A spherical vessel 0.3-m in diameter is located in a large room whose walls are at 27°C (see sketch). If the vessel is used to store liquid oxygen at –183°C and both the surface of the storage vessel and the walls of the room are black, calculate the rate of heat transfer by radiation to the liquid oxygen in watts and in Btu/h.
GIVEN
• A black spherical vessel of liquid oxygen in a large black room
• Liquid oxygen temperature (To) = –183°C = 90 K
• Sphere diameter (D) = 0.3 m
• Room wall temperature (Tw) = 27°C = 300 K
FIND
• The rate of radiative heat transfer to the liquid oxygen in W and Btu/h
ASSUMPTIONS
• Steady state prevails
• The temperature of the vessel wall is the same as the temperature of the oxygen
SKETCH
PROPERTIES AND CONSTANTS
The Stefan-Boltzmann constant (?) = 5.67 ? 10–8 W/(m2 K4)
The net radiative heat transfer to a black body in a black enclosure is given
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Replot the data points of Figure 5.9(b) on log-log paper and find an equation approximating the best correlation line. Compare your results with Figure 5.10. Then, suppose that steam at 1 atm and 100°C is flowing across a 5-cm-OD pipe at a velocity of 1 m/s. Using the data in Figure 5.10, estimate the Nusselt number, the heat transfer coefficient, and the rate of heat transfer per meter length of pipe if the pipe is at 200°C and compare with predictions from your correlation equation.
GIVEN
Figure 5.9(b) in text
Steam flowing across a pipe
Steam pressure = 1 atm
Steam temperature (Ts) = 100°C
Pipe outside diameter (D) = 5 cm = 0.05 m
Steam velocity (U?) = 1 m/s
Pipe temperature (Tp) = 200°C
FIND
(a) Replot Figure 5.9(b) on log-log paper and find an equation approximating the best correlation line
(b) Find the Nusselt number (Nu), the heat transfer coefficient (hc), and the rate of heat transfer per
unit length (q/L) using Figure 5.10
(c) Compare results with your correlated equation
ASSUMPTIONS
Steady state
Radiative heat transfer is negligible
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 35, for steam at 1 atm and 100°C
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A) a 7-cm-long wax candle. B) another name for a main-sequence star. C) another name for a barred-spiral galaxy. D) a light source of known luminosity.
How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s2?
A) 4.35 s B) 5.30 s C) 9.57 s D) 10.6 s E) 63.1 s
A 500-N weight sits on the small piston of a hydraulic machine. The small piston has an area of 2.0 cm2. If the large piston has an area of 40 cm2, how much weight can the large piston support? Assume the pistons each have negligible weight
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