MATRIB godina u Veloj Luci / 10 years in Vela Luka HRVATSKO DRUŠTO ZA MATERIJALE I

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1 HRVATSKO DRUŠTO ZA MATERIJALE I 1 of :06 HRVATSKO DRUŠTVO ZA MATERIJALE I TRIBOLOGIJU CROATIAN SOCIETY OF MATERIALS AND TRIBOLOGY I. Luia 5 HR Zagreb, Croatia T: F: hdmt@fsb.hr 10 godina u Veloj Luci / 10 years in Vela Luka MATRIB 2009 INTERNATIONAL CONFERENCE ON MATERIALS,TRIBOLOGY, RECYCLING Lipanj / June 24-26, 2009 KONA!AN PROGRAM / FINAL PROGRAMME MATRIB je uvršten u plan stru*nog usavršavanja Razreda inženjera strojarstva, Hrvatske komore arhitekata i inženjera u graditeljstvu i vrednuje se s 12 bodova.

2 ZBORNIK RADOVA PROCEEDINGS MATRIB 2009 VELA LUKA OTOK / ISLAND KORČULA, HRVATSKA lipnja / June ORGANIZATORI / ORGANIZED BY: HRVATSKO DRUŠTVO ZA MATERIJALE I TRIBOLOGIJU CROATIAN SOCIETY FOR MATERIALS AND TRIBOLOGY INSTITUTE OF MATERIALS AND MACHINE MECHANICS (SLOVAK ACADEMY OF SCIENCES) DUBLIN INSTITUTE OF TECHNOLOGY SUORGANIZATORI / CO-ORGANIZERS: FAKULTET STROJARSTVA I BRODOGRADNJE, ZAGREB FACULTY OF MECHANICAL ENGINEERING AND NAVAL ARCHITECTURE SPONZORI / SPONSORS: MINISTARSTVO ZNANOSTI OBRAZOVANJA I ŠPORTA PROPLIN d.o.o. - ZAGREB IDEF d.o.o. za industrijsku defektoskopiju ZAGREB ROBERT BOSCH d.o.o. ZAGREB

3 IZDAVAČ / PUBLISHER: Hrvatsko društvo za materijale i tribologiju Croatian Society for Materials and Tribology c/o FSB, Ivana Lučića 5, Zagreb tel.: ; fax: hdmt@fsb.hr, UREDNICI / EDITORS: Krešimir Grilec, Gojko Marić CIP zapis dostupan u računalnom katalogu Nacionalne i sveučilišne knjižnice u Zagrebu pod brojem ISBN NAKLADA / ISSUE: 150 TISAK / PRINT: Vizual media d.o.o., Zagreb II

4 DETERMINATION OF THERMAL CONDUCTIVITY BY TRANSIENT HOT WIRE METHOD Neven Ukrainczyk 1, Jurica Alešković 2, Juraj Šipušić 1 1 Faculty of Chemical Engineering and Technology, University of Zagreb, Marulićev trg 20, Zagreb, Croatia 2 Elektroda Zagreb d.d. Ruševje 7, Zaprešić - Zagreb, Croatia Corresponding author: N. Ukrainczyk: nukrainc@fkit.hr Izvorni znanstveni rad / Original scientific paper Abstract Thermal property data are important for the engineering solutions of the heat transfer problems. There are many cases in which thermal conductivity of the studied material is not available, eg. cement materials of different compositions during setting and hardening. Furthermore, these materials are wet and porous and in order to prevent development of humidity gradients under imposed thermal gradients, one finds transient measurement methods as preferable. This work describes a developed apparatus and a transient Hot Wire (HW) method to obtain the thermal conductivity of dry and wet materials. Single, thin platinum wire is used as both a constant power heater and temperature sensor. The result obtained from measurement is the temperature development of the HW during heating period, which is described by a theoretical model. The thermal conductivity of the material under study is obtained by the solution of the parameter estimation problem, utilizing the Levenberg-Marquardt method of optimization. The results of the method evaluation on reference materials indicated an accuracy of 3% and a uncertainty of 0.7% (for 95% confidence). The reference materials used were gelatinous water (Agar gel 0.7%), glycerol and Ottawa (quartz) sand. The values of the thermal conductivity for fresh calcium aluminate cement pastes with water to cement mass ratio of 30 and 40 % are documented. The systematic error arising due to the measured sample electrical conductivity is calculated to be less than 0.5% for the experimental configuration used. Keywords: thermal conductivity, hot wire method, reference materials, electrical conductivity, calcium aluminate cement. 418

5 1. Introduction Material thermal property data are important for the engineering solutions of the heat transfer problems. Measurements of thermal properties of heterogeneous, wet and porous materials by conventional steady-state methods are subject to large errors. In order to avoid water migration during the run-time of the thermal tests, transient measurement methods are preferable [1, 2]. The determination of thermal conductivity is very challenging since it belongs to a class of inverse problems where an estimated parameter is very sensitive to measured quantities necessary for its calculation. The hot wire method [1] involves an ideal line heat source, infinitely long with zero mass, immersed in an infinite sample. As the parallel wire method is very sensitive to the uncertainty of measuring the radial distance of a thermocouple from a heater, a resistance technique is employed. Furthermore, by this method, where the wire acts as both a heater and a resistance thermometer, the influence of local non-homogeneities of measured materials is minimized. Thermal conductivity is determined by inverse solution of the differential equation for radial heat conduction. In order to minimize errors due to an approximation of the used model and effects of the experimental setup a critical design of an experimental configuration is necessary. This work describes a developed apparatus and a method to obtain a thermal conductivity of dry and wet materials. The systematic error due to a electrical conductivity of cement paste is minimized by the used experimental configuration. The values of the thermal conductivity for fresh calcium aluminate cement (CAC) pastes are documented to the best of our knowledge for the first time and compared to the available literature data on portland cement. Research on thermal properties of CAC is particularly interesting due to rapid heat generation during hydration and development of significant temperature gradient in material [3, 4]. 2. Hot wire model When a heat generation is applied to the line heat source, its temperature response is based on an analytical solution [5] to the heat conduction model given in cylindrical coordinates: 2 t= t q r T( r, t) = E t= 0 i (1) 4πλ 4at where λ is the thermal conductivity of sample (Wm -1 K -1 ), r is the radius of the wire (m) a is thermal diffusivity of sample (m 2 s -1 ), t is time (s), q is rate of heat generation (W/m) and E i is the exponential integral computed as: z z z Ei ( z) = γ + ln z+ z (2) 2! 3! 4! in which γ = is Euler s constant and z = r 2 /(4 at). 3. Experiment 3.1. Materials The reference materials used to evaluate the used apparatus and method are gelatinous water (Agar gel 0.7%) and Ottawa sand. For detailed discussion on reference materials used please see further in 3.3 and

6 Furthermore, this paper documents the thermal conductivities of cement pastes obtained with sample of commercial CAC ISTRA 40 taken from a regular production of Istra Cement International, Pula, Croatia. The cement has the oxide mass fraction composition listed in Table 1. Physical properties of used cement are given in Table 2. All mixes were prepared with deionized water. The main compounds are CA (cement notation: C=CaO, A=Al 2 O 3, F=Fe 2 O 3, S=SiO 2, H=H 2 O) and ferrite phase (C 4 AF-C 6 AF 2 ), with mayenite, C 12 A 7, gehlenite, C 2 AS and β-c 2 S as minor compounds. Cement pastes with water to cement mass ratio of 0.3 and 0.4 were prepared. Table 1. Chemical composition of investigated CAC. CaO Al 2 O 3 Fe 2 O 3 FeO SiO 2 TiO 2 MgO SO 3 Na 2 O K 2 O Sum 37.10% 38.47% 14.39% 2.90% 4.43% 1.05% 0.90% 0.20% 0.14% 0.17% 99.8% Table 2. Physical properties of investigated CAC. >90 µm, Blaine, Specific Setting time, Standard Bulk density, kg/m 3 % cm 2 /g gravity, min consistency, Loose Compacte g/cm 3 initial final % d Measuring device The thermal conductivity is determined from the time dependant temperature rise of an electrically heated wire. The wire used is % platinum (Aldrich) with a diameter 2r = 76 µm and length of l = 176 mm. It is desired to have a wire with as small a diameter as possible because the theory assumes a true line heat source. The wire is heated by placing a constant voltage across the bridge, as suggested by Glatzmaier and Ramirez [6]. The supplied voltage has an output range of 0 25V and is stable to within ±10µV. Change in the wire electrical resistance is determined by measuring the unbalanced voltage of a precision Wheatstone bridge during heating period. This voltage is read by a computer via an 8 channel 10-bit A/D converter. Measuring apparatus is connected to the PC via RS232 protocol that provides the sampling rate of 15ms. Specially designed programs provide control of the automatic measuring apparatus and easy usage. The core of the measuring apparatus is a microcontroler PIC 16F877 which was programmed in MPLab by a direct RISC instructions and ICD-2 programmer/debugger. From the previously obtained resistance versus temperature calibration (least-squares regression) of the used Pt wire the change of the temperature is deduced. The low temperature rise of hot wire, obtained by applying low input voltage, is desirable in terms of minimizing the effects of natural convection, radiation and/or gas evolution. On the other hand, higher voltage reduces the effect of noise and allow for a more precise temperature measurement. In this work the applied voltage gave temperature rise of 5 C (during 2 min). Only for measurements on glycerol the temperature rise was reduced to 3 C in order to minimize the natural convection effect. 420

7 Figure 1. Thermal conductivity measuring setup Experimental setup The mould containing the investigated sample is obtained in the following manner. The specimens were cast in cylindrical copper containers with inner diameter 2R = 51 mm, length 250 mm and thickness of 1 mm. The Pt wire was placed in the center of the tube. A Pt wire supported by a tensioning system is placed in the tube, the frame being next to the inside surface of the copper pipe, Figure 1. Also the thermocouple is placed near the tube axis to monitor the temperature of the sample. The copper tube was carefully filled with the sample continuously applying vibrations in order to minimize air entrapment. Copper tube is sealed with styropore and rubber stoppers and placed in the temperature controlled water bath (±0.03 C). Thermal conductivities of reference materials were determined at 20 C. Prior to loading the Ottawa sand to mould, it was dried at 105 C. The gelatinous water was prepared by mixing 0.7 % of agar powder by weight with hot (85 C) deionized water in a laboratory glass. The mixture was heated and stirred vigorously using a magnetic stir hot plate. Once the gel was melted, it was poured into a mold by tapping it to help the air bubbles rise to the surface. The mold was put in a water bath at 20 C and waited for at least 4 h to attain uniform temperature. The fresh pastes were tested at temperature 20 C during the period of hours after mixing. 4. Results and discussion 4.1. Thermal conductivity determination Deviations from the idealized model in Eq. (1), classified as inner and outer, can be minimized by a proper selection of experimental conditions. Inner deviations arise from the non-ideality of the wire that has finite length, mass and heat capacity. These deviations, which depend on the properties of the wire, have significant impact only on the initial temperature response (t < t min ). Outer deviations are due to the finite dimensions of the sample and have impact at longer times (t > t max ) when the outer boundary conditions (of the sample) influence the wire temperature response. The so-called time window defines representative temperature response corresponding to the sample thermal properties. It is estimated by numerical simulation supposing a systematic error of 0.1 % to be between t min = 0.5 s and t max = 120 s. For simulations a numerical model of one dimensional radial heat conduction was built for the used experimental configuration and solved by using 421

8 MATLAB s built-in solver pdepe [7, 8]. The model employed two coupled partial differential equations of energy conservation: one for the wire and one for the sample [9]. The thermal conductivity was calculated by fitting the experimental results to a theoretical expression (1) by using literature values for thermal diffusivity [10-12], listed in Table 3, and eight terms for calculating the exponential integral according to the Eq. (2). This parameter estimation problem was solved by the Levenberg-Marquardt method of optimization [13, 14]. In order to investigate the sensitivity of thermal conductivity and thermal diffusivity a simulation analysis was performed by plotting predicted responses by Eq. (1) with ± 10 % change in the investigated parameters. The results on parameter sensitivity analysis, shown in Fig. 2, indicate a low impact of thermal diffusivity and good sensitivity of thermal conductivity onto the temperature response ( T). Therefore, an uncertainty of value on thermal diffusivity has little impact to estimation of thermal conductivity. Data on thermal diffusivity of fresh cement pastes are taken from independent transient measurements conducted in our laboratory [15]. Table 3. Literature data on thermal conductivity and thermal diffusivity at T = 20 C. Material λ / W m -1 K -1 a 10 7 / m 2 s -1 Ottawa sand [17] 2.33 [11] Gelatinous water (Agar) [10] 1.433[10] Glycerol [12] [12] Fresh cement paste w/c = [15] Fresh cement paste w/c = [15] 4.5 λ = λ = a = 3.3e-7 λ = 1.1 T / o C a = 3.0e-7 a = 2.7e Figure 2. Parameter sensitivity analysis. Impact of ± 10 % change in values of thermal conductivity and thermal diffusivity onto the theoretical temperature response Evaluation on reference materials The reference materials used to evaluate the used apparatus and method are gelatinous water (Agar gel 0.7%) and Ottawa sand. Ottawa sand consists of spherical grains (high purity silica) with an accurately graded particle size distribution to pass an 850-µ (US Standard No. t / s 422

9 20) sieve and to be retained on a 600-µ (US Standard No. 30) sieve. Data on the thermal conductivity of Ottawa sand in air is readily available from several sources, although no specific standard exists for this property. The solid density of the Ottawa sand was measured by submerging a known mass of sand in water and measuring the volume change of the liquid. The solid density was found to be 2.69 g/cm 3, which is very close to the published value of 2.65 g/cm 3 [16]. Knowledge of the bulk density is important because the thermal conductivity can change based on how tightly the sand particles are packed. Measured bulk density of investigated Ottawa sand of g/cm 3 is close to the published value of g/cm 3 [17]. The thermal diffusivity data on Ottawa sand were not readily found in literature. Hence, the used value in Eq. (1) is taken for sand in general [15]. The density and thermal conductivity of investigated Ottawa sand are 2.64 g/cm 3 and 0.31 Wm -1 K -1, which is close to the published value of 2.6 g/cm 3 and 0.3 Wm -1 K -1 [15]. Agar is gel-forming polysaccharide, widely used in industry and in scientific applications. Agar form gels at approximately 35 C and once formed does not melt below 85 C. Gelation occurs when a chain of macromolecules forms a network capable of entrapping the dispersing medium. Such gel has a composition close to a pure liquid but resemble a solid. In that way heat transfer through agar is by conduction solely, excluding natural convection. A repeatability analysis was conducted on samples by repeating the measurements 10 times. The mean values of the thermal conductivities and estimated precision at a 95 % confidence level are listed in Table 4. Very good agreement was found between the results of the experimental investigation and sources of available data. This finding validates the accuracy of the measurement apparatus and provides confidence that further results are accurate. It can be concluded that the results of the method evaluation on reference materials indicated an accuracy of 3 % and uncertainty of 0.7 % (for 95 % confidence) Effect of cement paste electrical conductivity The electrical conductivity of cement paste was measured by conductivity meter (Lab 960 Schott instruments) 0.5 h after mixing cement and water. For cement pastes with water to cement ratio 0.4 and 0.3 the measured electrical conductivities are 1287 µscm -1 and 1098 µscm -1, respectively. The resistance of the cement paste sample in a defined geometry (see 3.3) is calculated by referring to the values of the obtained electrical conductivity. The deviation of the overall electrical resistance (of the parallel system of sample and Pt resistance), RII from the Pt resistance is calculated to be less than 0.5 %. Hence, in the experimental configuration the systematic error due to the electrical conductivity of cement paste can be assumed to be less than 0.5 % Thermal conductivity of fresh cement pastes Cement based material is a complex heterogeneous, multiphase and polydisperse system. Through such a material the heat is transferred by a combination of different modes. They include conduction through the solid particles, conduction and convection through the gaseous and liquid phases, evaporation condensation mechanism [2], and radiation at the particle surfaces. However, this overall process is practically modelled solely by a heat conduction model considering the conduction parameters as apparent. Therefore, one should bear in mind that the physical parameters measured in this paper for cement paste and Ottawa sand are more properly called apparent thermal conductivity [2]. The values of the thermal 423

10 conductivity for fresh calcium aluminate cement pastes obtained show good agreement with the literature values for Portland cement (PC) [18], Table 4. Table 4. Measured and published data on thermal conductivity at T = 20 C. λ / W m -1 K -1 Material Measured Uncertainty Reported Accuracy Ottawa sand % [17] 3 % Gelatinous water (Agar) % [10] 3 % Glycerol % [12] 2 % Fresh cement paste w/c = % (PC)0.97[18] Fresh cement paste w/c = % (PC) 0.99 [18] - An example of a result for estimation of thermal conductivity based on the measured temperature response (cement w/c = 0.4) and the radial heat conduction model (1) is given in Fig. 3. A good fit with a standard deviation of C validates the appliance of the heat conduction model used for describing the heat transfer of investigated wet porous materials. 5 4 Data: FreshPaste w/c = 0.4 Model: hot_tau T / C Measured (HW) Analytic Fit Chi^2/DoF = 3.6e-4 R^2 = P (fix) l (fix) a 3.0e-7 (fix) λ ±5e-3 r 3.8e-5 (fix) t / s Figure 3. An example of a result for determination of thermal conductivity based on a measured temperature response and the heat conduction model (1). 5. Conclusion In order to minimize errors due to an approximation of the used model and effects of the experimental setup a critical design of an experimental configuration is necessary. The results of the method evaluation on reference materials indicated an accuracy of 3% and uncertainty of 0.7% (for 95% confidence). The values of the thermal conductivity for fresh calcium aluminate cement pastes with water to cement mass ratio of 30 and 40 % are 0.98 W m -1 K -1 and 1.06 W m -1 K -1, respectively. 6. Acknowledgement 424

11 The authors acknowledge support from the Croatian Ministry of Science, Education and Sports under project s no Development of Hydration Process Model. 7. Reference 1. Vozár L., A computer-controlled apparatus for thermal conductivity measurement by the transient hot wire, Journal of Thermal Analysis, 46 (1996) De Vries, D. A., The Theory Of Heat And Moisture Transfer In Porous Media Revisited, Int J Heat Mass Transfer, 30 (1987) Ukrainczyk, N., Šipušić, J., Dabić, P., Matusinović, T., Microcalorimetric Study On Calcium Aluminate Cement Hydration, 13. International conference on Materials, Processes, Friction and Wear - MATRIB'08 (2008) George C.M, Industrial aluminous cements, Structure and Performance of Cements (ed. P.Barnes), Applied Science, London, (1983) Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, 2nd Ed., Oxford University Press, London (1959). 6. Glatzmaier, G.C., Ramirez W. F., Simultaneous measurement of the thermal conductivity and thermal diffusivity of unconsolidated materials by the transient hot wire method, Rev. Sci. Instrum. 56 (1985) Skeel R. D, and Berzins M, A Method for the Spatial Discretization of Parabolic Equations, SIAM J Sci Stat Comput, 11 (1990) Shampine L. F., and Reichelt M. W., The MATLAB ODE suite, SIAM J Sci Stat Comput, 18 (1997) Assael M. J., Karagiannidis L., Malamataris N., and Wakeham W. A., The Transient Hot- Wire Technique: A Numerical Approach, International Journal of Thermophysics, 19 (1998) Lemmon E.W., McLinden M.O. and Friend D.G., "Thermophysical Properties of Fluid Systems" In NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg MD, ( 11. Beck M. W. and Brown M. E., Modification Of The Burning Rate Of Antimony/Potassium Permanganate Pyrotechnic Delay Compositions, Combustion And Flame, 66 (1986) Lienhard, J.H.V, and Lienhard, J.H.IV, A Heat Transfer Textbook, 3rd ed., Cambridge, MA: Phlogiston Press, ( 13. Levenberg, K., A Method for the Solution of Certain Problems in Least Squares, Quart. Appl. Math. 2, (1944) Marquardt, D.W., An Algorithm for Least-Squares Estimation of Nonlinear Parameters, SIAM Journal on Applied Mathematics 11 (1963) Ukrainczyk, N, Thermal Properties of Hydrating Calcium Aluminate Cement Pastes, to be published. 16. ASTM Density OTTAWA sand C NIST Standard Reference Database 81, Heat Transmission Properties of Insulating and Building Materials Database, ID 1023, ( 18. Bentz, D.P., "Transient Plane Source Measurements of the Thermal Properties of Hydrating Cement Pastes," Materials and Structures, 40 (2007),