Abstract
Measurements and calculations on a flow cryostat with serial cooling have given equivalent thermal schemes that have been tested for adequacy and consequent simple working formulas.
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Abbreviations
- Tc, Ti, Tw, Tf :
-
temperatures of case, body i, tube wall, and flowing coolant in K
- T0 and Te :
-
coolant temperatures at inlet and exit for heat exchanger and pipes in K
- Twi :
-
mean pipe wall temperature at points of attachment of bundles from body i in K
- Twn :
-
pipe wall temperature at point of attachment for bundle n in K
- (σi)n and σi :
-
thermal conductivities of bundle n and all bundles from body i in W/K
- σij :
-
thermal conductivity between bodies i and j in W/K
- σci, σΣ, σcw :
-
thermal conductivities from case to body i and total and radiative conductivities from case to pipe in W/K
- αc :
-
convective heat-transfer coefficient between pipe and coolant in W/m2·K
- αr :
-
radiative heat-transfer coefficient between case and pipe in W/m2·K
- λ:
-
pipe material thermal conductivity in W/m·K
- c:
-
specific heat of helium at constant pressure in J/kg·K
- q and qr :
-
correspondingly densities of the total heat flux and radiative flux to the pipe in W/m2
- Pr :
-
heat flux along bundle r in W
- M:
-
coolant mass flow rate in kg/sec
- F:
-
tube cross section area in m2
- Si and So :
-
inside and outside surface areas of pipe in m2
- L:
-
pipe length in m
- ¯x=x/L:
-
relative coordinate along pipe axis
- ¯xr :
-
relative coordinate for bundle r attachment
- R:
-
total number of bundles
- Ni :
-
number of bundles cooling body i
- Ji :
-
number of bodies linked by heat bridges to body i
- δi :
-
relative error in calculating the temperature of body i by comparison with numerical result in %
- δw :
-
mean relative error in heat exchanger temperature calculated numerically by comparison with temperature from (4) taken at ten equally separated points in %
- δ(¯x-¯xr):
-
Dirac function
Literature cited
M. Akamatsu, M. Taneda, Y. Ohtsu, et al., Adv. Cryog. Eng.,21, 559–566 (1986).
V. A. Romanenko, S. V. Tikhonov, S. I. Khankov, and N. K. Yagupova, Inzh.-Fiz. Zh.,56, No. 4, 617–625 (1989).
B. N. Yudaev, Heat Transfer [in Russian], Moscow (1981).
O. Ore, Graph Theory [Russian translation], Moscow (1980).
I. S. Zhitomirskii, A. V. Borisenko, L. A. Ishchenko, and V. A. Pestryakov, Heat and Mass Transfer V [in Russian], Minsk (1976), pp. 25–29.
I. S. Zhitomirskii and V. G. Romanenko, Hydrodynamics and Heat Transfer in Cryogenic Systems [in Russian], Kharkov (1974), Issue 4, pp. 23–28.
G. N. Dul'nev, Heat and Mass Transfer in Electronic Equipment [in Russian], Moscow (1984).
R. Siegel and D. Howell, Radiative Heat Transfer [Russian translation], Moscow (1975).
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 760–767, May, 1989.
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Gal'chuk, A.B., Lavrenchuk, S.V., Romanenko, V.A. et al. Tests on a flow cryostat with series cooling. Journal of Engineering Physics 56, 536–541 (1989). https://doi.org/10.1007/BF01297602
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DOI: https://doi.org/10.1007/BF01297602