The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is - 196°C. Therefore, nitrogen is commonly used in low temperature scientific studies since the temperature of liquid nitrogen in a tank open to the atmosphere remains constant at - 196°C until the liquid nitrogen in the tank is depleted. Any heat transfer to the tank results in the evaporation of some liquid nitrogen, which has a heat of vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm.
Consider a thick-walled spherical tank of inner radius r1 = 2 m, outer radius r2 = 2.1 m, and constant thermal conductivity k = 12 W/m · K. The tank is initially filled with liquid nitrogen at 1 atm and −196°C, and is exposed to ambient air at T∞ = 20°C with a heat transfer coefficient of h = 35 W/m2 · K. The inner surface temperature of the spherical tank is observed to be almost the same as the temperature of the nitrogen inside. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the tank, (b) obtain a relation for the Variation of temperature in the tank material by solving the differential equation, and (c) determine the rate of evaporation of the liquid nitrogen in the tank as a result of the heat transfer from the ambient air. Answer: (c) 1.62 kg/s
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