A cryogenic storage vessel is surrounded by a cylindrical
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A cryogenic storage vessel is surrounded by a cylindrical, three-layer protective shell of total surface area 4.5 m². From the inner surface outward, the layers are
1. Stainless steel, thickness 5.0 mm, thermal conductivity 15 W/(m·K)
2. An evacuated gap that behaves like a stationary gas with effective thermal conductivity 0.0020 W/(m·K) and thickness 25 mm
3. Aluminum alloy, thickness 3.0 mm, thermal conductivity 205 W/(m·K)
During normal operation the inner surface of the stainless-steel layer remains at −150 °C, while the outer surface of the aluminum layer is exposed to room air maintained at 22 °C. Neglect any surface resistances and assume radial effects are negligible so that the problem may be treated as one-dimensional across the total 33 mm composite thickness.
(a) Calculate the combined thermal resistance of the three-layer shell.
(b) Determine the temperature at the interface between the stainless-steel layer and the evacuated gap.
(c) Compute the steady-state rate at which energy enters the cryogenic vessel through the 4.5 m² shell.
(d) Identify which of the three layers contributes the largest fraction of the total thermal resistance and explain, with numerical support from your results, why this layer dominates.