Forty-five kilograms of carbon dioxide is stored in a high-pressure cylinder that is 25 cm in diameter (OD), 1.2 m long and 1.2 cm-thick. The cylinder is fitted with a safety rupture diaphragm designed to fail at 14 MPa (with the specified charge, this pressure will be reached when the temperature increases to 50°C). During a fire, the cylinder is completely exposed to the irradiation from flames at 1097°C (? = 1.0). For the specified conditions, c = 2.5 kJ/(kg K) for CO2. Neglecting the convective heat transfer, determine the length of the time the cylinder may be exposed to this irradiation before the diaphragm will fail if the initial temperature is 21°C and (a) the cylinder is bare oxidized steel(? = 0.79), (b) the cylinder is painted with aluminum paint (? = 0.30).

Question

GIVEN

- CO2 in a high pressure cylinder exposed to flames

- Mass of CO2 (mg) = 45 kg

- Cylinder dimensions

- Outside Diameter (D) = 25 cm = 0.25 m

- Length (L) = 1.2 m

- Thickness (s) = 1.2 cm = 0.012 m

- Rupture diaphragm fails at 14 MPa (Tgf = 50°C = 323 K)

- Temperature of flames (Tf) = 1097°C = 1370 K ( ?f = 1.0)

- Specific heat of CO2 (cv) = 2.5 kJ/(kg K)

- Initial temperature (Tgf) = 21°C = 394 K

FIND

The time for the diaphragm to fail if the cylinder is

(a) bare oxidized steel (?s = 0.79) or

(b) painted with aluminum paint (?2s = 0.30)

ASSUMPTIONS

Convective heat transfer is negligible

Cylinder is 1% carbon steel

Irradiation is constant and uniform over the entire cylinder

Quasi-steady state

Thermal resistance between the gas and the cylinder is negligible (Ts = Tg)

Variation of specific heat of gas and cylinder with temperature is negligible

SKETCH



PROPERTIES AND CONSTANTS

the Stephan-Boltzmann constant (?) = 5.67 x 10–8 W/(m2 K4

for 1% carbon steel at 21°C.

Density (ps) = 7801 kg/m3

Specific heat (cs) = 473 J/(kg K)

Answer 1

The exterior surface area of the cylinder is



The mass of steel in the cylinder is



Performing an energy balance on the gas

heat input = rate of increase in enthalpy



Solving for the rate of change of the gas temperature



Case (a)

Initially



Finally



The rate of change of the gas temperature is essentially constant, therefore, the time required for the gas to reach 120°F is



Case (b)