: Heat Transfer By Radiation

Section: Chapter Questions

Problem 11.25P

See similar textbooks

Similar questions

1.1 On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to temperature of –5°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the heat loss through the wall, which is 10-m long and 3-m high. Problem 1.1
(a) If the cost of producing the hot water is $0.10 per kWh, what is the representative daily costof heat loss from an uninsulated pipe to the air per meter of pipe length? The convectionresistance associated with water flow in the pipe may be neglected.(b) Determine the savings associated with application of a 10-mm-thick coating of urethaneinsulation (k = 0.026 W/m-K) to the outer surface of the pipe.
The emissivity of galvanized steel sheet, a common roofing material, is ε = 0.13 at temperatures around 300 K, while its absorptivity for solar irradiation is αS = 0.65. Would the neighborhood cat be comfortable walking on a roof constructed of the material on a day when GS = 750 W/m2, T∞ = 16°C, and h = 7 W/m2 · K? Assume the bottom surface of the steel is insulated.
Chips of width L _ 15 mm on a side are mounted to a substrate that is installed in an enclosure whose walls and air are maintained at a temperature of Tsur=T∞=25oC. The chips have an emissivity of ε=0.60 and a maximum allowable temperature of Ts=85oC. (a) If heat is rejected from the chips by radiation and natural convection, what is the maximum operating power of each chip? The convection coefficient may be approximated as h=11.7 W/m2K. (b) If a fan is used to maintain airflow through the enclosure and heat transfer is by only forced convection, with h=250 W/m2K, what is the maximum operating power
a) What regions show the largest oceanic latent heat loss? b) What regions show the saltiest surface waters? c) What is the main factor affecting the two radiation heat flux terms? Name the two fluxes. d) What is the main factor affecting the two turbulent heat flux terms? Name the two fluxes.
Steam at a temperature of 723 K is flowing through a pipe with an outer diameter of 100 mm. The pipe is insulated with 30-mm thick mineral wool, the average thermal conductivity of which is 0.065 W/m.K. Determine the outside surface temperature of mineral wool if the ambient air temperature is 300 Assume the hot-surface temperature of the mineral wool is the same as that of the flowing steam and the value of the surface coefficient of the insulating material is 33 W/m2.K.
The spherical, thin – walled metallic container is used to store liquid nitrogen at 77 K.The container has a diameter of 0.5 m and is covered with an evacuated insulationsystem composed of silica powder (k = 0.0017 W/m – K). The insulation is 25 mm thick,and its outer surface is exposed to ambient air at 300 K. The latent heat of vaporizationof liquid nitrogen is 2 x 105 J/kg. If the convection coefficient is 20 W/m2 – K over theouter surface. Determine the rate of liquid boil – off of nitrogen per hour. Showexpiration of critical radius of insulation.
An electrical heater 114 mm long and 7 mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of 9 W/m · K. Estimate the temperature reached by the heater when dissipating 54 W with the surface of the block at a temperature of 27°C.
How can we use the transient temperature charts when the surface temperature of the geometry is specified instead of the temperature of the surrounding medium and the convection heat transfer coefficient?
It is desired to heat the workshop with a stove made of falling cylindrical sheet material with an outer diameter of 400 mm and a height of 1600 mm. The surface temperature of the stove is 217 oC and the radiation emission coefficient is 0.92, the temperature of the workshop surfaces is 12 oC and the ambient temperature of the workshop is 17 oC. Next to the stove, the workshop surface area is very large. From the side surface of the stove to the workshop; a) By transport,b) with radiation Calculate the heat transfer.
1. (a) Consider a room with a 1.8-m-high and 2.0-m-wide double-pane window consisting of two 4-mm-thick layers of glass separated by a 10-mm-wide stagnant air space. The convection heat transfer coefficients on the inner and outer surfaces of the window are 12 W/m2 K and 25 W/m2 K, respectively, while the average thermal conductivity of glass is 0.78 W/m K; and the air, 0.026 W/m K. If the room is maintained at 22 oC, the outside temperature is -4 oC and heat transfer due to radiation can be neglected, determine: (i) Draw the sketch and thermal resistance network; (ii) the total thermal resistance; (iii) the steady rate of heat transfer through this double-pane window; (iv) the temperature of the inner surface of the window.…
In the design of electronic components, it is very desirable to attach the electronic circuitry to a substrate material that is a very good thermal conductor but also a very effective electrical insulator. If the high cost is not a major concern, what material would you propose for the substrate?