Thermal conductivity of liquid mercury

Transcription

1 High Temperatures ^ High Pressures, 2002, volume 34, pages 35 ^ ECTP Proceedings pages 1263 ^ 1267 DOI: /htwu63 Thermal conductivity of liquid mercury M Vita Peralta ô, Malcolm Dix, Markus Lesemann, William A Wakeham Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK; fax: ; v.peralta@ic.ac.uk Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. The thermal conductivity of liquid mercury has been measured in a range of temperature from 300 to 520 K at atmospheric pressure. The measurements were carried out with a new experimental technique based on the transient hot-wire technique. Special efforts have been made to ensure the elimination of the phenomenon of convection, which is one of the main problems found in the measurement of the thermal conductivity of molten metals. The results obtained demonstrate the validity of the theoretical model of the experimental technique and they support the claimed accuracy of 2%. The present results are compared with the disparate values reported in the literature by other authors and are thought to be of a superior accuracy. 1 Introduction The industrial importance of molten metals or salts is continuously increasing. The fluids themselves have applications as heat-transfer fluids and for heat storage but the properties of the fluids are also of significance in the modelling of the heat-transfer processes associated with continuous casting, the production of composite materials, and the growth of semiconductor crystals. Although reliable data for the thermal conductivity of molten metals are required, there have been a very limited number of experimental studies and often the discrepancies among the data are far beyond their claimed accuracy even under quite mild conditions (Sakonidou et al 1999). One of the main problems found in the measurements of the thermal conductivity of molten metals is the phenomenon of convection, which becomes much more severe at higher temperature, because precise temperature control and distribution becomes progressively more difficult as the temperature increases. In this work a new experimental technique based on the transient hot-wire technique has been developed, and a great deal of care has been taken to ensure the elimination of the phenomenon of convection, by ensuring that the free surface of the sample is at a higher temperature than that of the base. Furthermore, it has been imposed as a stringent condition that it should be possible to demonstrate that the apparatus operates in accordance with the theoretical model. 2 Experimental An outline of the experimental technique developed for the measurement of the thermal conductivity of molten metals has been given elsewhere (Assael et al 1997). The first preliminary measurements of the thermal conductivity of liquid mercury and gallium near ambient conditions have been published in a previous paper (Dix et al 1998). Figure 1 shows a schematic representation of the sensor, which has been fabricated with as substrate 96% pure green alumina. The connections were made with platinum ink and a screen-printing technique. The working element is made from platinum wire of 99.99% purity, and is mounted in the middle of the sensor both in the plane shown and in the cross-section AA 0. ô Current address: Instituto de Investigaciones Ele ctricas, Av. Reforma No. 113 Col. Palmira, Temixco Morelos, Mexico; fax: +52 (7) ; vperalta@iie.org.mx

2 36 M V Peralta, M Dix, M Lesemann, W A Wakeham 15 ECTP Proceedings page 1264 A A platinum wire mm 58.0 A Figure 1. The platinum-wire sensor; dimensions in millimetres. The liquid mercury, contained in an alumina crucible, was housed in a high-temperature furnace with a controlled atmosphere of argon on a pneumatically operated table. In the rest position the sensor was mounted from the top side of the furnace just above the liquid melt surface. During measurement the crucible was raised pneumatically to allow liquid melt to surround the sensor. An extra heater was mounted on the top of the sensor/furnace in order to minimise the loss of heat from the top of the furnace and to eliminate problems from convection by ensuring stable density stratification. The measurements were carried out at several temperatures in the range from 300 to 520 K. Each measurement consists of transient heating of the platinum wire by application of heat generation within it and subsequent monitoring of the temperature rise of the wire through its resistance change by means of an automatic bridge. The process and equipment have been described briefly elsewhere (Assael et al 1997; Dix et al 1998) and will be described in more detail later (Peralta et al 2000). For present purposes, it is sufficient to record that the estimated accuracy of the temperature rise measurements is better than 0:1%. The errors in the time measurements are insignificant. The analysis of an experimental measurement is performed by comparing the experimental results with a prediction carried out with a finite element solution of the full two-dimensional heat-transfer equation (Dix et al 1998; Peralta et al 2000). The program developed for this purpose calculates the temperature rise of the wire for presumed values of the thermophysical properties of the wire, the alumina substrate, and the melt, and the known dimensions of the sensor. The accuracy of the finite element solution of the transient heating problem has been verified by comparison with an analytical solution for the case when the heating source is a cylindrical wire immersed in a single material of infinite extent. The deviations do not amount to more than 0:15% (Peralta-Martinez 2000), and the time dependence, which is the important parameter, is even less. For very short times, t < 10 ms, the behaviour of the wire for a given heat input depends only upon the properties of platinum which are taken from the literature (CRC 1993 ^ 1994). For times between 100 ms and 10 ms the properties of the alumina substrate (density r, specific heat C p, and thermal conductivity l) influence the evolution of the temperature of the wire while the properties of the surrounding melt do not. Taking r and C p for alumina from the literature (Kingery and McQuarrie 1954) an optimum fit of the observed temperature rise to that calculated with the finite element program can be achieved by changing the thermal conductivity of alumina. A value is derived that, of course, corresponds to the particular sample of alumina being used in situ. It is important to note that values typical of samples of alumina are generally obtained (Peralta-Martinez 2000). For large times, t > 10 ms, the temperature of the wire depends upon the properties (r, C p, l) of the molten metal as well as those of the inner elements. Again we have adopted reference values of r and C p for mercury (Amitin et al 1979; Simon 1992; CRC 1993 ^ 1994) and sought to achieve optimum agreement between the measured and

3 Thermal conductivity of liquid mercury ECTP Proceedings page 1265 calculated temperature rise in this region by adjustment of the thermal conductivity of mercury. This process `determines' the thermal conductivity of mercury. The entire process of analysis is more complicated than described here; details are omitted but will be reported elsewhere (Peralta-Martinez 2000). Figures 2 and 3 show comparisons between the measured and calculated temperature rises for mercury at K and K, respectively, after the optimisation process. These two examples illustrate that the deviation seldom exceeds about 0.1% of the temperature rise and that it is essentially randomly distributed about zero over 5 decades of time during which the heat traverses three different materials. This is taken to be extremely strong evidence that the theoretical model is a faithful representation of the real sensor. It is noteworthy that this precision is commensurate with the mutual uncertainty of experiment and calculation. The sensitivity of the technique to the thermal conductivity of mercury is best illustrated by a numerical example, because there is no explicit working equation. Figure 4 shows us such an example for mercury at K where the effects of a change of 1% inthe assigned thermal conductivity of mercury are demonstrated. It can be seen that at times up to about 0.1s the thermal conductivity of the melt has no effect upon the heat transfer inside the sensor. Beyond that time the fit to the experimental data of the two presumed (T exp T sim ) K :005 0:010 0: t s Figure 2. Comparison between measured and simulated temperature rise data for a measurement in mercury at K. The experimental temperature rise employed was 5 K. (T exp T sim ) K :005 0:010 0: t s Figure 3. Comparison between measured and simulated temperature rise data for a measurement in mercury at K. The experimental temperature rise employed was 5 K. (T exp T sim ) K :005 0:010 0: t s Figure 4. Sensitivity to the thermal conductivity of mercury at K: ~, l Hg ˆ 10:8 Wm 1 K 1 ; &, l Hg ˆ 10:692 ( 1%) W m 1 K 1 ; ^, l Hg ˆ 10:908 ( 1%) W m 1 K 1.

4 38 M V Peralta, M Dix, M Lesemann, W A Wakeham 15 ECTP Proceedings page 1266 values of the thermal conductivity is discernibly worse than for the optimum value. Accordingly, we assigned a precision of 1% to our thermal conductivity measurements. If we allow for errors in the temperature resistance characterisation of platinum, as well as for the precision of the resistance and temperature measurements, it is estimated that the accuracy of the thermal conductivity reported is 2%. 3 Results The results for the measurements of the thermal conductivity of liquid mercury within the temperature range 300 ^ 520 K are shown in table 1. Figure 5 shows the dependence of the thermal conductivity on temperature, observed in this work. The data are evidently smooth within the observed accuracy of 2%. It is possible to represent the thermal conductivity of mercury obtained in this work with the following correlation: l Hg =Wm 1 K 1 ˆ 0:4682 8:92909 T=K 2 T=K 0: :15 273:15 for 300 < (T=K) < 520. Figure 6 shows the comparison of this correlation with the results reported by othert authors. In this chart it is possible to discern that there is good agreement with Hall (1936, 1938) with differences between 5%; the same differences are observed up to 350 K for data reported by Powell and Tye (1961), PTB (1995), and Prabhuram and Saksena (1982). The differences for the last three increase for temperatures from 350 to 400 K, being between 5% and 15%, and up to 20% from 400 to 500 K. The differences with the data reported by Vel'tishcheva et al (1958), Nikol'skii et al (1959), Duggin (1968), and Vukalovich et al (1971) are within 5% to 15% for temperatures from 330 to 400 K and up to about 20% for temperatures from 450 to 500 K. There is a wide gap between l Wm 1 K % Temperature K Figure 5. Thermal conductivity of mercury as a function of temperature. Table 1. Thermal conductivity of mercury. Temperature=K Thermal conductivity=w m 1 K

5 Thermal conductivity of liquid mercury ECTP Proceedings page [(l corr l exp )=l corr ] % T K Figure 6. Comparison of the results of earlier measurements of the thermal conductivity of liquid mercury with the correlation of the present work: &, Hall (1936, 1938); +, Powell and Tye (1961) 6, Prabhuram and Saksena (1982); *, Vel'tishcheva et al (1958) and Nikol'skii et al (1959); ö, Duggin (1968); ~, PTB (1995); ^, Vukalovich et al (1971); ~, Gehlhoff and Neumeier (1919). the results reported by Gelhoff and Neumeier (1919) and the rest of the authors with discrepancies up to about 60% at about 430 K. 4 Conclusions The thermal conductivity of liquid mercury has been measured in the range of temperature from 300 to 500 K. Evidence is given to demonstrate that the experimental technique operates in accordance with the theoretical model. If we take this into account and allow for the precision of the measurements, the accuracy of the present results is estimated to be 2%. The comparison between the results of various earlier measurements of the thermal conductivity of mercury reveals differences amounting to almost 60% at 420 K. It is noteworthy that the present results which have been conducted with a validated experimental technique have a superior accuracy to any of those measured earlier. References Amitin E B, Ledeva E G, Paukov I E, 1979 Russ. J. Phys. Chem ^ 1530 Assael M J, Dix M, Drummond I W, Karagiannidis L, Lourenc o M J, Nieto de Castro C, Papadaki M, Ramires M L, van den Berg H R, Wakeham W A, 1997 Int. J. Thermophys ^446 CRC, 1993 ^ 1994 Handbook of Chemistry and Physics 74th edition (Boca Raton, FL: CRC) Dix M, Drummond I W, Lesemann M, Peralta-Martinez V, Wakeham W A, Assael M J, Karagiannidis L, van den Berg H R, 1998, in Proceedings of the Fifth Asian Thermophysical Properties Conference Eds M S Kim, S T Ro (Seoul: National University) pp 113 ^ 117 Duggin M J, 1968 Phys. Lett. A ^ 258 Gehlhoff G, Neumeier F, 1919 Verh. Dtsch. Phys. Ges ^217 Hall W C, 1936, PhD thesis, University of Kansas, USA Hall W C, 1938 Phys. Rev ^1009 Kingery W D, McQuarrie M C, 1954 J. Am. Ceram. Soc ^ 108 Nikol'skii N A, Kalakutskaya N A, Pchelkin I M, Klassen T V, Vel'tishcheva V A, 1959 Vopr. Teploobmena Termodin. 11 ^ 45 Peralta V, Dix M, Assael M J, Karagiannidis L, Lesemann M,Wakeham W A, 2000 (to be published) Peralta-Martinez M V, 2000 Thermal Conductivity of Molten Metals PhD thesis, University of London, UK Powell R W, Tye R P, 1961 International Developments in Heat Transfer, ASME ^ 862 Physikalisch-Technische Bundesanstalt (PTB), 1995 Quecksilber: Hg (Braunschweig: Physikalisch- Technische Bundesanstalt Braunschweig, Berlin: FIZ Chemie) PTB-Stoffdatenbla«tter 1 Prabhuram, Saksena M P, 1982 Ind. Eng. Chem. Fundam ^ 485 Sakonidou E P, Assael M J, Nieto de Castro C A, van den Berg H R, Wakeham W A, 1999, in Thermal Conductivity 24 Eds P S Gaal, D E Apostolescu (Lancaster, PA: Technomic) Simon F, 1992 Ann. Phys ^ 280 Vel'tishcheva V A, Kalakutskaya N A, Nikol'skii N A, 1958 Teploenergetika 5 80^82 Vukalovich M P, Ivanov A I, Fokin L R, Yakovlev A T, 1971, Teplofizicheskie Svoistva Rtuti (Thermophysical properties of mercury), Monograph No. 9 State Committee for Standards at the Council of Ministers of the Soviet Union, Moscow

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