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The use of semiconductors for the study of boiling heat transfer to low temperature liquids
The study of heat transfer in the cryogenic range presents a number of technical difficulties. The authors show how several of these problems can be resolved. Advantages in accuracy of data and speed of iesponse can also be gained by the techniques described here
THE USE OF SEMICONDUCTORS FOR THE STUDY OF BOILING HEAT TRANSFER TO LOW TEMPERATURE LIQUIDS G. G. H A R M A N and L. H. G O R D Y t
MANY studies of heat transfer from solids to low temperature liquefied gases have been made. I Frequently electrically heated wires are used as a convenient means of controlling and measuring the heat flux.2-4 These studies are generally concerned with two regimes of heat transfer, the nucleate (wet wall) and the film (dry wall or burn-out) boiling regime. In order to study the second regime it is necessary to pass through a transition from nucleate into film boiling--a region of poor,heat transfer. Thus if the same amount of input power is continued into the second region, the heater temperature will rise rapidly and actual burn-out may ensue. Generally this is prevented by observing the transition visually or electrically (thermocouple output) and manually reducing the heat input. If the heating element had a sufficiently large positive temperature coefficient of resistance it would be thermally self-limiting and data could easily be obtained from both regimes. It is the purpose of this investigation to show that semiconductors have these desirable characteristics and may be advantageously used in the study of boiling heat-transfer. The increase in a semiconductor's resistance, as the temperature is raised from 77 to ~ 300 ° K, is generally much greater than that of the purest metals. For appropriate materials it can be greater than a factor of 10. This immediately offers the advantage that the temperature rise will always be self-regulating after the nucleate to t Electron Devices Section, National Bureau of Standards, Washington, D.C., U.S.A. Received 20 December 1966. CRYOGENICS'
A P R I L 1967
film boiling transition. Thus there is no danger of heating element burn-out and the transition can be repeated dozens of times. All necessary data for nucleate and film boiling curves can be automatically and continuously recorded on an X Y recorder over a several hundred degree range. Because of the large number of available semiconductors, doping impurity depths, and resistivity ranges, it is possible to obtain almost any desired resistance versus temperature characteristic. Three characteristic curves are represented in this investigation, as shown in Figure 1. They were selected for the temperature of their resistance minima with respect to the boiling point of the liquid, in this case nitrogen. From the shape of the curves it is possible to predict the nature of the nucleate to film boiling transition. Let a semiconductor heat element (sample) with the properties of curve A, Figure 1, be electrically heated to the peak nucleate flux. The applied voltage is then raised incrementally and held constant. As the heat transfer mechanism begins the transition to film boiling, the sample will at first experience a sharp decrease in resistance and a resulting increase in I2R heat generation. This causes the sample temperature to rise rapidly, within a few milliseconds, to a point where the heat flux reaches equilibrium with the input power, as indicated by the arrow (1 -+2) in curve A. A sample having the characteristics of curve B will undergo a slower transition because initially there is no significant power increase. Thus transition times in fens of milliseconds can be anticipated, The germanium sample, curve C, undergoes an immediate decrease of I2R power 89
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It is absolutely necessary to have good ohmic contacts, as described above, in order to obtain meaningful • resistance versus temperature curves. If the sample has poor electrodes, their contact resistance will vary with both voltage and temperature, and the results cannot be used for preparing boiling curves. After first obtaining the resistance versus temperature data, the sample is suspended in the liquid and power is applied, as in the simple measuring circuit of Figure 2. The voltage is slowly increased, either automatically or manually, from zero to an appropriate maximum value. The voltage and current supplied to the semiconductor sample are recorded on an X Y recorder. The heat flux (II1) can be calculated at any point from the recorder trace. The sample resistance (V/I) is likewise obtained. Finally, the sample temperature is determined by comparing this resistance with the previously measured resistance versus temperature curve.
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Figure 2. Diagram of simple measuring equipment. V: Regulated variable voltage supply; S: Immersed sample; R: 1 t~ or 10 ~ precision current-reading resistor; M: Precision X)' recorder
4,° 1
0
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50
100
150 T
I
200
I
250
"
300 (*K)
Figure 1. Resistance versus temperature curves for three semiconductor samples. For convenience of presentation, the data were normalized to the resistance minima. Broken lines indicate characteristics below the boiling point of nitrogen
at the transition and can be considered to drift upward to its new equilibrium temperature (~170 ° K) in a period of several hundred milliseconds. The semiconductors used in this investigation are hard and brittle, but any desired shape and length can be sawed, ground, or ultrasonically cut. These materials are available in large single crystal boules and in thin sheets (silicon web s) having lengths up to several metres. The two silicon samples were cut from silicon web and had naturally grown untreated single crystal surfaces ((11 I) orientation). These samples were approximately 10 mm long, 2 mm wide, and 0-01 mm thick. (The samples must be thin because of their low thermal conductivity.) Ohmic contacts were made by alloying aluminium on the bulbous dendrite ends of the P-type sample. The N-type sample was phosphorus-diffused on the ends which were then over-evaporated with aluminium. The N-type germanium sample was cut from a large boule and then heavily etched. Thus its surface condition was quite different from that of the silicon samples. Its dimensions were slightly larger than the silicon ones and it had alloyed tin-antimony ohmic contacts. All of the above are conventional procedures and techniques which are available in any semiconductor laboratory. 90
Figure 3 gives the X Y recorder trace for the sample of Figure 1, curve A. For a sample of this type, the nucleate to film boiling transition is highly reproducible, almost regardless of the time required to raise the power. Programmed times, from zero to the peak nucleate flux, of 10 s to 10 min yielded variations in the peak flux of only 7 per cent. Some noise is evident on the trace just before the transition and in the entire film boiling region. This is due to small local variations of the sample temperature, resulting from turbulence of the liquid. The retrace curve (decreasing power) on this sample is very unusual since it shows what appears to be hysteresis. This is actually the result of decreasing the flux below the power that was required for the nucleate to film boiling transition, to a point where the reverse transition occurs. Since this passes through a resistance minimum, the current actually overshoots before rejoining the nucleate boiling portion of the I - V curve. The interpreted data, however, appear quite normal when presented in the usual manner of Q/A versus AT. Figure 4 shows the I- V data for the germanium sample (Figure 1, curve C). There is no decrease in resistance at the transition to serve as a precise trigger as in curve A. Therefore the general characteristics are similar to those obtained with wires and a variation in the peak nucleate flux of about I0 per cent has been observed• The most reproducible results from this sample were obtained when the power was increased slowly from zero to the peak value, taking at least 1 min. The I-Vcurve for the N-type silicon s sample (Figure 1, curve B) resembles that of Figure 4 and is therefore not given. Its relatively flat resistance versus temperature curve changes only ,~5 per cent from 77 to 107 ° K. This is CRYOGENICS" APRIL 1967
a major disadvantage when it comes to using the sample's resistance to determine its temperature. Thus, samples having such a characteristic curve cannot be used for making experimental nucleate and film-boiling graphs. Such samples nevertheless may be interesting. In this case intermediate quasi-stable states were observed which lasted for several seconds. The electrical characteristics have been observed and photographed from a storage oscilloscope and are shown in Figure 5. These intermediate states presumably occur when only a portion, perhaps one face of the sample, undergoes the nucleate to film boiling transition. They are probably a result of the large temperature coefficient of resistance.
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12 16 20 Sample voltage
24
Figure 4. The XY recorder trace of current versus voltage for a 2 ~ cm (at 300° K) N-type germanium sample that is immersed in liquid nitrogen. Arrows indicate direction of the trace. A indicates the nucleate boiling region and B indicates film boiling
200
160
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120
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80
Figure 5. Oscilloscope trace displaying current versus time for a 9 ~ cm (at 300° K) N-type silicon sample that is immersed in liquid nitrogen. Each division on the ordinate represents 10 mA, on the abscissa 1 s. The trace begins ( A ) where the voltage (and current) are preset at a level just below the nucleate to film-boiling transition.The voltage was then raised to the transition flux B and held constant. C is the intermediate transition level and D indicates the complete film boiling region
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Figure 3. The XY recorder trace of current versus voltage for a 1.5 ~ cm (at 300° K) P-type silicon sample that is immersed in liquid nitrogen. Arrows indicate the direction of the trace, either increasing or decreasing voltage. A indicates the nucleate boiling region and B indicates film boiling
Figure 6 presents the experimental nucleate and film boiling curves for two samples. The heat flux was obtained from Figures 3 and 4, and the temperature from the original data of Figure 1. All points lie well within the previously reported range. 1 Data for the silicon sample appear further from the theoretical value. This may be due to its more bulbous metal electrodes which could lead to inaccuracies in estimating the surface area. The effect of the naturally grown silicon surfaces or the etched germanium ones cannot be estimated, but the former may contribute to the formation of quasi-stable states. The preceding results were obtained with samples vertically suspended in the liquid by the small conducting wires at each end. Less than 10 per cent variations in the peak nucleate flux resulted from measurements in CRYOGENICS"
A P R I L 1967
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Temperature
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15 ~ cm P-type silicon
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2 ~ cm N-type germanium
Figure 6. Boiling curves for a silicon and a germanium sample immersed in liquid nitrogen 91
horizontal positions, in agreement with previous work on wires. 3 It was assumed that end effef,t~ modified the results from such short samples. Te~atative experiments were performed to determine the extent of this by grossly changing the thermal characteristics of the ends. The samples were mounted so that the electroded ends were attached to copper heat sink strips. The thermal conductivity of these semiconductors is quite low, so that relatively little flux from the thin body region should be lost to the end sinks. As expected, the measured peak nucleate flux increased, but less than I0 per cent. This peak flux was more reproducible ( < 5 per cent) and there was a considerable decrease in the electrical noise near the transition. The transition time was shorter by a factor of 2 or 3. More accurate results would probably be obtained with much longer samples. However, heat sinking showed that the end effects are small and this method of mounting even offered some advantages. The use of semiconductors in obtaining heat transfer data from liquid nitrogen has been demonstrated. They are accurate, fast responding, and thermally self-limiting above the nucleate to film-boiling transition. Because of their large positive temperature coefficient of resistance, certain samples can be used to study intermediate transitions between the nucleateand film boiling regimes.
92
Germanium may be used for studies in the range from about 20 to 300 ° K. Silicon is useful from 50 to about 450 ° K. Above these temperatures the temperature coefficients of resistance become negative and the samples will burn up. However, other semiconductors, such as gallium arsenide and silicon carbide, can be used for measurements at temperatures several hundred degrees higher. The authors wish to acknowledge many valuable discussions with M. C. Jones of the N.B.S. Cryogenics Division.
REFERENCES 1. For instance see the compendium : BRENTARI,E. G., GIARRATANO, P. J., and SMITH, R. V. N.B.S. Tech. Note No. 317 0965) 2. RALLIS, C. J., and JA'~VUREK, H. H. htt. J. Heat and Mass Transfer 7, 1051 (1964) 3. FREDERKING, T., and GRASSMANN, P. Supplement au Bulletin de I'lnstitut International du Froid, Annex, 1958-1, p. 317 4. RUZIt~KA, J. Supplement all Bulletin de/'htstitut International du Froid, Annex, 1958-1, p. 323 5. Dow Corning, Electronic Products Division, Hemlock, Mich.
CRYOGENICS'
APRIL
1967
THE USE OF SEMICONDUCTORS FOR THE STUDY OF BOILING HEAT TRANSFER TO LOW TEMPERATURE LIQUIDS G. G. H A R M A N and L. H. G O R D Y t
MANY studies of heat transfer from solids to low temperature liquefied gases have been made. I Frequently electrically heated wires are used as a convenient means of controlling and measuring the heat flux.2-4 These studies are generally concerned with two regimes of heat transfer, the nucleate (wet wall) and the film (dry wall or burn-out) boiling regime. In order to study the second regime it is necessary to pass through a transition from nucleate into film boiling--a region of poor,heat transfer. Thus if the same amount of input power is continued into the second region, the heater temperature will rise rapidly and actual burn-out may ensue. Generally this is prevented by observing the transition visually or electrically (thermocouple output) and manually reducing the heat input. If the heating element had a sufficiently large positive temperature coefficient of resistance it would be thermally self-limiting and data could easily be obtained from both regimes. It is the purpose of this investigation to show that semiconductors have these desirable characteristics and may be advantageously used in the study of boiling heat-transfer. The increase in a semiconductor's resistance, as the temperature is raised from 77 to ~ 300 ° K, is generally much greater than that of the purest metals. For appropriate materials it can be greater than a factor of 10. This immediately offers the advantage that the temperature rise will always be self-regulating after the nucleate to t Electron Devices Section, National Bureau of Standards, Washington, D.C., U.S.A. Received 20 December 1966. CRYOGENICS'
A P R I L 1967
film boiling transition. Thus there is no danger of heating element burn-out and the transition can be repeated dozens of times. All necessary data for nucleate and film boiling curves can be automatically and continuously recorded on an X Y recorder over a several hundred degree range. Because of the large number of available semiconductors, doping impurity depths, and resistivity ranges, it is possible to obtain almost any desired resistance versus temperature characteristic. Three characteristic curves are represented in this investigation, as shown in Figure 1. They were selected for the temperature of their resistance minima with respect to the boiling point of the liquid, in this case nitrogen. From the shape of the curves it is possible to predict the nature of the nucleate to film boiling transition. Let a semiconductor heat element (sample) with the properties of curve A, Figure 1, be electrically heated to the peak nucleate flux. The applied voltage is then raised incrementally and held constant. As the heat transfer mechanism begins the transition to film boiling, the sample will at first experience a sharp decrease in resistance and a resulting increase in I2R heat generation. This causes the sample temperature to rise rapidly, within a few milliseconds, to a point where the heat flux reaches equilibrium with the input power, as indicated by the arrow (1 -+2) in curve A. A sample having the characteristics of curve B will undergo a slower transition because initially there is no significant power increase. Thus transition times in fens of milliseconds can be anticipated, The germanium sample, curve C, undergoes an immediate decrease of I2R power 89
9
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,
//
/
O
//
~t.
J
,
.E 0
o
/
It is absolutely necessary to have good ohmic contacts, as described above, in order to obtain meaningful • resistance versus temperature curves. If the sample has poor electrodes, their contact resistance will vary with both voltage and temperature, and the results cannot be used for preparing boiling curves. After first obtaining the resistance versus temperature data, the sample is suspended in the liquid and power is applied, as in the simple measuring circuit of Figure 2. The voltage is slowly increased, either automatically or manually, from zero to an appropriate maximum value. The voltage and current supplied to the semiconductor sample are recorded on an X Y recorder. The heat flux (II1) can be calculated at any point from the recorder trace. The sample resistance (V/I) is likewise obtained. Finally, the sample temperature is determined by comparing this resistance with the previously measured resistance versus temperature curve.
77* K
"~
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I
l-*
;~F/
x
! ,,7 R:
Y
o o
M.
I n.
Figure 2. Diagram of simple measuring equipment. V: Regulated variable voltage supply; S: Immersed sample; R: 1 t~ or 10 ~ precision current-reading resistor; M: Precision X)' recorder
4,° 1
0
"~
I
50
100
150 T
I
200
I
250
"
300 (*K)
Figure 1. Resistance versus temperature curves for three semiconductor samples. For convenience of presentation, the data were normalized to the resistance minima. Broken lines indicate characteristics below the boiling point of nitrogen
at the transition and can be considered to drift upward to its new equilibrium temperature (~170 ° K) in a period of several hundred milliseconds. The semiconductors used in this investigation are hard and brittle, but any desired shape and length can be sawed, ground, or ultrasonically cut. These materials are available in large single crystal boules and in thin sheets (silicon web s) having lengths up to several metres. The two silicon samples were cut from silicon web and had naturally grown untreated single crystal surfaces ((11 I) orientation). These samples were approximately 10 mm long, 2 mm wide, and 0-01 mm thick. (The samples must be thin because of their low thermal conductivity.) Ohmic contacts were made by alloying aluminium on the bulbous dendrite ends of the P-type sample. The N-type sample was phosphorus-diffused on the ends which were then over-evaporated with aluminium. The N-type germanium sample was cut from a large boule and then heavily etched. Thus its surface condition was quite different from that of the silicon samples. Its dimensions were slightly larger than the silicon ones and it had alloyed tin-antimony ohmic contacts. All of the above are conventional procedures and techniques which are available in any semiconductor laboratory. 90
Figure 3 gives the X Y recorder trace for the sample of Figure 1, curve A. For a sample of this type, the nucleate to film boiling transition is highly reproducible, almost regardless of the time required to raise the power. Programmed times, from zero to the peak nucleate flux, of 10 s to 10 min yielded variations in the peak flux of only 7 per cent. Some noise is evident on the trace just before the transition and in the entire film boiling region. This is due to small local variations of the sample temperature, resulting from turbulence of the liquid. The retrace curve (decreasing power) on this sample is very unusual since it shows what appears to be hysteresis. This is actually the result of decreasing the flux below the power that was required for the nucleate to film boiling transition, to a point where the reverse transition occurs. Since this passes through a resistance minimum, the current actually overshoots before rejoining the nucleate boiling portion of the I - V curve. The interpreted data, however, appear quite normal when presented in the usual manner of Q/A versus AT. Figure 4 shows the I- V data for the germanium sample (Figure 1, curve C). There is no decrease in resistance at the transition to serve as a precise trigger as in curve A. Therefore the general characteristics are similar to those obtained with wires and a variation in the peak nucleate flux of about I0 per cent has been observed• The most reproducible results from this sample were obtained when the power was increased slowly from zero to the peak value, taking at least 1 min. The I-Vcurve for the N-type silicon s sample (Figure 1, curve B) resembles that of Figure 4 and is therefore not given. Its relatively flat resistance versus temperature curve changes only ,~5 per cent from 77 to 107 ° K. This is CRYOGENICS" APRIL 1967
a major disadvantage when it comes to using the sample's resistance to determine its temperature. Thus, samples having such a characteristic curve cannot be used for making experimental nucleate and film-boiling graphs. Such samples nevertheless may be interesting. In this case intermediate quasi-stable states were observed which lasted for several seconds. The electrical characteristics have been observed and photographed from a storage oscilloscope and are shown in Figure 5. These intermediate states presumably occur when only a portion, perhaps one face of the sample, undergoes the nucleate to film boiling transition. They are probably a result of the large temperature coefficient of resistance.
E
200
A... I too
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o
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I
I
4
8
12 16 20 Sample voltage
24
Figure 4. The XY recorder trace of current versus voltage for a 2 ~ cm (at 300° K) N-type germanium sample that is immersed in liquid nitrogen. Arrows indicate direction of the trace. A indicates the nucleate boiling region and B indicates film boiling
200
160
- -
i
t E
120
2~ U
E m
80
Figure 5. Oscilloscope trace displaying current versus time for a 9 ~ cm (at 300° K) N-type silicon sample that is immersed in liquid nitrogen. Each division on the ordinate represents 10 mA, on the abscissa 1 s. The trace begins ( A ) where the voltage (and current) are preset at a level just below the nucleate to film-boiling transition.The voltage was then raised to the transition flux B and held constant. C is the intermediate transition level and D indicates the complete film boiling region
/,0
I
10
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I
20
30
Applied vo|toge
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1,0
Figure 3. The XY recorder trace of current versus voltage for a 1.5 ~ cm (at 300° K) P-type silicon sample that is immersed in liquid nitrogen. Arrows indicate the direction of the trace, either increasing or decreasing voltage. A indicates the nucleate boiling region and B indicates film boiling
Figure 6 presents the experimental nucleate and film boiling curves for two samples. The heat flux was obtained from Figures 3 and 4, and the temperature from the original data of Figure 1. All points lie well within the previously reported range. 1 Data for the silicon sample appear further from the theoretical value. This may be due to its more bulbous metal electrodes which could lead to inaccuracies in estimating the surface area. The effect of the naturally grown silicon surfaces or the etched germanium ones cannot be estimated, but the former may contribute to the formation of quasi-stable states. The preceding results were obtained with samples vertically suspended in the liquid by the small conducting wires at each end. Less than 10 per cent variations in the peak nucleate flux resulted from measurements in CRYOGENICS"
A P R I L 1967
10
I
I
•
I
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./
E
/
~t-C
O.¸ I.O
I
Temperature
•
15 ~ cm P-type silicon
I
10
difference
•
[
tOO
AT (degK)
2 ~ cm N-type germanium
Figure 6. Boiling curves for a silicon and a germanium sample immersed in liquid nitrogen 91
horizontal positions, in agreement with previous work on wires. 3 It was assumed that end effef,t~ modified the results from such short samples. Te~atative experiments were performed to determine the extent of this by grossly changing the thermal characteristics of the ends. The samples were mounted so that the electroded ends were attached to copper heat sink strips. The thermal conductivity of these semiconductors is quite low, so that relatively little flux from the thin body region should be lost to the end sinks. As expected, the measured peak nucleate flux increased, but less than I0 per cent. This peak flux was more reproducible ( < 5 per cent) and there was a considerable decrease in the electrical noise near the transition. The transition time was shorter by a factor of 2 or 3. More accurate results would probably be obtained with much longer samples. However, heat sinking showed that the end effects are small and this method of mounting even offered some advantages. The use of semiconductors in obtaining heat transfer data from liquid nitrogen has been demonstrated. They are accurate, fast responding, and thermally self-limiting above the nucleate to film-boiling transition. Because of their large positive temperature coefficient of resistance, certain samples can be used to study intermediate transitions between the nucleateand film boiling regimes.
92
Germanium may be used for studies in the range from about 20 to 300 ° K. Silicon is useful from 50 to about 450 ° K. Above these temperatures the temperature coefficients of resistance become negative and the samples will burn up. However, other semiconductors, such as gallium arsenide and silicon carbide, can be used for measurements at temperatures several hundred degrees higher. The authors wish to acknowledge many valuable discussions with M. C. Jones of the N.B.S. Cryogenics Division.
REFERENCES 1. For instance see the compendium : BRENTARI,E. G., GIARRATANO, P. J., and SMITH, R. V. N.B.S. Tech. Note No. 317 0965) 2. RALLIS, C. J., and JA'~VUREK, H. H. htt. J. Heat and Mass Transfer 7, 1051 (1964) 3. FREDERKING, T., and GRASSMANN, P. Supplement au Bulletin de I'lnstitut International du Froid, Annex, 1958-1, p. 317 4. RUZIt~KA, J. Supplement all Bulletin de/'htstitut International du Froid, Annex, 1958-1, p. 323 5. Dow Corning, Electronic Products Division, Hemlock, Mich.
CRYOGENICS'
APRIL
1967