Because you forgot to let the pipes drip during a freezing night, a section of an outdoor pipe is now frozen. The frozen section is L = 1 m long and the inner pipe diameter is D = 1.8 cm. During the day, the pipe is exposed to the cold air, the Sun, and the radiating surroundings. The cold air temperature is T∞ = -10°C, and has convection heat transfer coefficient h = 20 W/m2·K. The Sun provides solar irradiance of Gsun = 1350 W/m2. The steel pipe surface has absorptivity α = 0.6 and emissivity ε= 0.1. The surroundings, such as vegetation, houses, ground, etc. can be assumed to be blackbody held at Tsur = 280 K. A) Using the energy conservation system illustrated below, establish an equation that describes the stored energy in the section of frozen water (Est). B) Determine the amount of time needed to melt the ice in the pipe. Ice has density ρ= 920 kg/m3, and latent heat of fusion hsf = 334 kJ/kg. The ice is Tw = 0°C. Ignore conduction through the pipe walls – assume the pipe itself is thin and thermally conducting metal.
Because you forgot to let the pipes drip during a freezing night, a section of an outdoor pipe is now frozen. The frozen section is L = 1 m long and the inner pipe diameter is D = 1.8 cm. During the day, the pipe is exposed to the cold air, the Sun, and the radiating surroundings. The cold air temperature is T∞ = -10°C, and has convection heat transfer coefficient h = 20 W/m2·K. The Sun provides solar irradiance of Gsun = 1350 W/m2. The steel pipe surface has absorptivity α = 0.6 and emissivity ε= 0.1. The surroundings, such as vegetation, houses, ground, etc. can be assumed to be blackbody held at Tsur = 280 K. A) Using the energy conservation system illustrated below, establish an equation that describes the stored energy in the section of frozen water (Est). B) Determine the amount of time needed to melt the ice in the pipe. Ice has density ρ= 920 kg/m3, and latent heat of fusion hsf = 334 kJ/kg. The ice is Tw = 0°C. Ignore conduction through the pipe walls – assume the pipe itself is thin and thermally conducting metal.
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