Where does heat leak into a cryogenic tank?

Mainly three paths: thermal radiation from the outer vessel to the inner vessel, conduction through the neck tube and supports, and residual gas conduction if the vacuum is poor. In the example 1 m³ liquid nitrogen tank, radiation alone brings in about 57 W even between surfaces of emissivity 0.05, so multilayer insulation (MLI) to cut radiation is the foundation.

Does liquid hydrogen boil off faster than liquid nitrogen?

For the same heat input, liquid hydrogen has about one fifth the latent heat per volume (31.6 versus 161 MJ/m³), so it boils off about five times faster. In the example, 5 W of heat leak evaporated 0.27%/day of LN2 and 1.37%/day of LH2. Radiation from 300 K, meanwhile, is almost the same whether the cold side is 77 K or 20 K.

What should cryogenic conduction calculations watch for?

Conductivity varies strongly with temperature. Stainless steel 304 is 15 W/mK at 300 K, 7.9 at 77 K and 2.2 at 20 K. Using the room-temperature value overestimates the example neck tube's heat leak by 26% down to 77 K and 42% down to 20 K. Use the temperature-integrated value.

Cryogenic Thermal Analysis (Heat Leak into Vacuum-Insulated Tanks)

Category: Thermal–Fluid Coupling | Revised 2026-10-01

CAE visualization for cryogenic thermal theory - technical simulation diagram

Cryogenic Thermal-Fluid Analysis

Theory: three heat-leak paths

Overview

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I'm designing a liquid nitrogen tank. Can I estimate how much boils off per day beforehand?

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Yes. A cryogenic tank evacuates the space between inner and outer vessels to minimise incoming heat. Heat still arrives three ways: radiation from the outer vessel, conduction through the neck and supports, and residual gas conduction if the vacuum is poor. All of it goes into evaporating liquid, so heat leak divided by latent heat gives the boil-off. Cryogenic pitfalls are that conductivity changes greatly with temperature, and that liquid hydrogen has little latent heat.

Radiation and boil-off

$$ q = \frac{\sigma\left(T_h^4 - T_c^4\right)}{(N+1)\left(\frac{2}{\varepsilon} - 1\right)}, \qquad \dot m = \frac{Q}{h_{fg}} $$

$\varepsilon$ is the emissivity of both surfaces (taken equal) and $N$ the number of floating radiation shields between them; each shield cuts radiation to $1/(N+1)$. $h_{fg}$ is latent heat.

Temperature-dependent conduction

$$ Q = \frac{A}{L}\int_{T_c}^{T_h} k(T)\,dT $$

Because $k$ varies strongly with temperature, integrate it over temperature rather than using a constant. These conductivity integrals are tabulated per material and are independent of geometry.

Coffee Break Trivia

The vacuum flask came from cryogenics

The household vacuum flask began as a cryogenics research tool. In 1892 the British chemist Dewar built a double-walled glass vessel with a vacuum between the walls and silvered inner surfaces to store liquefied gases. The vacuum stopped conduction and convection and the silver mirror reduced radiation — the same principle as today's vacuum-insulated tanks. Using it, Dewar first liquefied hydrogen in 1898, which is why cryogenic vessels are still called 'dewars'.

Worked example: a 1 m³ spherical tank

A 1 m³ spherical inner vessel (radius 0.62 m, area 4.84 m²) is held in vacuum inside a 300 K outer vessel. With emissivity 0.05 on both surfaces, radiative heat leak was calculated for various shield counts:

Radiation shields	Heat flux	Heat leak (LN2, 77 K)	Heat leak (LH2, 20 K)
None	11.7 W/m²	56.7 W	57.0 W
10 (ideal)	1.07 W/m²	5.15 W	5.18 W
30 (ideal)	0.38 W/m²	1.83 W	1.84 W
Typical real MLI	0.5–1 W/m²	2.4–4.8 W	—

Radiation barely differs between a 77 K and a 20 K cold side: it scales with the fourth power of temperature, so the 300 K outer vessel dominates. Real multilayer insulation, with layer contact, seams and pipe penetrations, is typically several times worse than the ideal calculation.

Boil-off

Heat leak	Liquid nitrogen	Liquid hydrogen
1 W	0.43 kg/day (0.05%/day)	0.19 kg/day (0.27%/day)
5 W	2.17 kg/day (0.27%/day)	0.97 kg/day (1.37%/day)
10 W	4.34 kg/day (0.54%/day)	1.94 kg/day (2.74%/day)

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Liquid hydrogen loses five times as much for the same heat leak.

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Right. Per mass, liquid hydrogen's latent heat is more than twice nitrogen's, but its density is only one eleventh, so per volume it's about one fifth. Radiation leak is the same, yet the tank contents deplete five times faster. That's why LH2 tanks add a liquid-nitrogen-cooled shield or use boil-off vapour to cool the neck, cutting heat leak by another order of magnitude.

Example 2: neck tube conduction

Heat leak through a stainless steel 304 neck tube (OD 50 mm, wall 0.5 mm, length 0.3 m) was computed. Conductivity is 15.3 W/mK at 300 K, 11.2 at 150 K, 7.9 at 77 K and 2.2 at 20 K.

Cold end	Conductivity integral	Heat leak (variable k)	Constant room-temperature k	Overestimate
77 K	2,705 W/m	0.71 W	0.89 W	26%
20 K	3,012 W/m	0.79 W	1.12 W	42%

Analysis workflow

List heat-leak paths: radiation, conduction through supports and piping, residual gas.
Estimate radiation from measured MLI performance, not the ideal calculation.
Compute conduction with conductivity integrals, and consider vapour cooling of the neck.
From total heat leak, derive boil-off and holding time, and check pressure rise if the vessel is closed.
Where needed, analyse thermal stratification and flow instability from boiling in lines.

Coffee Break Trivia

“It boils off three times the calculation”

A newly built liquid nitrogen tank boiled off nearly three times the design calculation. Radiation had been estimated from ideal MLI theory, but around pipe penetrations the insulation was compressed and layers touched. Neck conduction had been computed with room-temperature conductivity — an overestimate — which masked the cause. Estimate MLI from measured values and settle installation details (penetrations, seams) at the drawing stage.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Ideal MLI calculation	Heat leak underestimated	Measured-based values
Constant conductivity	Conduction badly off	Use integrals
Treating LH2 like LN2	About 5× boil-off	Compare volumetric latent heat
Ignoring vacuum level	Gas conduction added	Allow for vacuum degradation
Omitting penetrations	Local heat leaks missed	Count pipes and wiring individually

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I'd like to try related calculations.

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Use the blackbody radiation simulator and radiation network simulator for radiation and the boiling curve simulator for boiling. Related analyses include boiling heat transfer, thermal stratification and heat pipes.

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