A vertical cylinder with 100 cm outer diameter contains a cryogenic system, and its outer surface is maintained at a temperature of –150°C. To insulate the cylinder from outside, it is placed in...

A vertical cylinder with 100 cm outer diameter contains a cryogenic system, and its outer surface is maintained at a temperature of –150°C. To insulate the cylinder from outside, it is placed in another coaxial cylinder with an inner diameter of 101 cm, and the annular space between the two cylinders is evacuated to a pressure of 0.1 Pa. A leakage occurs, however, and air pressure in the annulus space reaches 10 Pa. The inner surface of the outer cylinder is 20°C.

a. What is the regime in the annulus space before leakage?

b. After leakage, is rarefaction important?

 c. Assuming that air in the annular space is stagnant, calculate the heat transfer to the inner cylinder, per unit length, after leakage occurs. Calculate the temperature jump at each surface.

For simplicity, neglect the effect of thermal radiation and the effect of gravity.