4. At the intersection of 7th Avenue South and 20th Street there are several lar

Question

4. At the intersection of 7th Avenue South and 20th Street there are several large cylindrical tanks containing liquid oxygen. Such tanks are not usually pressurized, but are vented to the atmosphere, so the contents are at the boiling temperature of liquid oxygen at atmospheric pressure: -183 °C, and the inside surface of the tank is at the same temperature. ppose the space between a tank and its outer shell is 0.3 m thick and is filled with a high ation and evacuated, so the thermal conductivity of the space is only 0.02 W/(m·K) The thickness of the insulating space is much smaller than the diameter of the tank, therefore the tank surface, insulation, and outer shell may all be treated as approximately flat. Neglect the heat transfer resistance of both the metal tank wall and the outer shell. The emissivity of the surface of the outer shell is 0.9 and the convective heat transfer coefficient, with a light breeze blowing, is 25 W/(m .K). Let the temperature of the ambient air on a warm day be 30 °C and the temperature of the surroundings (average Su of surrounding buildings, pavement, and sky) be 20 °C a. Calculate the temperature on the surface of the outer shell. b. Estimate the rate of heat leakage per unit area, q", into the tank, causing boiloff of the liquid oxygen.

Explanation / Answer

Let us first calculate the heat transfer rate through the wall.

Heat transfer Q = ( To - Ts) / Rth.

T0 = Ambient temperature = 30 C.

Ts = Surface temperature of cylinder = -183 C.

Rth = Total thermal resistance.

Rth1 =Coducrive Thermal resistance of wall

Area = A = 1 m2.

Rth1 = L/KA = 0.3/0.02*1 = 15

Rth2 = Convective thermal resistance of wall = 1/hA = 1/25*1 = 0.04.

Rth = Rth1 + Rth2 = 15+0.04 = 15.04.

Heat transfer = (30+183) / (15.04) = 14.16 J.

Surface temperature = T.

14.16 = -0.02*1*(-183-T)/0.3

T = 29.4 C.

heat leak = q = 14.16 W/m2

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