A system operating at cryogenic temperatures is not a scaled-down version of a room-temperature one. Several things change qualitatively.
Material properties are not constant
Around room temperature, treating thermal conductivity and specific heat as constants is usually reasonable. In the cryogenic range it is not: specific heat varies by orders of magnitude with temperature, and conductivity peaks in many materials.
The direct consequence: using constant properties in a transient analysis gets the cool-down time and the temperature distribution markedly wrong. Properties must be defined as functions of temperature.
The heat leak budget
A few watts that would be negligible at room temperature can be a significant part of the cooling load in a cryogenic system — because the work needed to remove that watt is, by the Carnot limit, far greater.
The purpose of the analysis is therefore usually not "what is the temperature" but "what is the total heat leak, and from where". The items: conduction through supports, convection through residual gas, radiation between surfaces, cable and pipe penetrations.
Radiation matters more than expected
Because convection is almost entirely suppressed by vacuum, radiation becomes the main channel. Multi-layer insulation and radiation shields are therefore central to cryogenic design, and surface emissivity sets the performance directly. See the radiation note.
The fluid side
Cryogenic fluids operate close to the critical point; density and specific heat change greatly for small pressure changes. Two phases form easily and the cavitation risk in pumps is high. See the cavitation note.
Thermal contraction is also not negligible: dimensions differ between the cold and warm states, which affects both sealing and contact resistance. See the thermal contact resistance note.
References
- Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.
- Shah, R. K. & Sekulić, D. P. (2003). Fundamentals of Heat Exchanger Design. John Wiley & Sons. DOI: 10.1002/9780470172605