Heat Leak

Heat Leak is a common term used in the cryogenic industry. Heat leak is assumed to mean the amount of heat transferred into the contents of a vessel under standard ambient conditions for a given object. ‘Heat Leak’ is sometimes used because of the potential confusion of using heat loss since the main concern is the heat gained in the cryogenic liquid.

Ambient conditions are usually defined as 70 degrees F (English units) per hour, no forced surface airflow, and a defined cryogen such as liquid hydrogen or nitrogen. Actual heat leaks will vary depending on the cryogen used since different cryogens are stored at different temperatures.

Note that this measurement is sometimes expressed without precise dimensions; for example, the dimensional units are sometimes left off for a bayonet or a given diameter of a Vacuum Jacketed Pipe (VJP). The number given often implies an energy loss per unit of time over a given surface area instead of an object. In the case of transfer hoses and pipe, heat leak is the heat transferred per length of hose or pipe. Thus it may be expressed as BTU/hr per foot in English units or Watts/m in metric.

About Heat Leak

The following information is reproduced from Dr. Thomas Flynn’s “Cryogenic Engineering” 1997 Marcel Dekker, Inc., p. 64 (conversions courtesy of Technifab).

Heat leak(BTU/hr per foot) for typical rigid vacuum insulated pipe
Pipe Size
(Inner X Jacket)
 BTU/hr-ft   W/m  BTU/hr-ft   W/m
0.75* X 1.5 (19 x 38) 0.38 0.365 0.41 0.394
0.75 X 2.0 (19 x 51) 0.43 0.413 0.46 0.442
1.0 X 2.5 (25 x 64) 0.48 0.462 0.52 0.5
1.5 X 3.0 (38 x 76) 0.58 0.558 0.63 0.606
2.0 X 4.0 (51 x 102) 0.79 0.76 0.85 0.817
3.0 X 5.0 (76 x 127) 0.99 0.952 1.08 1.038
4.0 X 6.0 (102 x 152) 1.29 1.24 1.41 1.356
6.0 X 8.0 (152 x 203) 1.66 1.596 1.84 1.769

*Outer Diameter (O.D.) of tube. All other sizes are nominal pipe sizes (NPS).

The various fittings, spacers, valves, and bayonet connections in a typical vacuum-jacketed pipe system will reduce each amount to about 1.24 equivalent feet (0.38m) of pipe.

The above table gives the expected heat leak per foot of pipe for both liquid nitrogen and liquid hydrogen as a function of pipe size.  The flow rate is not a parameter.  This is the case because a fully developed turbulent flow is assumed.  For laminar flow to exist, the pipe diameter would have to be extremely large, resulting in high capital cost per foot and unnecessarily high heat leak per foot.  At turbulent flow conditions, the controlling thermal resistance to heat leak is that of the vacuum space.  Solid thermal conductivity through the pipe walls and heat transfer coefficient to turbulent cryogenic liquid is negligible compared to the apparent thermal conductivity of the vacuum space.  Thus, under conditions of use, heat leak per foot of pipe is entirely determined by the effectiveness of the vacuum insulation alone and hence depends primarily upon the pipe diameter.

The table shows very little increase in heat leak in changing from liquid nitrogen to liquid hydrogen.  The two heat leak conditions are about 10% of each other even though the temperature of the inner pipe has dropped from 77 K to 20 K.  From simple relative heat transfer calculations alone; we would expect the heat leak to increase by a factor of 16 = (77/20).  However, the actual case is that the hydrogen temperatures do a much better job of cryo-pumping than the liquid nitrogen-cooled surfaces.  Thus, at 77 K, there is still some residual gas conduction, which is not present at 20 K.  Hence, the apparent thermal conductivities are not that much different.