- Email: [email protected]
Effect of centrifugal acceleration on heat transfer during cooling of metal-oxide ceramics with liquid nitrogen
Effect of centrifugal acceleration on heat transfer during cooling of metal-oxide ceramics with liquid nitrogen S.M. Kozlov, N.M. Levchenko, S.V. Nozdrin, K.V. Rusanov and E.G. Tyurina Institute for Low Temperature Physics and Engineering, Academy of Sciences of the Ukraine, 47, Lenin Avenue, 310164 Kharkov, Ukraine Received 26 October 1992 This paper reports an experimental investigation of heat transfer to liquid nitrogen from samples of high temperature superconductor (HTSC) ceramics YBa2Cu30 x in the range of relative centrifugal accelerations from 1 to 1434. The effect of the porous, penetrable structure of the samples on thermal processes on their surface and inside them is shown. It has been established that in the porous samples an evaporation front arises, whose position depends on the centrifugal acceleration and on the heat flux density. For ceramics with lower porosity and higher thermal conductivity the heat transfer characteristics are similar to those for metallic samples.
Keywords: heat transfer; centrifugal acceleration; high Tc superconductor ceramics
Nomenclature g gc p q r Ar T AT fiT
(= 9.81 m s - 2 ) Acceleration due to gravity Centrifugal acceleration Pressure Heat flux density Radius of rotation Distance along radius of rotation temperature of ceramics temperature drop ( = T-- T~) Ceramics-liquid temperature difference
Greek letters 2
Heat transfer coefficient Thermal conductivity
High temperature superconductors (HTSC) can be used for the rotor windings of cryoturbogenerators cooled with liquid nitrogen. The intensive centrifugal accelerations acting on the liquid and the vapour during rotor rotation significantly affect most of the heat transfer characteristics 1. HTSC manufactured using ceramic technology have a penetrable porous structure and low thermal conductivity compared to metals. These factors
0
Liquid subcooling
~l
( = go~g) Relative acceleration
/9
Density
Subscripts f H 1 max o s T v 1, 2 2
Evaporation front Heat transfer surface conditions Liquid Heat transfer crisis in nucleate boiling Boiling onset Saturation Thermometer Vapour Numbers of thermometers Sample thermal conductivity
also lead to a variety of peculiarities with respect to heat transfer during boiling2' 3. The joint influence of these factors on heat transfer should be investigated for appropriate design of HTSC windings cooled with liquid nitrogen. Such investigations can also yield estimations of the effects of intensive centrifugal forces on the mechanical strength of HTSC ceramics. And, finally, apart from these practically orientated tasks, it is of interest to
0011-2275/93/090851-06 © 1993 Butterworth-Heinemann Ltd Cryogenics 1993 Vol 33, No 9
851
Centrifugal acceleration and heat transfer." S.M. Kozlov analyse the thermal and hydrodynamic processes occurring during evaporation inside the porous structure, in terms of the pressure and acceleration fields, which vary over its thickness. Here we describe the results of an experimental investigation of such a system, including some preliminary data published earlier4.
Experimental
details
The experiments involved using a high speed cryogenic centrifuge with a vertical axis of rotation. Its design is described in detail in reference 5. The ceramic samples were prepared by cold-pressing of finely dispersed YBa2Cu30 x powder, which was then formed into pellets (discs). After heat treatment the oxygen index reached values of x = 6.93-6.95, and the average grain size was ~ 10 #m. The superconducting transition temperature of the samples was 90-92 K. Table 1 presents the sizes and certain properties of the samples. Sample S1 contained a 0.3 volume fraction of metallic silver, giving a value of porosity half as large as and thermal conductivity significantly larger than those for samples of series A. As shown in reference 6, during nitrogen boiling the heat transfer characteristics of such HTSC composites are similar to those for metal heaters. The temperature of the samples was measured in the experiments with germanium resistance thermometers. Keeping the measured signal levels high reduced the errors from contact resistances in the rotating current collector. These errors prevent the use of thermocouples employed in our preceding studies 2' 3,6. It should be noted, however, that the thermometers were rather large ( ~ 1.8 mm across), which increased the uncertainty with Table 1
et al.
respect to the sensitive element location as compared to that of the thermocouple junction (0.3 mm). Otherwise, the design of the experimental equipment was quite similar to that described in our earlier papers2~. 6. The heat flux was directed from one face of the pellet, to which the heater was cemented, along the pellet axis, where thermometers were mounted, to the opposite face (the heat transfer surface), wetted by the liquid. This direction of heat flow was made possible by appropriate thermal insulation of the sample with a foam plastic case. The experimental cell was so arranged in the test vessel that the heat transfer surface was facing the axis of rotation and was perpendicular to the radius, i.e. to the vector of go. The radius of rotation of the heat transfer surface centre was 308 mm. As the rotational speed rose from 180 to 2040 rev min- 1, the magnitude of ~/= go/# increased from 11.1 to 1434 (for details see Table 2). The liquid layer thickness over the heat transfer surface was maintained constant during the experiments (10 mm) by continuously charging liquid nitrogen into the test vessel. The excess liquid was discharged through an opening in the side wall of the vessel. Table 2 presents the calculated liquid pressure near the heat transfer surface PH and the corresponding saturation temperature Tsri. The real temperature of the liquid was measured by two germanium resistance thermometers, one over the heat transfer surface (near the liquid-vapour interface) and the other away from the experimental cell at the same radius of rotation as the heat transfer surface. The readings of the latter thermometer were used for calculation of the temperature drop AT = TH -- T~. Here Tn was calculated from the temperature measured in the bulk of the ceramic, taking into consideration the thermal conductivity of the sample material (presented in Table 1).
Characteristicsof HTSC samples
Sample
Diameter (mm)
Thickness (mm)
Porosity
Thermal conductivity at T = 90 K (W m -1 K -1 )
A1 A2 $1
19.7 19.4 18.4
6.4 15.2 6.0
0.224 0.216 0.111
4.7 4.8 37.3
Distance of thermometer Number of thermometers
centre to heat transfer surface (mm)
1
3.2
2
4.2; 8.8
1
2,4
Table 2 Parametersof centrifuge experiments
TI
Rotation speed
(K)
0H
Sample
(rev min -1 )
~/
PH (kPa)
TSH (K)
q ( k W m -2)
A1
180 540 2040
11.1 100 1434
102 110 222
77.42 77.98 84.77
0.097-74
77.35 77.48 77.85
77.35 77.67 78.23
0.07 0.3-0.5 6.5-6.9
180 540 2010
11.1 100 1390
102 109 213
77.42 77.95 84.3
0.32-36
77.39 77.43 77.46
77.35 77.55 77.9
0.05 0.4-0.5 6.5
180 540 820 2020
11.1 100 231 1405
102 110 120 222
77.43 77.99 78.75 84.76
77.62 77.41 77.46 77.65
77.64 77.44 77.49 77.84
0 0.5 1.3 7.0
A2
$1
852
Cryogenics 1993 Vol 33, No 9
0.19-340
q=lkWm
-2
q=20kWm
-2
(K)
Centrifugal acceleration and heat transfer: S.M. Kozlov et al. The difference between Tsx and T~(i.e. the liquid subcooling) increases with the acceleration. The boundaries of the heat flux density ranges realized in our experiments are shown in Table 2. These values of q correspond to single-phase convection and nucleate boiling of nitrogen on metallic heat transfer surfaces 1. For cell S1 the heat transfer crisis was attained at ~/= 1 and 11.1. For the other cells it was not attained because of the low thermal conductivity of the ceramic and the resulting very high temperature of the heater at q > 80 kW m - 2. Besides tests in the centrifuge, each cell was subjected to measurements at ~/= 1 at atmospheric pressure. It will be shown below that under certain conditions an evaporation front may arise inside the porous sample. In this case pores in the part of the ceramic adjacent to the heater are filled with vapour. In the pores of the remaining part of the sample the liquid and the vapour move in opposite directions. Since, in this part, the heat flux is much lower than that supplied to the sample because of evaporation in the front the temperature gradient is rather small. Under such conditions calculations of Tx values including only the thermal conductivity do not represent the real physical process. This should be taken into account in analysing experimental data. The error in the determined values of q and AT can only be estimated when the evaporation front is driven out on to the sample surface (with a large release of heat in the heater). These errors are 3-10~o for q, and from 15-20~ (S1) to 4 0 - 5 0 ~ (A2) for AT. It should be noted that the main contribution to the total error is given by the systematic error in locating the thermometer centre with respect to the heat transfer surface. This error does not vary with the centrifugal acceleration and thus does not influence the relative positions of the curves q = q(AT) obtained for the same sample.
Experimental results It should be noted at this point that repeated subjection of the ceramics to the action of intensive centrifugal accelerations even combined with thermocycling four or five times did not affect its strength: no cracking or splintering were observed. However, the thermometers that had been easily put into the radial bores in the ceramics before the experiments were found to be jammed after measurements in the centrifuge. This could be the result of residual deformation due to contraction of the ceramics. The lines in Figure 1 represent averaged experimental data obtained in repeated experiments on sample A1 for r / = constant. Figure lb shows raw data for the region of the transition from one branch of the dependence q = q(AT) to the other which is typical of this sample at r / > 1. The arrows indicate a decrease in the temperature drop with increasing heat flux density. At r / = 1 this transition does not take place over the whole q range studied. The slope of the branches does not change after the transition. The exponent in the relation q c~ AT", as estimated from experimental data, is slightly above unity when averaged (n = 1.1-1.3), both before and after the transition, except for the upper portions of certain curves. This character of the dependence q = q(AT) is indicative
5./!~
a
i!
~'~ 102 E
/ / //~"
>.
•~
101
o
i~
/" //,~/~//
.// ~/~ ,,'"
o! i
lO(
o !!
×
~- 100
/S~,&3
I
10-1
10 10 o 101 Temperature drop (K) Figure 1 Dependence q = q ( A T ) for sample AI. (a) Averaged data from present work for: 1, ~/= 1; 2, 11.1; 3, 100; 4, 1434; averaged data from references 7 and 9 for: 5, r/= 10.2; 6, 1000. (b) C), Raw data, r/= 100 100
of there being a significant input from convective and maybe conductive heat transfer up to q = 60-70 kW m-2, because boiling is characterized by a steep dependence q = q(AT). The range of the transition (qo, ATo) is shifted towards larger q and AT, as the centrifugal acceleration rises. At q > qo and A T > ATo the heat transfer coefficient • = q/AT grows with ~/, which is typical, not for nucleate boiling, but for single-phase convection 1. For comparison, Figure la presents data from references 7 and 8, which had been obtained earlier on the same centrifuge during nitrogen boiling on a copper sample based on the same design. The test conditions (liquid layer thickness and ~/magnitudes) were similar to those in the present work, although the heat transfer surface centre was 220 mm from the axis of rotation. It is seen that the curves of q = q(AT) for nitrogen boiling on a metal with a high thermal conductivity are qualitatively different from those for boiling on HTSC ceramics. The curve for boiling on copper characteristically has a steep section representing nucleate boiling and does not show the above mentioned transition, i.e. a double kink. Here, the change of the curve slope corresponds to the onset of nitrogen boiling on the heat transfer surface. Figure 2 shows the results of measurements for sample S1, which has the same dimensions as sample A1, but a porosity half as large and a higher thermal conductivity (cf. an order of magnitude lower than that of copper). We see that for this sample the dependence q = q(AT) is much more similar to that of a metal than that of a ceramic in character. The systematic upward shift of the curves in the single-phase convection region with increasing acceleration, the characteristic double kink of the q = q(AT) curves and the stratification of the data for various values of r/in the nucleate boiling region (Figure 2a) can be clearly seen. This stratification is more conspicuous than in references 7 and 8, since the subcooling of the liquid at the heat transfer surface of sample S 1 is, all other factors being equal, larger because of the larger radius of rotation. However, the temperature drops in the case of boiling on the ceramic sample surface for large heat fluxes are, on average, still larger than those for a copper sample (see Figure 2b). The formal procedure of calculation of AT from data for the porous ceramic sample A2, with a larger thickness than A1, leads to an unexpected result. Over a certain
Cryogenics 1993 Vol 33, No 9
853
Centrifugal acceleration and heat transfer." S.M. Kozlov et al. i
i
i i g l , ,
~
i
i
, l l , l t
associated with the onset of liquid boiling; however the position of the point where boiling starts (inside the sample or at its surface) and of the evaporation front with respect to the sensor are still to be investigated.
Z,
a 102
// ! /
E
Discussion £
101
XY
× n
z ://,' ,,,:,y,,,,:,
-I100
."./Z / / / //,' //f~,/ i
100
ilfJ,,
101
,
,
,
i , , , i ,
100
101
Temperature drop (K)
Figure 2 Dependence q = q(AT) for sample $1. (a) Averaged data from present work for: 1, r / = 1 ; 2, 11.1 ; 3, 100; 4, 1405. (b) O, Raw data from present work, r / = 11.1 ; O, raw data from references 7 and 8, r / = 10.2
range of heat flux densities the calculated temperature drop AT tends to zero; this range is shifted upwards as r/ increases (Figure 3a). This effect is reproducible for both increasing and decreasing q and in subsequent series of measurements; the raw data for one acceleration value are shown in Figure 3b. Outside the region of the 'degenerate' calculated temperature drop the slope of the curves for q = q(AT) is, on average, close to the typical value for sample A1 (see Figure 1). For ~/= 1 and for the thinner ceramic sample this peculiarity is not observed. The results we have at present are not sufficient to conclude the existence of a dependence of • on r/; however the curve of q = q(AT) for r / = 1390 outside the transition region is the furthest to the right of all the other curves, thus corresponding to a lower value of ~. Thus the dependences q = q(AT) for all three HTSC ceramic samples have transition regions which shift to larger q as the acceleration rises, although the transition shapes are different: a double kink for A1, a single kink (a change of slope of the curve) for S1 and 'degeneracy' in AT for A2. Obviously, in all three cases these features are
...... S
E
b
___o2J
101
) r-
/
/
X m q-
100
o //
-r" O
i
100
i
i~lll,
101
i
100
I
t I I till
101
Temperature drop (K)
Figure 3 Dependence q = q(AT) for sample A2. (a) Averaged data for: 1, r / = l ; 2, 11.1; 3, 100; 4, 1390. (b) O, Raw data, t / = 1390
854
Cryogenics 1993 Vol 33, No 9
It was reported earlier 2' 6 that in the case of nitrogen boiling on porous samples of HTSC ceramics at r / = 1 it was often observed that q oc AT", with n close to unity up to q = qma~ and with a steep transition section in the range of small heat flux densities. It is assumed that as q rises from 0 to qma~the heat transfer process goes through several stages. As long as the heat flux applied is insufficient for the onset of boiling of the liquid in the pores, heat transfer to the outside occurs by conduction through the porous skeleton structure and by convection of the liquid in the pores; this is the first stage. Because of the low efficiency of these mechanisms the temperature gradient and the temperature measured inside the sample increase with q. The second stage begins when the liquid starts to boil at the heated sample bottom. We assume that a vapourfilled region forms here with a high temperature gradient dT/dr separated from the liquid-filled part of the sample by the evaporation front. The heat transfer in the vapourfilled part is dominated by thermal conduction through the skeleton and convection in the vapour. Since part of the heat flux q is consumed by vaporization the dT/dr value in the liquid-filled area is not large. As q increases the front moves closer to the heat transfer surface. Before it reaches the point where the temperature is measured, the latter is only slightly dependent on q, but starts to rise rapidly once this point has been encircled by the expanding vapour-filled region. As soon as the evaporation front reaches the heat transfer surface, boiling takes place on it; and this is the third stage. The heat transfer crisis now manifests itself in the appearance of a continuous vapour film separating the surface from the liquid. The thermal conductivity used in the calculation of Tn and AT was determined for the case of gaseous nitrogen in pores and r / = i. Therefore, linear extrapolation based on the weak dependence 2 = 2(T) in the ceramic temperature range employed is legitimate in the third and, possibly, the first stages. As seen in Figure 4, for the case where the evaporation front exists inside the sample, such a procedure is sure to yield underestimates of Tn and AT. Within the framework of this concept, increases in the centrifugal acceleration are expected to have a dual effect on the heat transfer processes. Firstly, convective heat transfer is intensified both through pores and on the sample surface. This means that the sections of the q = q(A T) curves dominated by thermal resistance of the single-phase (vapour or liquid) layer should be shifted upwards. Secondly, the pressure and the saturation temperature rise at all points of the sample. The liquid can only start to boil when the ceramic temperature becomes higher than T=; hence the evaporation front can only be formed and displaced on to the heat transfer surface at higher T and q values. As Figure 1 suggests, both these effects were indeed observed in sample A1. Let us consider in greater detail the causes of the 'degeneracy' of the AT values in sample A2. Figure 5 plots the difference fiT between the measured ceramic
Centrifugal acceleration and heat transfer: S.M. Kozlov et al. Heated sample bottom
Heat transfer surface
Sample
ql < q2 < q3 < q4
Liquid /
'T(ql) l
L~rf(q 2)
Ar T LXrf(q 3)
L~r H
Distance from heated sample bottom Figure 4 Scheme of temperature distribution along heat flow direction in sample and temperature drop calculations for ql < q2 < q3 < q4' The location of the heat transfer surface, the thermometer and the evaporation front at q2 and q3 are represented by Ar H, Ar T and ~'f, respectively; the solid lines show the real distribution of T; the broken lines represent calculated values without taking into account the presence of the front; AT and AT' are the real and calculated temperature drops at q2
102 ~_
I
I
I
I I IIII
I
I
i
I I l lll
I
n ~
-
/X
,~
,
101
0 0
n
•
~o~ A~ ° / :
,
'Q
-
Arf = A(q - qo)
" / 9 "•
zx
u e-
~IC
•
/
0 ~ • // eAA/
LX:/
E 110 °
a & /
I 10-1
I 1,4'11111 100
I
I I I illll
I
values of subcooling 01 and 02 at the radii of rotation of thermometers 1 and 2. It can be seen that with growing q values at r / = constant, 6TL2 values above the local liquid subcooling result in a change from the region with fiT L 2 oc q to the region where the temperatures of sensors do not depend on q and are almost equal. The difference ( r T - fiTx) ~ 0 and for a certain region of q becomes even smaller than zero, suggesting the inapplicability of correction 6T~ under such conditions. Thermometer 2, which is fixed closer to the heater and further away from the heat transfer surface (at lower q) is superheated above T s sooner than thermometer 1. The sharp temperature rise after the horizontal section of the T = 6 T(q) curves, which is indicative of the passage of the evaporation front through the thermometer, occurs in the same succession. The dependence 67"1,2 oc q then becomes linear again with 6T2/rT1 being constant, as it was before the transition region. The sample temperature is lower at q = 1390 than at q = 100, as would be expected owing to the intensified convective heat transfer. Let us estimate the propagation of the evaporation front in the sample with increasing q, measuring the distance from the heater. Then if Arf = 6.4, 11.0 and 15.2 mm the passage of the front as detected by the said criteria corresponds to the heat flux densities q = 1.6, 2.3 and 2 . 8 k W m -2 ( r / = 1 0 0 ) and q = 1 4 , 20 and 2 5 k W m -2 (r/= 1390), respectively. These values, as well as the averages over the two thermometers, qo = 0.8 k W m -2 ( t / = 100) and qo = 5 kW m -2 (17 = 1390), at which the front forms give a near-linear dependence
I
101
Heat flux density {kWm -2} Figure 5 Dependences of fiT 1, fiT 2, 6Ta, 01 and 02 values for sample A2 on heat flux density. Open and solid symbols are for ~T 2 and 6T 1; A, A , q = 100; (3, O, r / = 1390; - - - , 6Tx; arrows indicate 01 and 0 2
temperature and the temperature of the liquid outside the sample, as a function of q for two values of q. In addition, it shows the values of 6T~ = q(Ar H - Arrl)/2 for thermometer 1, which is nearest to the heat transfer surface. The calculated temperature drop represented in Figures 1-3 was determined from the measured quantities as A T = 6 T x - 6 T ~ . The arrows on Figure 5 indicate the
(1)
where A = 7.75 mm kW -1 m -2 for q = 100 and A = 7.55 x 10-1 mm k W - ~ m - 2 for ~/= 1390. The larger the acceleration, the larger the increase of q required for the front to move towards the heat transfer surface. Similar results (though less definite, because three closely spaced points are used) have been obtained for sample A1 (Figure 1). It can be assumed that the stable position of the front is controlled by the rate of vapour removal from it, which depends on the driving head Ap oc gc(Pl - Pv) and is proportional to the first power of the acceleration. Indeed, the coefficient in (1) is more likely to depend on q as A oc q - 1 than as A oc q - 1/3, the latter being the case for convective heat removal from the front. It can be expected that at q = constant and with rising acceleration the reverse process will ensue, i.e. gradual motion of the evaporation front into the sample from the heat transfer surface, after boiling has been suppressed at this surface. Thus, experimental results for porous samples of ceramics qualitatively corroborate the idea of an internal evaporation front. Indeed, by varying the acceleration and the related pressure and subcooling of the liquid, one can influence the conditions of the phase transition and therefore those of the appearance of the front for a wide range of q; note this was not possible at r/--1. For complete understanding of the complicated processes going on in ceramics, a mathematical model of the system is to be developed. This is beyond the purpose of this paper which does, however, provide the basic data for such a model. Sample S1 with its relatively high thermal conductivity
Cryogenics 1993 Vol 33, No 9
855
Centrifugal acceleration and heat transfer: S.M. Kozlov et al. has a low thermal resistance, so that the form of the dependence of q on A T is mainly controlled by processes at the heat transfer surface, as in bulk metallic samples. In Figure 2 we see linear sections of the curve of q = q(AT) which are characteristic of single-phase convection at the heat transfer surface when 0.2 k W m - 2 < q < q0. The exponent n in q ~ AT", which was determined from experimental data, does not depend on ~/and is 1.29-1.43. The heat transfer coefficient increases with increase in the acceleration as ~oc r/°'16. The heat flux density qo at which the slope of the curve of q = q(AT) changes, i.e. nitrogen starts to boil, also rises: qo = 2.5, 4.4, 14, 32 and 69 kW m -~ at r / = 1, 11.1, 100, 231 and 1405, respectively. These data show fairly good agreement with those of reference 9 for the onset of nitrogen boiling on a steel tube of diameter 2.5 mm. The same is true of the temperature drops corresponding to qo: ATo = 2.8, 3.3, 6.8, 7.9 and 17.0 K at t / = 1, 11.1, 100, 231 and 1405, respectively. As the acceleration increases, so does the magnitude of ATos = ATo - (T~. - T1), i.e. superheating of the surface with respect to the local saturation temperature (2.8, 3.3, 6.3, 6.6 and 10.0 K for the given accelerations, respectively), whereas in the case of onset of nitrogen boiling for a tube 9, AToscharacteristically decreased. At the same time, in the case of onset of nitrogen boiling on a flat copper surface, ATo~rose from 2.25 to 5.7 K as r/increased from 1 t o 2000 7, 8.
In the region of nucleate boiling on the heat transfer surface (q > qo) the heat transfer coefficient decreases with growing r/, as calculated from both the temperature drop AT and from AT~ = AT - OH. This is in qualitative agreement with data recorded for nitrogen boiling on metallic surfaces 1' 7-9. The quantitative dependence ~ = 0t(t/) for the ceramics is, however, stronger. The additional decrease in heat transfer seems to be due to processes inside pores which are predominant in the highly porous samples A1 and A2, but also take place, though weakly, in sample $1. The heat transfer crisis on sample S1 occurred for t / = l at qmax=135kW m -2, ATmax = 8 . 6 K and for t / = 11.2 at qmax= 257kW m - 2 , ATraax = 11.9 K. Such magnitudes of qmx are also typical of nitrogen boiling on metallic surfaces ~, and their dependence on acceleration qm~, oc t/°'26 is consistent with the hydrodynamic model of the boiling crisis. The values of ATma~ here are larger than those for the case of boiling on metals and grow
856
Cryogenics 1993 Vol 33, No 9
faster with r/; this reminds us that sample S1 is more than half HTSC ceramic, which typically has high critical temperature drops 2' 3.
Conclusions The experimental investigation carried out has yielded new data supporting the hypothesis of the existence in porous ceramics of an evaporation front whose location depends on the acceleration and on the heat flux density. As the thermal conductivity increases and the porosity decreases, the internal processes cease to be predominant, and the heat transfer characteristics become similar to those typical of metallic samples with an outer surface cooled.
References 1 Verkin, B. I., Kirichenko, Yu. A. and Rusanov, K. V. Heat Transfer during Boiling in Fields of Mass Forces of Various Intensities
Naukova Dumka, Kiev, Russia (1988) 256 (in Russian) 2 Baranets, V. V., Kiriehenko, Yu. A., Kozlov, S. M., Nozdrin, S. V, et al. Experimental investigations of heat transfer from the surface of YBa2Cu307 ceramics cooled with liquid nitrogen Inzh Fiz Zhurn (1990) 59 533-538, 772-775 (in Russian) 3 Kirichenko, Yu. A., Kozlov, S. M., Rusanov, K. V. and Tyurina, E. G. Heat transfer crisis during liquid nitrogen cooling of high temperature superconductors Cryogenics (1991) 31 979-984 4 Kozlov, S. M., Kolod'ko, I. M., Levchenko, N. M., Nozdrin, S. V. et al. Preliminary results of heat transfer studies during nitrogen boiling on YBa2Cu30 7 ceramics in the field of centrifugal forces Preprint A N UkrSSR FTINT 11 (1991) No. 24 5 Kirichenko, Yu. A., Levehenko, N. M., Kozlov, S. M., Kudryavtseva, K. A. et aL An apparatus for investigation of the heat transfer in cryogenic liquids in the fields of centrifugal forces Cryogenic Electric Machine Engineering Naukova Dumka, Kiev, Russia (1983) 128-134 (in Russian) 6 Bratchenko, I. E., Dotsenko, V. I., Kislyak, I. F., Kozlov, S. M. et aL Heat transfer during nitrogen boiling on the surface of YBa2Cu307-Ag composites with various silver contents Preprint A N UkrSSR FTINT 14 (1991) No. 21 7 Levehenko, N. M. Visualization, boiling onset and heat transfer crises during boiling of cryogenic liquids Preprint A N UkrSSR FTINT24 (1986) No. 12 8 Levehenko, N. M. Heat transfer intensity and regimes during boiling of cryogenic liquids Preprint A N UkrSSR FTINT 32 (1986) No. 13 9 Verkin, B. I., Kirichenko, Yu. A., Levehenko, N. M. and Rusanov, K. V. Heat transfer during nitrogen boiling in the field of centrifugal forces Proc ICEC 7 IPC~Science and Technology Press, Guildford, UK (1978) 394-398
Keywords: heat transfer; centrifugal acceleration; high Tc superconductor ceramics
Nomenclature g gc p q r Ar T AT fiT
(= 9.81 m s - 2 ) Acceleration due to gravity Centrifugal acceleration Pressure Heat flux density Radius of rotation Distance along radius of rotation temperature of ceramics temperature drop ( = T-- T~) Ceramics-liquid temperature difference
Greek letters 2
Heat transfer coefficient Thermal conductivity
High temperature superconductors (HTSC) can be used for the rotor windings of cryoturbogenerators cooled with liquid nitrogen. The intensive centrifugal accelerations acting on the liquid and the vapour during rotor rotation significantly affect most of the heat transfer characteristics 1. HTSC manufactured using ceramic technology have a penetrable porous structure and low thermal conductivity compared to metals. These factors
0
Liquid subcooling
~l
( = go~g) Relative acceleration
/9
Density
Subscripts f H 1 max o s T v 1, 2 2
Evaporation front Heat transfer surface conditions Liquid Heat transfer crisis in nucleate boiling Boiling onset Saturation Thermometer Vapour Numbers of thermometers Sample thermal conductivity
also lead to a variety of peculiarities with respect to heat transfer during boiling2' 3. The joint influence of these factors on heat transfer should be investigated for appropriate design of HTSC windings cooled with liquid nitrogen. Such investigations can also yield estimations of the effects of intensive centrifugal forces on the mechanical strength of HTSC ceramics. And, finally, apart from these practically orientated tasks, it is of interest to
0011-2275/93/090851-06 © 1993 Butterworth-Heinemann Ltd Cryogenics 1993 Vol 33, No 9
851
Centrifugal acceleration and heat transfer." S.M. Kozlov analyse the thermal and hydrodynamic processes occurring during evaporation inside the porous structure, in terms of the pressure and acceleration fields, which vary over its thickness. Here we describe the results of an experimental investigation of such a system, including some preliminary data published earlier4.
Experimental
details
The experiments involved using a high speed cryogenic centrifuge with a vertical axis of rotation. Its design is described in detail in reference 5. The ceramic samples were prepared by cold-pressing of finely dispersed YBa2Cu30 x powder, which was then formed into pellets (discs). After heat treatment the oxygen index reached values of x = 6.93-6.95, and the average grain size was ~ 10 #m. The superconducting transition temperature of the samples was 90-92 K. Table 1 presents the sizes and certain properties of the samples. Sample S1 contained a 0.3 volume fraction of metallic silver, giving a value of porosity half as large as and thermal conductivity significantly larger than those for samples of series A. As shown in reference 6, during nitrogen boiling the heat transfer characteristics of such HTSC composites are similar to those for metal heaters. The temperature of the samples was measured in the experiments with germanium resistance thermometers. Keeping the measured signal levels high reduced the errors from contact resistances in the rotating current collector. These errors prevent the use of thermocouples employed in our preceding studies 2' 3,6. It should be noted, however, that the thermometers were rather large ( ~ 1.8 mm across), which increased the uncertainty with Table 1
et al.
respect to the sensitive element location as compared to that of the thermocouple junction (0.3 mm). Otherwise, the design of the experimental equipment was quite similar to that described in our earlier papers2~. 6. The heat flux was directed from one face of the pellet, to which the heater was cemented, along the pellet axis, where thermometers were mounted, to the opposite face (the heat transfer surface), wetted by the liquid. This direction of heat flow was made possible by appropriate thermal insulation of the sample with a foam plastic case. The experimental cell was so arranged in the test vessel that the heat transfer surface was facing the axis of rotation and was perpendicular to the radius, i.e. to the vector of go. The radius of rotation of the heat transfer surface centre was 308 mm. As the rotational speed rose from 180 to 2040 rev min- 1, the magnitude of ~/= go/# increased from 11.1 to 1434 (for details see Table 2). The liquid layer thickness over the heat transfer surface was maintained constant during the experiments (10 mm) by continuously charging liquid nitrogen into the test vessel. The excess liquid was discharged through an opening in the side wall of the vessel. Table 2 presents the calculated liquid pressure near the heat transfer surface PH and the corresponding saturation temperature Tsri. The real temperature of the liquid was measured by two germanium resistance thermometers, one over the heat transfer surface (near the liquid-vapour interface) and the other away from the experimental cell at the same radius of rotation as the heat transfer surface. The readings of the latter thermometer were used for calculation of the temperature drop AT = TH -- T~. Here Tn was calculated from the temperature measured in the bulk of the ceramic, taking into consideration the thermal conductivity of the sample material (presented in Table 1).
Characteristicsof HTSC samples
Sample
Diameter (mm)
Thickness (mm)
Porosity
Thermal conductivity at T = 90 K (W m -1 K -1 )
A1 A2 $1
19.7 19.4 18.4
6.4 15.2 6.0
0.224 0.216 0.111
4.7 4.8 37.3
Distance of thermometer Number of thermometers
centre to heat transfer surface (mm)
1
3.2
2
4.2; 8.8
1
2,4
Table 2 Parametersof centrifuge experiments
TI
Rotation speed
(K)
0H
Sample
(rev min -1 )
~/
PH (kPa)
TSH (K)
q ( k W m -2)
A1
180 540 2040
11.1 100 1434
102 110 222
77.42 77.98 84.77
0.097-74
77.35 77.48 77.85
77.35 77.67 78.23
0.07 0.3-0.5 6.5-6.9
180 540 2010
11.1 100 1390
102 109 213
77.42 77.95 84.3
0.32-36
77.39 77.43 77.46
77.35 77.55 77.9
0.05 0.4-0.5 6.5
180 540 820 2020
11.1 100 231 1405
102 110 120 222
77.43 77.99 78.75 84.76
77.62 77.41 77.46 77.65
77.64 77.44 77.49 77.84
0 0.5 1.3 7.0
A2
$1
852
Cryogenics 1993 Vol 33, No 9
0.19-340
q=lkWm
-2
q=20kWm
-2
(K)
Centrifugal acceleration and heat transfer: S.M. Kozlov et al. The difference between Tsx and T~(i.e. the liquid subcooling) increases with the acceleration. The boundaries of the heat flux density ranges realized in our experiments are shown in Table 2. These values of q correspond to single-phase convection and nucleate boiling of nitrogen on metallic heat transfer surfaces 1. For cell S1 the heat transfer crisis was attained at ~/= 1 and 11.1. For the other cells it was not attained because of the low thermal conductivity of the ceramic and the resulting very high temperature of the heater at q > 80 kW m - 2. Besides tests in the centrifuge, each cell was subjected to measurements at ~/= 1 at atmospheric pressure. It will be shown below that under certain conditions an evaporation front may arise inside the porous sample. In this case pores in the part of the ceramic adjacent to the heater are filled with vapour. In the pores of the remaining part of the sample the liquid and the vapour move in opposite directions. Since, in this part, the heat flux is much lower than that supplied to the sample because of evaporation in the front the temperature gradient is rather small. Under such conditions calculations of Tx values including only the thermal conductivity do not represent the real physical process. This should be taken into account in analysing experimental data. The error in the determined values of q and AT can only be estimated when the evaporation front is driven out on to the sample surface (with a large release of heat in the heater). These errors are 3-10~o for q, and from 15-20~ (S1) to 4 0 - 5 0 ~ (A2) for AT. It should be noted that the main contribution to the total error is given by the systematic error in locating the thermometer centre with respect to the heat transfer surface. This error does not vary with the centrifugal acceleration and thus does not influence the relative positions of the curves q = q(AT) obtained for the same sample.
Experimental results It should be noted at this point that repeated subjection of the ceramics to the action of intensive centrifugal accelerations even combined with thermocycling four or five times did not affect its strength: no cracking or splintering were observed. However, the thermometers that had been easily put into the radial bores in the ceramics before the experiments were found to be jammed after measurements in the centrifuge. This could be the result of residual deformation due to contraction of the ceramics. The lines in Figure 1 represent averaged experimental data obtained in repeated experiments on sample A1 for r / = constant. Figure lb shows raw data for the region of the transition from one branch of the dependence q = q(AT) to the other which is typical of this sample at r / > 1. The arrows indicate a decrease in the temperature drop with increasing heat flux density. At r / = 1 this transition does not take place over the whole q range studied. The slope of the branches does not change after the transition. The exponent in the relation q c~ AT", as estimated from experimental data, is slightly above unity when averaged (n = 1.1-1.3), both before and after the transition, except for the upper portions of certain curves. This character of the dependence q = q(AT) is indicative
5./!~
a
i!
~'~ 102 E
/ / //~"
>.
•~
101
o
i~
/" //,~/~//
.// ~/~ ,,'"
o! i
lO(
o !!
×
~- 100
/S~,&3
I
10-1
10 10 o 101 Temperature drop (K) Figure 1 Dependence q = q ( A T ) for sample AI. (a) Averaged data from present work for: 1, ~/= 1; 2, 11.1; 3, 100; 4, 1434; averaged data from references 7 and 9 for: 5, r/= 10.2; 6, 1000. (b) C), Raw data, r/= 100 100
of there being a significant input from convective and maybe conductive heat transfer up to q = 60-70 kW m-2, because boiling is characterized by a steep dependence q = q(AT). The range of the transition (qo, ATo) is shifted towards larger q and AT, as the centrifugal acceleration rises. At q > qo and A T > ATo the heat transfer coefficient • = q/AT grows with ~/, which is typical, not for nucleate boiling, but for single-phase convection 1. For comparison, Figure la presents data from references 7 and 8, which had been obtained earlier on the same centrifuge during nitrogen boiling on a copper sample based on the same design. The test conditions (liquid layer thickness and ~/magnitudes) were similar to those in the present work, although the heat transfer surface centre was 220 mm from the axis of rotation. It is seen that the curves of q = q(AT) for nitrogen boiling on a metal with a high thermal conductivity are qualitatively different from those for boiling on HTSC ceramics. The curve for boiling on copper characteristically has a steep section representing nucleate boiling and does not show the above mentioned transition, i.e. a double kink. Here, the change of the curve slope corresponds to the onset of nitrogen boiling on the heat transfer surface. Figure 2 shows the results of measurements for sample S1, which has the same dimensions as sample A1, but a porosity half as large and a higher thermal conductivity (cf. an order of magnitude lower than that of copper). We see that for this sample the dependence q = q(AT) is much more similar to that of a metal than that of a ceramic in character. The systematic upward shift of the curves in the single-phase convection region with increasing acceleration, the characteristic double kink of the q = q(AT) curves and the stratification of the data for various values of r/in the nucleate boiling region (Figure 2a) can be clearly seen. This stratification is more conspicuous than in references 7 and 8, since the subcooling of the liquid at the heat transfer surface of sample S 1 is, all other factors being equal, larger because of the larger radius of rotation. However, the temperature drops in the case of boiling on the ceramic sample surface for large heat fluxes are, on average, still larger than those for a copper sample (see Figure 2b). The formal procedure of calculation of AT from data for the porous ceramic sample A2, with a larger thickness than A1, leads to an unexpected result. Over a certain
Cryogenics 1993 Vol 33, No 9
853
Centrifugal acceleration and heat transfer." S.M. Kozlov et al. i
i
i i g l , ,
~
i
i
, l l , l t
associated with the onset of liquid boiling; however the position of the point where boiling starts (inside the sample or at its surface) and of the evaporation front with respect to the sensor are still to be investigated.
Z,
a 102
// ! /
E
Discussion £
101
XY
× n
z ://,' ,,,:,y,,,,:,
-I100
."./Z / / / //,' //f~,/ i
100
ilfJ,,
101
,
,
,
i , , , i ,
100
101
Temperature drop (K)
Figure 2 Dependence q = q(AT) for sample $1. (a) Averaged data from present work for: 1, r / = 1 ; 2, 11.1 ; 3, 100; 4, 1405. (b) O, Raw data from present work, r / = 11.1 ; O, raw data from references 7 and 8, r / = 10.2
range of heat flux densities the calculated temperature drop AT tends to zero; this range is shifted upwards as r/ increases (Figure 3a). This effect is reproducible for both increasing and decreasing q and in subsequent series of measurements; the raw data for one acceleration value are shown in Figure 3b. Outside the region of the 'degenerate' calculated temperature drop the slope of the curves for q = q(AT) is, on average, close to the typical value for sample A1 (see Figure 1). For ~/= 1 and for the thinner ceramic sample this peculiarity is not observed. The results we have at present are not sufficient to conclude the existence of a dependence of • on r/; however the curve of q = q(AT) for r / = 1390 outside the transition region is the furthest to the right of all the other curves, thus corresponding to a lower value of ~. Thus the dependences q = q(AT) for all three HTSC ceramic samples have transition regions which shift to larger q as the acceleration rises, although the transition shapes are different: a double kink for A1, a single kink (a change of slope of the curve) for S1 and 'degeneracy' in AT for A2. Obviously, in all three cases these features are
...... S
E
b
___o2J
101
) r-
/
/
X m q-
100
o //
-r" O
i
100
i
i~lll,
101
i
100
I
t I I till
101
Temperature drop (K)
Figure 3 Dependence q = q(AT) for sample A2. (a) Averaged data for: 1, r / = l ; 2, 11.1; 3, 100; 4, 1390. (b) O, Raw data, t / = 1390
854
Cryogenics 1993 Vol 33, No 9
It was reported earlier 2' 6 that in the case of nitrogen boiling on porous samples of HTSC ceramics at r / = 1 it was often observed that q oc AT", with n close to unity up to q = qma~ and with a steep transition section in the range of small heat flux densities. It is assumed that as q rises from 0 to qma~the heat transfer process goes through several stages. As long as the heat flux applied is insufficient for the onset of boiling of the liquid in the pores, heat transfer to the outside occurs by conduction through the porous skeleton structure and by convection of the liquid in the pores; this is the first stage. Because of the low efficiency of these mechanisms the temperature gradient and the temperature measured inside the sample increase with q. The second stage begins when the liquid starts to boil at the heated sample bottom. We assume that a vapourfilled region forms here with a high temperature gradient dT/dr separated from the liquid-filled part of the sample by the evaporation front. The heat transfer in the vapourfilled part is dominated by thermal conduction through the skeleton and convection in the vapour. Since part of the heat flux q is consumed by vaporization the dT/dr value in the liquid-filled area is not large. As q increases the front moves closer to the heat transfer surface. Before it reaches the point where the temperature is measured, the latter is only slightly dependent on q, but starts to rise rapidly once this point has been encircled by the expanding vapour-filled region. As soon as the evaporation front reaches the heat transfer surface, boiling takes place on it; and this is the third stage. The heat transfer crisis now manifests itself in the appearance of a continuous vapour film separating the surface from the liquid. The thermal conductivity used in the calculation of Tn and AT was determined for the case of gaseous nitrogen in pores and r / = i. Therefore, linear extrapolation based on the weak dependence 2 = 2(T) in the ceramic temperature range employed is legitimate in the third and, possibly, the first stages. As seen in Figure 4, for the case where the evaporation front exists inside the sample, such a procedure is sure to yield underestimates of Tn and AT. Within the framework of this concept, increases in the centrifugal acceleration are expected to have a dual effect on the heat transfer processes. Firstly, convective heat transfer is intensified both through pores and on the sample surface. This means that the sections of the q = q(A T) curves dominated by thermal resistance of the single-phase (vapour or liquid) layer should be shifted upwards. Secondly, the pressure and the saturation temperature rise at all points of the sample. The liquid can only start to boil when the ceramic temperature becomes higher than T=; hence the evaporation front can only be formed and displaced on to the heat transfer surface at higher T and q values. As Figure 1 suggests, both these effects were indeed observed in sample A1. Let us consider in greater detail the causes of the 'degeneracy' of the AT values in sample A2. Figure 5 plots the difference fiT between the measured ceramic
Centrifugal acceleration and heat transfer: S.M. Kozlov et al. Heated sample bottom
Heat transfer surface
Sample
ql < q2 < q3 < q4
Liquid /
'T(ql) l
L~rf(q 2)
Ar T LXrf(q 3)
L~r H
Distance from heated sample bottom Figure 4 Scheme of temperature distribution along heat flow direction in sample and temperature drop calculations for ql < q2 < q3 < q4' The location of the heat transfer surface, the thermometer and the evaporation front at q2 and q3 are represented by Ar H, Ar T and ~'f, respectively; the solid lines show the real distribution of T; the broken lines represent calculated values without taking into account the presence of the front; AT and AT' are the real and calculated temperature drops at q2
102 ~_
I
I
I
I I IIII
I
I
i
I I l lll
I
n ~
-
/X
,~
,
101
0 0
n
•
~o~ A~ ° / :
,
'Q
-
Arf = A(q - qo)
" / 9 "•
zx
u e-
~IC
•
/
0 ~ • // eAA/
LX:/
E 110 °
a & /
I 10-1
I 1,4'11111 100
I
I I I illll
I
values of subcooling 01 and 02 at the radii of rotation of thermometers 1 and 2. It can be seen that with growing q values at r / = constant, 6TL2 values above the local liquid subcooling result in a change from the region with fiT L 2 oc q to the region where the temperatures of sensors do not depend on q and are almost equal. The difference ( r T - fiTx) ~ 0 and for a certain region of q becomes even smaller than zero, suggesting the inapplicability of correction 6T~ under such conditions. Thermometer 2, which is fixed closer to the heater and further away from the heat transfer surface (at lower q) is superheated above T s sooner than thermometer 1. The sharp temperature rise after the horizontal section of the T = 6 T(q) curves, which is indicative of the passage of the evaporation front through the thermometer, occurs in the same succession. The dependence 67"1,2 oc q then becomes linear again with 6T2/rT1 being constant, as it was before the transition region. The sample temperature is lower at q = 1390 than at q = 100, as would be expected owing to the intensified convective heat transfer. Let us estimate the propagation of the evaporation front in the sample with increasing q, measuring the distance from the heater. Then if Arf = 6.4, 11.0 and 15.2 mm the passage of the front as detected by the said criteria corresponds to the heat flux densities q = 1.6, 2.3 and 2 . 8 k W m -2 ( r / = 1 0 0 ) and q = 1 4 , 20 and 2 5 k W m -2 (r/= 1390), respectively. These values, as well as the averages over the two thermometers, qo = 0.8 k W m -2 ( t / = 100) and qo = 5 kW m -2 (17 = 1390), at which the front forms give a near-linear dependence
I
101
Heat flux density {kWm -2} Figure 5 Dependences of fiT 1, fiT 2, 6Ta, 01 and 02 values for sample A2 on heat flux density. Open and solid symbols are for ~T 2 and 6T 1; A, A , q = 100; (3, O, r / = 1390; - - - , 6Tx; arrows indicate 01 and 0 2
temperature and the temperature of the liquid outside the sample, as a function of q for two values of q. In addition, it shows the values of 6T~ = q(Ar H - Arrl)/2 for thermometer 1, which is nearest to the heat transfer surface. The calculated temperature drop represented in Figures 1-3 was determined from the measured quantities as A T = 6 T x - 6 T ~ . The arrows on Figure 5 indicate the
(1)
where A = 7.75 mm kW -1 m -2 for q = 100 and A = 7.55 x 10-1 mm k W - ~ m - 2 for ~/= 1390. The larger the acceleration, the larger the increase of q required for the front to move towards the heat transfer surface. Similar results (though less definite, because three closely spaced points are used) have been obtained for sample A1 (Figure 1). It can be assumed that the stable position of the front is controlled by the rate of vapour removal from it, which depends on the driving head Ap oc gc(Pl - Pv) and is proportional to the first power of the acceleration. Indeed, the coefficient in (1) is more likely to depend on q as A oc q - 1 than as A oc q - 1/3, the latter being the case for convective heat removal from the front. It can be expected that at q = constant and with rising acceleration the reverse process will ensue, i.e. gradual motion of the evaporation front into the sample from the heat transfer surface, after boiling has been suppressed at this surface. Thus, experimental results for porous samples of ceramics qualitatively corroborate the idea of an internal evaporation front. Indeed, by varying the acceleration and the related pressure and subcooling of the liquid, one can influence the conditions of the phase transition and therefore those of the appearance of the front for a wide range of q; note this was not possible at r/--1. For complete understanding of the complicated processes going on in ceramics, a mathematical model of the system is to be developed. This is beyond the purpose of this paper which does, however, provide the basic data for such a model. Sample S1 with its relatively high thermal conductivity
Cryogenics 1993 Vol 33, No 9
855
Centrifugal acceleration and heat transfer: S.M. Kozlov et al. has a low thermal resistance, so that the form of the dependence of q on A T is mainly controlled by processes at the heat transfer surface, as in bulk metallic samples. In Figure 2 we see linear sections of the curve of q = q(AT) which are characteristic of single-phase convection at the heat transfer surface when 0.2 k W m - 2 < q < q0. The exponent n in q ~ AT", which was determined from experimental data, does not depend on ~/and is 1.29-1.43. The heat transfer coefficient increases with increase in the acceleration as ~oc r/°'16. The heat flux density qo at which the slope of the curve of q = q(AT) changes, i.e. nitrogen starts to boil, also rises: qo = 2.5, 4.4, 14, 32 and 69 kW m -~ at r / = 1, 11.1, 100, 231 and 1405, respectively. These data show fairly good agreement with those of reference 9 for the onset of nitrogen boiling on a steel tube of diameter 2.5 mm. The same is true of the temperature drops corresponding to qo: ATo = 2.8, 3.3, 6.8, 7.9 and 17.0 K at t / = 1, 11.1, 100, 231 and 1405, respectively. As the acceleration increases, so does the magnitude of ATos = ATo - (T~. - T1), i.e. superheating of the surface with respect to the local saturation temperature (2.8, 3.3, 6.3, 6.6 and 10.0 K for the given accelerations, respectively), whereas in the case of onset of nitrogen boiling for a tube 9, AToscharacteristically decreased. At the same time, in the case of onset of nitrogen boiling on a flat copper surface, ATo~rose from 2.25 to 5.7 K as r/increased from 1 t o 2000 7, 8.
In the region of nucleate boiling on the heat transfer surface (q > qo) the heat transfer coefficient decreases with growing r/, as calculated from both the temperature drop AT and from AT~ = AT - OH. This is in qualitative agreement with data recorded for nitrogen boiling on metallic surfaces 1' 7-9. The quantitative dependence ~ = 0t(t/) for the ceramics is, however, stronger. The additional decrease in heat transfer seems to be due to processes inside pores which are predominant in the highly porous samples A1 and A2, but also take place, though weakly, in sample $1. The heat transfer crisis on sample S1 occurred for t / = l at qmax=135kW m -2, ATmax = 8 . 6 K and for t / = 11.2 at qmax= 257kW m - 2 , ATraax = 11.9 K. Such magnitudes of qmx are also typical of nitrogen boiling on metallic surfaces ~, and their dependence on acceleration qm~, oc t/°'26 is consistent with the hydrodynamic model of the boiling crisis. The values of ATma~ here are larger than those for the case of boiling on metals and grow
856
Cryogenics 1993 Vol 33, No 9
faster with r/; this reminds us that sample S1 is more than half HTSC ceramic, which typically has high critical temperature drops 2' 3.
Conclusions The experimental investigation carried out has yielded new data supporting the hypothesis of the existence in porous ceramics of an evaporation front whose location depends on the acceleration and on the heat flux density. As the thermal conductivity increases and the porosity decreases, the internal processes cease to be predominant, and the heat transfer characteristics become similar to those typical of metallic samples with an outer surface cooled.
References 1 Verkin, B. I., Kirichenko, Yu. A. and Rusanov, K. V. Heat Transfer during Boiling in Fields of Mass Forces of Various Intensities
Naukova Dumka, Kiev, Russia (1988) 256 (in Russian) 2 Baranets, V. V., Kiriehenko, Yu. A., Kozlov, S. M., Nozdrin, S. V, et al. Experimental investigations of heat transfer from the surface of YBa2Cu307 ceramics cooled with liquid nitrogen Inzh Fiz Zhurn (1990) 59 533-538, 772-775 (in Russian) 3 Kirichenko, Yu. A., Kozlov, S. M., Rusanov, K. V. and Tyurina, E. G. Heat transfer crisis during liquid nitrogen cooling of high temperature superconductors Cryogenics (1991) 31 979-984 4 Kozlov, S. M., Kolod'ko, I. M., Levchenko, N. M., Nozdrin, S. V. et al. Preliminary results of heat transfer studies during nitrogen boiling on YBa2Cu30 7 ceramics in the field of centrifugal forces Preprint A N UkrSSR FTINT 11 (1991) No. 24 5 Kirichenko, Yu. A., Levehenko, N. M., Kozlov, S. M., Kudryavtseva, K. A. et aL An apparatus for investigation of the heat transfer in cryogenic liquids in the fields of centrifugal forces Cryogenic Electric Machine Engineering Naukova Dumka, Kiev, Russia (1983) 128-134 (in Russian) 6 Bratchenko, I. E., Dotsenko, V. I., Kislyak, I. F., Kozlov, S. M. et aL Heat transfer during nitrogen boiling on the surface of YBa2Cu307-Ag composites with various silver contents Preprint A N UkrSSR FTINT 14 (1991) No. 21 7 Levehenko, N. M. Visualization, boiling onset and heat transfer crises during boiling of cryogenic liquids Preprint A N UkrSSR FTINT24 (1986) No. 12 8 Levehenko, N. M. Heat transfer intensity and regimes during boiling of cryogenic liquids Preprint A N UkrSSR FTINT 32 (1986) No. 13 9 Verkin, B. I., Kirichenko, Yu. A., Levehenko, N. M. and Rusanov, K. V. Heat transfer during nitrogen boiling in the field of centrifugal forces Proc ICEC 7 IPC~Science and Technology Press, Guildford, UK (1978) 394-398