Cryogenic Heat Transfer

Cryogenic heat transfer is the process by which energy in the form of heat is exchanged between bodies at different temperatures.  Heat is generally transferred through convection, radiation, or conduction.

  • Convection
  • Conduction
  • Radiation
  • Conduction Calculations
  • Radiation Calculations
Technifab Vacuumed Jacketed Pipe heat transfer diagram


Convection may occur within a body or between two bodies if they are brought into contact.  The fluid motion will almost certainly occur if one of the bodies is a liquid or gas.  Convection is the conduction process between a solid surface and a moving fluid.  The motion of the fluid may be natural or forced.  Convection cannot occur in a vacuum.  Convection above a hot surface occurs because hot air expands, becomes less dense, and rises.  Hot water is less dense than cold water and rises, causing convection currents, which transport energy.  Convection can lead to circulation in a liquid, as in heating a pot of water over a flame.  Heated water expands and becomes more buoyant.  Cooler, denser water near the surface descends, and patterns of circulation are formed.


Conduction is the only method of heat transfer in opaque solids.  If the temperature at one end of a metal rod is raised by heating, then heat is conducted to the colder end raising its temperature.  Conduction is heat transfer utilizing molecular agitation within a material without any motion of the material.  Suppose one end of a metal rod is at a higher temperature. In that case, energy will be transferred down the rod toward the colder end because higher-speed particles will collide with the slower ones, with a net transfer of energy to the slower ones.


Radiation fundamentally differs from conduction and convection in that the bodies exchanging heat are not in contact.  They are many times separated by a vacuum space.  All substances emit radiant energy merely by having a positive absolute temperature.  The higher the temperature, the higher the amount of energy radiated.  All substances also are capable of absorbing radiated energy.  Generally, dull, rough surfaces absorb more heat than bright polished surfaces.  Bright surfaces reflect more energy than dull surfaces.  It is generally accepted that good emitters are sound absorbers, while poor emitters are poor absorbers.

General Heat Conduction Equation

Consider that a rectangular body of length “l” and opposite faces of area “A”, has one face at temperature t’ and the other face at temperature t.  Then (t’-t)/l is the temperature drop per unit distance called the temperature gradient.  The quantity of heat transmitted per second (Q) from one face to the opposite face is proportional to the area of the face and the temperature gradient.

The proportionality constant “k” depends upon the nature of the substance conducting the heat.  The value “k” is the substance’s thermal conductivity (coefficient of thermal conductivity).

It logically follows that “k” for a given substance is the amount of heat conducted per unit time per unit area per unit temperature gradient.

When Q is expressed in terms of BTU/Hour, area in square feet, (t’-t”) in degrees F, and “l” in feet, then k must be expressed in terms of BTU / Hour /degree F / foot.

In engineering work, the area is expressed in square feet, the temperature gradient in degrees F per inch, and the rate of heat conduction in BTU / Hour.  Using these units, k for a given substance is the number of BTU’s conducted per hour per square foot for a temperature gradient of 1 degree F per inch of thickness.

Q = k * area * temperature gradient = kA ((t’-t”)/l)

Properties for Common Materials
@ 20°C (k)BTU/h/sq. ft.
°F / in
@ 20°CKg/m3
@ 20°C106 J/m3
@ 20°C10-8 m2/s
Olive oil1.189201.65010
Silicone oil0.6947601.3707
G-10 Fiberglass2.03
Stainless Steel11179003.950405
Aluminum Oxide20839003.413879
Pyrex 77406.97022301.68160
Nylon 61.73411401.93813
Corian (ceramic filled)7.3518002.30746
Sand (dry)2.4316001.27028
Sand (saturated)18.7221002.640102
Glass pearls (dry)1.2518001.14016
Glass pearls (saturated)5.2721002.71028
Foam glass0.3121200.09249
Mineral insulation materials0.281000.09044
Plastic insulation materials0.21500.10030

General Radiation Heat Transfer Equation

The Stefan-Boltzmann equation relates the total amount of radiation emitted by an object to its temperature:

P = e * s * A *(Th4-Tc4)
P = power radiated in watts / square meter / second
e = emissivity
s = 5.6703 * 10-8 watt /( meter2K4)(Stefan-Boltzmann Constant)
A = radiating area in square meters
Th= Temperature of warm surface in K
Tc= Temperature of cold surface in K

Emissivity is the ratio of radiation emitted by a blackbody or a surface and the theoretical radiation predicted.  A material’s surface emissivity is a measure of the energy emitted when a surface is directly viewed.  Surface emissivity is generally measured indirectly by assuming that e = 1 reflectivity.  A single energy bounce is measured and the reflected energy measured.

Material Emmissivity Chart

Type of MaterialSpecific MaterialEmissivity
Black Coatings & MaterialsAnodize Black0.88
Rough Plate0.77
Carbon Black Paint NS-70.88
Catalac Black Paint0.88
Chemglaze Black Paint Z3O60.91
Delrin Black Plastic0.87
Ebanol C Black0.73
Ebanol C Black-384 ESH* UV0.75
EOI Mid-Temperature Black Coating (Up to 200°C)0.965 ±0.005
EOI High-Temperature Black Coating (Up to 1400°C)0.93 ±0.02
GSFC Black Silicate MS-940.89
GSFC Black Paint 3l3-10.86
Hughson Black Paint H3220.86
Hughson Black Paint L-3000.84
Martin Black Paint N-15O-10.94
Martin Black Velvet Paint0.94
3M Black Velvet Paint0.91
Paladin Black Lacquer0.75
Parsons Black Paint0.91
Polyethylene Black Plastic0.92
Pyramil Black on Beryllium Copper0.72
Tedlar Black Plastic0.90
Velesat Black Plastic0.85
White Coatings & MaterialsBarium Sulphate with Polyvinyl Alcohol0.88
Biphenyl-White Solid0.86
Catalac White Paint0.90
Dupont Lucite Acrylic Lacquer0.90
Dow Corning White Paint DC-0070.88
GSFC White Paint NS43-C0.92
GSFC White Paint NS44-B0.91
GSFC White Paint NS-740.92
GSFC White Paint NS-370.91
Hughson White Paint A-2760.88
Hughson White Paint A-276+lO36 ESH UV0.88
Hughson White Paint V-2000.89
Hughson White Paint Z-2020.87
Hughson White Paint Z-202+1OOO ESH UV0.87
Hughson White Paint Z-2550.89
Mautz White House Paint0.90
3M-401 White Paint0.91
Magnesium Oxide White Paint0.90
Magnesium Oxide Aluminum Oxide Paint0.92
Opal Glass0.87
OSO-H White Paint 63W0.83
P764-lA White Paint0.92
Potassium Fluorotitanate White Paint0.88
Sherwin Williams White Paint (A8W11)0.87
Sherwin Williams White Paint (F8WJ2O3O)0.82
Sherwin Williams F8W2030 w Polasol V6V2410.87
Sperex White Paint0.85
Tedlar White Plastic0.87
Titanium Oxide White Paint with Methyl Silicone0.90
Titanium Oxide White Paint with Potassium Silicate0.92
Zerlauts S-13G White Paint0.90
Zerlauts Z-93 White Paint0.92
Zinc Orthotitanate with Potassium Silicate0.92
Zinc Oxide with Sodium Silicate0.92
Zirconium Oxide with 650 Glass Resin0.88
Conductive PaintsBrilliant Aluminum Paint0.31
Epoxy Aluminum Paint0.81
Finch Aluminum Paint 643-1-10.23
Leafing Aluminum in Epon 8280.36
Leafing Aluminum (80-U)0.32
NRL Leafing Aluminum Paint0.24
NRL Leafing Aluminum Paint0.29
Silicone Aluminum Paint0.30
Dupont Silver Paint 48l70.49
Chromeric Silver Paint 5860.30
GSFC Yellow NS-43-G0.90
GSFC Green NS-53-B0.87
GSFC Green NS-43-E0.89
GSFC White NS-43-C0.92
GSFC Green NS-55-F0.91
GSFC Green NS-790.91
Anodized AluminumBlack0.82
Black (2nd Sample)0.86
Blue (2nd Sample)0.82
Clear (2nd Sample)0.84
Blue Anodized Titanium Foil0.13
Metals and Conversion CoatingsAluminumHighly Polished0.039-0.057
Commercial Sheet0.09
Heavily Oxidized0.20-0.31
Surface Roofing0.216
Alzac A-20.73
Black Chrome0.62
Black Copper0.63
Black Irridite0.17
Black Nickel0.66
BrassHighly Polished0.028-0.037
Dull Plate0.22
Buffed Aluminum0.03
Buffed Copper0.03
Constantan-Metal Strip0.09
Thick Oxide Layer0.78
Dow 23 on Magnesium0.67
Ebanol C Black0.77
Electroplated Gold0.03
Electroless Nickel0.07
Iron, Polished0.14-0.38
Cast Iron0.60-0.70
Mild Steel0.20-0.32
Iron Plate, Rusted Red0.61
Sheet Sheet, Rough Oxide Layer0.81
Gold – Pure, Highly Polished0.018-0.035
Irridite Aluminum0.11
Inconel X Foil (1 mil)0.10
Iron and Steel (Not Stainless)Kannigen-Nickel Alloy0.08
Steel, Polished0.066
Gray Oxidize0.28
Massive, Polished0.071
Nickel Oxide0.59-0.86
Plain Beryllium Copper0.03
Platinum Foil0.04
Quartz, Rough, Fused0.93
Stainless SteelPolished0.11
Machine Rolled0.11
Silver – Pure, Polished0.0.020-0.032
Tantalum Foil0.05
Tungsten Polished0.03
Vapor Deposited CoatingsAluminum0.02
Aluminum on Fiberglass0.07
Aluminum on Stainless Steel0.02
Chromiumlon 5-mil Kapton0.24
Iron Oxide0.56
MiscAsbestos, Board0.96
Aluminum Oxide (Al2o3)-(12/4) on Buffed Alum Initial0.23
Aluminum Oxide (Al2O3)(12/4) on Fused Silica0.24
BrickRed, Rough, No Gross Irregularities0.93
Concrete Tiles0.63
Pyrex, Lead, and Soda0.95
Porcelain, Glazed0.92
GSFC Dark Mirror Coating – SiO-Cr-Al0.04
GSFC Composite SiOx – Al2O3-Ag0.68
Inconel with Teflon Over coating -1 mil0.46
Kapton Over coating0.57
Parylene C Over coating0.34
Roofing Paper0.91
Silver Beryllium Copper Coating (AgBeCu)0.03
Teflon Over coating0.38
Vespel Polyamide SP10.90
Tapes & FilmAclar Film (Aluminum Backing)1 mil0.45
2 mil0.62
5 mil0.73
Copper Foil TapePlain0.02
Kapton Film (Aluminum Backing)0.08 mil0.24
0.15 mil0.34
0.25 mil0.45
0.50 mil0.55
1.0 mil0.67
1.5 mil0.71
2.0 mil0.75
3.0 mil0.82
5.0 mil0.86
Kapton Film (Chromium-Silicon Oxide-Aluminum Backing (Green)) 1.0 mil0.78
235-3M Black0.90
425-3M Aluminum Foil0.03
850-3M Mylar-Aluminum Backing0.59
7361-Mystic Alummized Kapton0.03
7452-Mystic Aluminum Foil0.03
7800-Mystic Aluminum Foil0.03
Y9360-3M Aluminized Mylar0.03