K. Fukuda

Fukuda,  K.

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§19. Study of Convective Heat Transfer by Mutual Convection of Helium II Fukuda, K. (Dept. Nucl. Eng., Kyushu U.) As a fundamental research on the cooling of superconductor magnet coil using superfluid Helium (Helium II), numerical study is carried out on mutual convection heat transfer in a Gorter-Mellink duct heated at the closed end and kept at constant temperature at the other end that is open to a Helium bath. 1\vo-fluid model is adopted with the Gorter-Mellink mutual friction term to cover the interaction between the normal and the superfluid components. The thermodynamic properties are assumed to be functions of only temperature. The governing equations are solved with the finite difference method. The transient results are obtained for two types of heating conditions: one is stepwise heating; the other rampwise heating (i.e., the heat flux increases linearly with time). For the case of stepwise heating, Fig.l shows the relation of initial temperature and limiting heat flux beyond which film boiling will occur at the heated surface. At the lower temperature region, considerable difference exists between the analytical and experimental results[ 1 ].Fig.2 shows the relation between the wall heat flux and the time to reach film boiling. The trend generally agrees with the experimental observation by Van Sciver[2] of a relation ~ oc q4 , except that the data for T1=1.6K and 1.8K deviate from the relationship at some values of heat fluxes. If we regard these heat fluxes as the limiting ones and plot them as curve C in Fig.2, the difference between experimental and analytical results at lower temperature becomes smaller. For the case of rampwise heating, Fig.3 shows wall temperature transients with tan6 ( = q/t, wall heat flux increasing rate) as the parameter. It is found that all curves rise at a temperature of about 1.802K, independent of the heat flux increasing rate. This suggests that the boiling would occur rapidly once the system stored enough internal energy. The critical super component velocity is calculated to be 1.66crnlsec, which is qualitatively in agreement with Van Alphen's estimation of 10°cm/sec. N' 5 ~ _, 0" 2-/ ~ 1 ii iii ~ (a) -- calc. 1 (b)- -········ exp. o (c) -·- · - · - calc. 2 1.6 1.8 2 Initial Temperature Tl (K) Fig.1 Limiting heat flux vs. initial temperature. N 5 4 ~ 0" 3 X :l u:: iii 2 C1) I -- --- · exp . -calc. 10-2 10° Time to Boiling (sec) Fig.2 Heat flux vs.time needed to reach boiling. ,..,.,---.~"11~...,.....,..,.,--.--..,.,.....,..,,--.--.~ Tb TI=1.8K f II I 1.86 0 tan e =5. 0N/cm2sec) 2. ~ ~ 1.84 : ~ 1. g 0.5 g 0.05 g C1) a. E 0 0 ~ 1.82-1 8 _ • o ooooelllll!iiool!l&151111::;...._--• 10-2 10-1 100 101 Time (sec) Fig.3 Transient results for wall temperature at different heat flux increasing rates. Reference 1) Linnet, C. & Frederking, T. H. K., J. Low Temperature, 21 (1975) 447 2) VanSciver, S.W., Cryogenics, 21 (1981) 531 3) Van Alphen, W.M., Phys. Lett., 20 (1966) 474 25 

Study of Convective Heat Transfer by Mutual Convection of Helium II

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