Abstract
The heat-transfer problem in an insulation consisting of layers which receive heat from external source through radiation is numerically solved in the one-dimensional approximation.
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Abbreviations
- T:
-
temperature
- x:
-
coordinate in the direction normal to the stack
- δ :
-
stack thickness
- λ:
-
thermal conductivity of the vacuum-shield thermal insulation along the x-coordinate
- qv :
-
amount of heat released in a unit volume of vacuum-shield thermal insulation as a result of the incidence of radiation on the face of the shield layers
- ɛ:
-
emissivity
- B:
-
density of effective radiant flux
- σ :
-
Stefan-Boltzmann constant
- N:
-
number of surfaces
- Sins :
-
surface of a vacuum-shield thermal insulation stack
- dϕdi-dj :
-
angular coefficient between elementary areas i and j of a surface
- Qo :
-
thermal flux through the insulation without a hole
- QT :
-
thermal flux through the insulation with a hole Qrad thermal flux through the insulation with radiative heat transfer to the bottom base of the hole
- Qs :
-
thermal flux reaching the insulation with a hole
- Qrad :
-
thermal flux through the insulation with radiative heat transfer to the bottom base of the hole
- Qs :
-
thermal flux reaching the stack face by radiative heat transfer through the hole (channel)
- Δx:
-
thickness of the i-th insulation layer including one or more shields
- ɛeff :
-
effective emissivity of the gap face
- qrad :
-
amount of heat reaching a unit area of the bottom base of the hole
- T0 and T0 :
-
boundary temperatures
- λ :
-
length of the gap between layers of the insulation stack and the length of the vacuum-shield thermal insulation stack
- h:
-
width of the gap between layers of the insulation stack
- λ∥:
-
longitudinal thermal conductivity of the vacuum-shield thermal insulation
Literature cited
M. G. Kaganer, Thermal Insulation in Low-Temperature Techniques [in Russian], Mashinostroenie, Moscow (1966).
G. A. Bell, T. C. Nast, and R. K. Wedel, “Thermal performance of multilayer insulation applied to small cryogenic tankage,” Adv. Cryogen. Eng.,22, 272–282 (1977).
V. F. Getmanets, R. S. Mikhal'chenko, and V. D. Vakulenko, “Nonadditivity of thermal fluxes through ‘thermal bridges’ and vacuum-shield thermal insulation of cryogenic devices,” in: Heat Transfer at Low Temperatures [in Russian], Naukova Dumka, Kiev (1979), pp. 120–130.
I. A. Paivanas, O. F. Roberts, and I. J. Wang, “Multishielding in advanced superinsulation technique,” Adv. Cryogen. Eng.,10, 197 (1965).
R. S. Mikhal'chenko, N. P. Pershin, E. I. Shchirov, and N. I. Gerasimenko, “Experimental study of the dependence of the thermal properties of multilayer insulation on the temperature, the vacuum level, and on the stacking density,” in: Problems of Hydrodynamics and Heat Transfer in Cryogenic Systems [in Russian], No. 3, Izd. Fiz.-Tekh. Inst. Nizk. Temp. Akad. Nauk Ukr. SSR, Kharkov (1973), pp. 100–105.
E. M. Sparrow and R. D. Cess, Radiation Heat Transfer, Brooks-Cole (1969).
R. Siegel and J. R. Howell, Thermal Heat Transfer, McGraw-Hill (1972).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 78–85, January, 1982.
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Getmanets, V.F., Mikhal'chenko, R.S. & Yurchenko, P.N. One-dimensional model of heat transfer in cryogenic vacuumshield thermal insulation with radiant heat sources. Journal of Engineering Physics 42, 63–69 (1982). https://doi.org/10.1007/BF00824994
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DOI: https://doi.org/10.1007/BF00824994