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RODNEY D. SUTHERLAND, ROBERT S. DAVIS, and WILLIAM F. SEYER Department of Engineering, University of California, Los Angeles, Calif.
Heat Transfer Effects Molecular Orientation of Octadecane High molecular weight hydrocarbons get hot -to a degree and depth
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data are recorded for the thermal conductivity of hydrocarbons having more than 10 carbon atoms. In 1933 Bates ( 7 ) questioned the validity of all thermal conductivities measured by the thin film method and recommended the use of a thick film. Recently his contentions have been supported by the work of Sakiadis and Coates (7) who state that values obtained by the latter method are about 5 70higher than those of the former. This diffrrence is attributed to surface irregularities and film effects. These same effects could explain the fact that while Bates, with his thick film method, obtained a value of 0.000145 gram cal. sec.-1-cm.-2 for water at 30° C. (2) others using a film thickness of only 0.4 mm. obtained 0.000144 cal./ gram, second (3, 9 ) . Thus the physiochemical nature of the interface may also be a contributing factor, particularly the degree and depth of orientation imposed on the liquid molecules by forces on the metal surface. The extent of these forces has been much discussed (5), and experimental evidence indicates that orientation effects in a solid-liquid interface are not limited to a single molecular layer but may extend in some liquids through tens or hundreds of Angstroms. This distance could be several centimeters. particularly for a large molecule such as pazoxyanisole (5). Therefore, this orientation could, at least in part, be responsible for the difference in thermal conductivities obtained by the thick and thin film methods. The activity of these orientating forces could reasonably be a function of molecular weight, especially if the long chain axis of the molecule normal to the surface is relatively large compared to the diameter-e.g., in the aliphatic series. T o obtain experimental evidence for this assumption, the over-all heat transfer of octadecane was measured through various layer thicknesses as it has a convenient melting point. For
this study n-paraffins were chosen instead of their polar derivatives because sufficient quantities of relatively pure compounds were available. They also are capable of building an ordered, closepacked layer on a metal surface similar to the corresponding polar compounds,
the acids and alcohols ( i l ) . Copper was selected for the source and sink pl'ites for the calorimeter because of its high thermal conductivity and chemical inertness. The over-all resistance to heat flow R is the sum of two quantities: R = r,:+ rI
INSULATION
Figure 1 . Heating and cooling units were placed in a stainless steel sphere which could be evacuated, and this in turn was placed in an insulated wooden box with controlled air temperature VOL. 51, NO. 4
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where T , is the film resistance and r l that of liquid proper. Obviously under thick film conditions T , could become negligible. Downward heating was adopted as it has been shown by Bates (2) and Sakiadis and Coates (7) that for distances of 5 cm. or less between the plates convection does not occur.
A ppurutus The calorimeter (Figure 1) was similar to that used by Kaye and Higgins (6) except that for simplicity the guard plate above the heater was eliminated and the heating and cooling units were placed in a highly polished stainless steel sphere that could be evacuated. The sphere was set in an insulated wooden box whose air temperature could be controlled within 1" C. Generally, the guard heater accurately measures heat input into the heater block and also ensures a uniform temperature distribution. Against this advantage is the heat conducted from the sides of the hot block to the cold one because of the increased area. Kaye and Higgins (6) measured this heat loss and found it to be only a small fraction of total heat input to the heater block. They also considered the heat conducted from the top face of the guard heater around to the cold block as negligible. The copper heat source and sink plate, 10.17 cm. in diameter, were constructed as described by Bates (2). Temperature of the upper plate was measured by placing three thermocouples in holes 0.1 5 cm. from the inner surface spaced 120" apart and connected in parallel so as to
obtain the average temperature. Thermocouple e.m.f. was measured with a Leeds & Northrup k-2 potentiometer with which it was possible to estimate voltage differences within 0.1 pv. by carefully following the instructions given with the instrument and by observing and controlling room temperature. Thermocouple temperatures were compared with those of an L&N resistance thermometer capable of measuring to 0.001" c. Owing to the absence of a guardheater plate energy input into the heater was very carefully controlled to ensure a uniform temperature during any one measurement. This was done by utilizing four heavy-duty storage batteries connected to give 12 volts, and, with the series of resistances, 0.6 to 1.2 amperes. Current flowing through the heater was measured with a Weston Model 1326 ammeter calibrated to 0.002 ampere. and voltage was measured across the heater with a Weston Model 5 voltmeter calibrated to 0.005 volt. I t was thus nominally possible to control amperage within 0.01 ampere for a period of 10 hours or more. Temperature increase of the cooling water was obtained with a 12-junction, multiple differential couple placed between the water inlet and outlet. Calibration curves indicated that these temperature measurements were reliable to at least 0 . 0 1 O C.. while temperature rise of the water during all runs was between 0.5' to 0.8' C. All thermocouples were calibrated from time to time against a standardized L&?; platinum resistance
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Influence of pressure on contact resistance agreed with literature results
INDUSTRIAL AND ENGINEERING CHEMISTRY
thermometer and a Beckman differentia1 type. Because the amount of heat conducted in unit time was obtained by the rise of temperature of flowing water accurate flow rate measurements were essential. After some experimentation, the conventional method of allowing cooling water to flow from a constant level. constant temperature bath through the heat exchanger was abandoned. .4 recirculating method was used instead because of the relatively large amount of water needed. Many of the runs required as much as 20 hours for completion with a flow rate of from 1 to 2 ml. per second. Thus effluent was first cooled and then reheated to the desired temperature by the usual laboratory method so that temperature of the water just before entering the vats never varied more than 0.02' C. Flow rate was measured by a carefully calibrated Fisher and Porter Type 01-N-15 rotameter. Temperature of the wooden housing chamber was always set to within 1' C. of that of the cold block to minimize heat loss from the cooling water while in the metal sphere. Temperature variation of the inside air was of the order of 0.1" C.
Procedure Five sets of runs were made measuring resistance to heat transfer: with copper to copper contact only, both as a function of pressure and with different temperatures; for a thin layer of unknown thickness of the hydrocarbon in the monoclinic, rhombic, and liquid phase at several temperatures; finally for various liquid layer thicknesses and temperatures at constant pressure. The procedures varied somewhat depending on the nature of layer thickness of the liquid or solid hydrocarbon. The first experiments were performed without any extraneous material, with only the two smooth copper surfaces in contact. After the lapping operation the two contact surfaces were thoroughly rinsed with specially purified acetone and then with petroleum ether as it was thought unsafe to use water. After each washing the plates were placed in contact inside the sphere, which was evacuated to 8 mm. of mercury and heated to approximately one hour to remove the wash liquid. I n the course of these initial experiments the extreme sensitivity of heat transfer to the washing technique was revealed by the fact that when either petroleum ether or acetone alone were used the contact resistance changed from 160 to 75 sq. cm./second/" C./cal. for the same temperature. Hence to get a clean plate-i.e., one with the lowest contact resistance-petroleum ether was always used first and then acetone. followed by heating. T o obtain the resistance of the clean
MOLECULAR O R I E N T A T I O N plates with change of pressure an insulating layer was first placed on the heater plate and superimposed on this a series of cylindrical lead blocks of the same diameter. For thin film resistance measurements finely divided octadecane was placed on the cooling plate and then melted to form a continuous liquid surface. Next the heating plate was carefully slid over this to avoid trapping any air until the txvo plates were concentric, after which excess liquor was squeezed out and wiped off as thoroughly as possible. Attempts to measure the thickness of this layer by an electrical capacitance method were futile as the system showed zero capacity, indicating a certain amount of metal to metal contact. Two sets of runs were made with this unknown layer thickness in both liquid and solid states, the first after a week. the second after 6 months. The object was to test the sensitivity of the experimental set-up and to determine whether time was a factor in film structure. Xleasurement of heat transfer for the final operation required the cementing of a special transite ring about the upper edge of the cooling block to serve as a reservoir for surplus liquid. T o separate the two plates three tiny Teflon supports were used as in the Kaye and Higgins (6) experiment. Thickness of the layers was measured by noting the difference in height between two marked points on the copper plates using a cathetometer. I t required 6 to 8 hours tc, reach a steady state. Readings were then taken every 0.5 hour over a period of 8 to 10 hours, and results were averaged to obtain final values. Resistance R was calculated from Equation 1.
Atc = 0.419" C. 43.988 - 27.924 = 16.064' C. At, G = 0.679 ml./second C, = 0.998 cal./ml./o C. A = 81.08 sq. cm. K = 0.000360 tal./' C./second/cm.
Discussion of Results
The resistance of metal to metal contact increased linearly with temperature, with a slope of approximately 40" between 30' and 60" C. This is much greater than for pure copper and was probably due to the fact that only the asperities were in contact and to the production of an oxide film as the plate surfaces showed some darkening. The effect of pressure (Figure 2) is in agreement with results recorded by W'eills and Ryder (70). Plastic deformations between contact surfaces must have occurred during loading because upon removal of the load heat resistance fell to about half of the original value. Results obtained with only a very thin film of hydrocarbon of unknown thickness under a pressure of 10 grams 'sq. cm. (Figure 3) show two partially enclosed areas. These are significant in connection with behavior of the solid state which shows a transition point where the rhombic form changes to monoclinic. This change is more pronounced when the film is 6 months old than when it is only 1 week old. There is also an overall increase in resistance which may have been due to oxidation Examination of the copper surfaces at the end of the test showed a slight blackening. The results were identical qualitatively with those obtained previously by the dilatometer method (7). The slope of the rhombic and monoclinic lines indicates that the tempera-
ture effect on resistivity varies with crystalline forms. Further: dk/'dt is negative. as is the case for metals and many nonmetallic substances. The drop in resistivity when starting with the liquid and cooling can be shown by simple calculation to be close to the change in density in going from liquid to solid. Raising the temperature of the solid monoclinic form rapidly to the melting point brings the resistivity back to it5 original value. The significance of the resistancetemperature lines of Figure 3 becomes apparent when their slopes are compared with slopes of the apparent conductivitytemperature lines of Figure 4. Slopes of the thin film resistance lines are negative hence the conductivity lines would be positive. At a layer thickness of 0.0102 cm. dk/dt approaches zero and becomes: above that thickness, increasingly negative. This leads to the conclusion that over-all resistance to heat flow is the sum of two separate resistances, an interfacial resistance which decreases with temperature and a liquid resistance factor which increases. These become equal to each other at a definite layer thickness of octadecane 1%hen between copper plates. The increase in conductivity is further illustrated in Figure 5. Not until a layer thickness of 0.7 cm. is reached does thermal conductivity approach a value equivalent to that computed from the scanty data given in the literature ( 9 ) . At all thicknesses above the critical [one, thermal conductivities are highest for the lowest temperature which agrees with the observations of other workers in this field. The concave nature of the three curves ( A to B ) raises some doubt as to the absolute values of K as heat
For example, the thermal resistance of a layer of n-octadecane was calculated : Run N 18. Air temperature, 34.9' C. Thermocouple 4 9 16 21 Temp., O C. 0.479 37.015 34.100 36. 047 Atw = 0.479' C . A t , = 37.015 - 36.100 = 0.915' C. G = 0.938 ml./second C, = 0.998 cal./ml./' C. R = 2.04' C./second/cal.
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Thermal conductivity is given by Equation 2.
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A calculation for determining thermal conductivity of various thicknesses of octadecane layers follows. Run A 2. Air temperature, 27.8 O C. Layer thickness, 0.690 cm. Thermocouple 7 9 16 19 Temp., C. 0.419 43.988 27.924 28.698
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Figure 3. Thin film of unknown thickness shows transition point a t line a where rhombic (R, R') changes to monoclinic (M, M ' ) left o f melting point line b. Solid heating i s represented b y H, H' and liquid heating and cooling b y 1, L'
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transfer by radiation has been neglected and the use of a guard ring avoided. This latter aspect was a reason for not continuing measurements for thicker liquid layers with the described method. The results supply further evidence that under nonflow conditions the orienting forces of a metal surface may extend many Angstrom units deep into the liquid. Its industrial significance is obvious in heat and mass transfer and in such other processes as liquid-liquid extraction, solvent removal from solids, and in the solution of solids itself. Similar conditions appear to exist at the metalsolid hydrocarbon interface. This is to be expected as the solid phase was always formed by cooling the liquid between the plates. However, in the thin film case the orienting forces were not great enough to prevent transformation of the rhombic into the monoclinic crystalline state.
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Conclusions
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TEMPERATURE
60
50
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Figure 4. These plots illustrate effect o f temperature on thermal conductivity for layer thickness of liquid and difference between solid and liquid and change for liquid as thickness increases
Under quiescent conditions the orientating forces on a copper surface can extend several millimeters deep into liquid octadecane, and this depth appears to be dependent upon the size and shape of the molecule. The most reliable method for determining the heat conductivity of a liquid is the thick film method. Nomenclature
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References
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(1) Bates, 0. K., IND. ENG. CHEM.2 5 ,
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431-7 (1933).
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(2) Zbzd.,’28,494-8 (1936). (3) Bridgeman, P. W., Proc. ,Vatl. Acad. SGZ. 9, 344-93 (1923). (4) Hardy, W. B., Doubleday, I., Proc. Roy. Soc. (London) A104, 25-38 (1923). (5) Henniker, J. C., Reus. Modern Phys.
21, 322-41 (1949).
(6) Kaye, G. W. C., Higgins, W. F., Proc. Roy. Soc. (London) A117, 459-70
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riaure inerrnai conatmiviw ala nor auuroacii r i l e v u i u e __ s - - J. calculated from literature until film thickness o f 0.7 cm. was reached -
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(1928). (7) Sakiadis, B. C., Coates, J., A.I.Ch.E. Journal 1,275-88 (1935). (8) Seyer, W. F., Patterson, R . F., Keys, J. L.. J . Am. Chem. Sor. 66, 179-82 (19443. (9) Smith, J. F. D., Trans. A m Sod. Mech. Engrs. 58, 719-23 (1936). (IO) Weills, N. D., Ryder, E. A., Zbid., 71, 259-67 (1949). RECEIVED for review March 31, 1958 ACCEPTEDOctober 20, 1958
