A thin tube has a diameter of 10 mm. Inside the tube, there is a cold...

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A thin tube has a diameter of 10 mm. Inside the tube, there is a cold fluid flow at 255 K. Outside the tube, air flows at 270 K with convection coefficient of 100 W/m²K. (a) If the convection heat transfer coefficient of the cold fluid is very very large, what is the temperature of the tube wall at the inner surface of the tube? (b) What is the heat flow rate per unit length of the tube? (c) In more humid conditions, the water vapor in the air creates a 4-mm thick frost layer on the outer side of the tube. What is the heat flow rate per unit length with the frost layer assuming the frost conductivity is 0.4 W/mK? (ignore the heat transfer due to frost formation) (d) If the frost layer thickness grows to 8 mm, how does thermal resistance for convection heat transfer per unit length vary? Provide proof of your answer. SCHEMATIC: Frost k=0.4 W/m K Ambient air h=100 W/m².K Refrigerant Part(c) Ts.2 ₁=5 mm Ts.1 12 = 1 +4 mm A thin tube has a diameter of 10 mm. Inside the tube, there is a cold fluid flow at 255 K. Outside the tube, air flows at 270 K with convection coefficient of 100 W/m²K. (a) If the convection heat transfer coefficient of the cold fluid is very very large, what is the temperature of the tube wall at the inner surface of the tube? (b) What is the heat flow rate per unit length of the tube? (c) In more humid conditions, the water vapor in the air creates a 4-mm thick frost layer on the outer side of the tube. What is the heat flow rate per unit length with the frost layer assuming the frost conductivity is 0.4 W/mK? (ignore the heat transfer due to frost formation) (d) If the frost layer thickness grows to 8 mm, how does thermal resistance for convection heat transfer per unit length vary? Provide proof of your answer. SCHEMATIC: Frost k=0.4 W/m K Ambient air h=100 W/m².K Refrigerant Part(c) Ts.2 ₁=5 mm Ts.1 12 = 1 +4 mm