A NEW METHOD FOR APPARENT THERMAL CONDUCTIVITY MEASUREMENT OF MOULD FLUX
Mu Li1, Rie Endo1, Li Ju Wang2 and Masahiro Susa1
1Department of Metallurgy and Ceramics Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, 152-8552 Japan
2School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, 99164, USA
Keywords: quasi-steady state hot plate method, mould flux, thermal conductivity, silica glass.
Abstract
A new quasi-steady state hot plate method has been proposed to measure heat flux across a sheet sample such as mould flux film, finally to determine its apparent thermal conductivity via Fourier’s equation. The heat flux across the sheet sample is derived from the volume change caused by melting of ice utilizing a modified Bunsen Ice Calorimeter. This measurement method was applied to Ni-base super alloy (Inconel 600), alumina and PTFE (Teflon) with known thermal conductivity values to confirm the reliability of this new method. The experimental thermal conductivity values obtained were in good agreement with the respective reported values. Measurements were also conducted on sheet silica glasses which sized 20×20×0.5 mm3 and 20×20×1.0 mm3, and produced a value of 1.34 ± 0.03 Wm-1K-1 at 293 K – 303 K under a temperature gradient of 20 Kmm-1, which value is reasonable compared with the reported one. In addition, a process simulation has been applied to confirm the applicability of the present method to mould flux used in continuous casting under a steep temperature gradient at high temperature.
Introduction
In the continuous casting, various factors affect the surface quality of slab, including cooling conditions [1] and physical properties [2] of mould powders that are placed on the surface of molten steel in the mould. The heat transfer mechanism from the shell to the mould is very complicated [3] but the heat flux is dominated by the properties of solid mould flux film. Thus, in order to obtain qualified steel, it is necessary to evaluate the conductive heat transmission between the steel and the mould.
Advances in Molten Slags, Fluxes, and Salts: Proceedings of The 10th International Conference on Molten Slags, Fluxes and Salts (MOLTEN16) Edited by: Ramana G. Reddy, Pinakin Chaubal, P. Chris Pistorius, and Uday Pal TMS (The Minerals, Metals & Materials Society), 2016
There are some researches focusing on the thermal conductivity of mould fluxes [4, 5], Yamauchi et al. [4] reported the values at temperature range between 573 K – 1073 K, Ozawa et al. [5]
measured the thermal conductivity from 773 K to 1053 K. Both the data are almost at the same order of magnitude, however, the thermal conductivity has not been yet evaluated under steep temperature gradients close to the actual operation.
Bunsen [6] has reported an ice-calorimeter that can determine a quantity of heat transferred to an ice/water mixture by measuring the volume change of the mixture due to melting of ice. Jessup [7]
has applied this technique to obtain a heat quantity of the magnitude of 160 J with a precision of about 0.05%, and also succeeded in measuring the heat quantity change associated with chemical reaction using a Bunsen Ice Calorimeter. More recently a quasi-steady state hot plate method has been established utilizing the principle of Bunsen Ice Calorimeter to measure the apparent thermal conductivity of oxide scale on steel under steep temperature gradients. [8] Thus, it is possible to apply this method to a mould flux film to determine its apparent thermal conductivity using the temperature gradient in the mould flux on the basis of Fourier’s law.
Consequently, the present work aims to determine the apparent thermal conductivity of a silica plate as a model of mould flux film using the quasi-steady state hot plate method.
Experimental
Principle of Quasi-steady State Hot Plate Method
Figure 1 shows a schematic diagram of the heat flux measurement apparatus developed for the quasi-steady state hot plate method utilizing the principle of a Bunsen Ice Calorimeter. A vertical barrel container (calorimeter) that was filled with an ice/water mixture inside was placed in an ice box to reduce the effect of surrounding conditions. Ice was made by an ice-making machine from distilled water, and crushed into small pieces sized around 10×10×10 mm3. The container was hermetically sealed with a copper lid, which had 77 fins 50 mm long at the downside to promote the heat transmission from the sample to the ice/water mixture. In addition, there was a stirrer placed at the bottom of the container to keep the temperature more uniform. The sheet sample was placed upon the copper lid. Two aluminum metal blocks sized 20×20×10 mm3 weighing ca. 11 g were positioned on the sample: the lower was used to accommodate a thermocouple and the upper was used as a heat source. In principle, heat transmits from the heat source to the ice/water mixture across the sample and melts parts of ice; thereby the volume of the mixture changes. The volume change was detected by a laser displacement meter as the liquid height decrease in the pipe that was connected to the container.
The liquid height change provides the number of moles of melted ice, ∆𝑛H2O, as follows:
∆𝑛H2O=𝜋𝑟2∙∆ℎ
𝑀H2O/( 1
𝜌water− 1
𝜌ice) (1)
where r is the radius of the pipe, ρ is the density of each substance, h is the liquid height and 𝑀H2O is the molar mass of water. The number of moles of melted ice, in turn, provides the heat deposited to the ice/water mixture. Thus, the heat flux (qice) across the sample is derived from the derivative of the liquid height with respect to time as follows:
𝑞ice=∆𝑡𝑟𝑠𝐻H2O∙𝜋𝑟2∙𝜌ice∙𝜌water
𝐴∙𝑀H2O∙(𝜌ice−𝜌water) ∙𝑑ℎ
𝑑𝑡 (2)
where A is the surface area of the sample across which area heat transmits and ∆𝑡𝑟𝑠𝐻H2O is the enthalpy for fusion of ice at 273.15 K.
As shown in Figure 1, a sheathed K-type thermocouplewas positioned inside the aluminium block 1.3 mm away from its bottom surface and a platinum thermometry resistance element was placed at the lower surface of the copper lid to monitor temperatures 𝑇up and 𝑇down, respectively. Using Fourier’s law, the relationship between the temperature difference and the heat flux (𝑞temp) can be given as follows:
𝑞temp= ( 𝑇𝑢𝑝−𝑇𝑑𝑜𝑤𝑛
𝑥sample⁄𝑘sample+𝑅) (3)
where x is the thickness and k is the thermal conductivity of a sample and the term R is the heat resistance factor that contributes from parts other than the sample.
It has been confirmed that this heat-transfer system reaches a quasi-steady state in a time as short as 20 s. As a consequence, the term 𝑞temp can be replaced by 𝑞ice. Now consider measurements of heat fluxes for two same samples with different thicknesses. The heat resistance factor is originated from the aluminum block, the two interfaces and the copper plate, and thus values of R should be the same with each other as long as the samples have the same surface roughness. Finally the thermal conductivity of the sample can be derived by the following equation:
(1 𝑞⁄ ice1− 1 𝑞⁄ ice2)−1= 𝑘sample∙𝑥 𝑇up−𝑇down
sample1−𝑥sample2 (4)
Samples and Measurements
To confirm the reliability of this new quasi-state hot plate method and to validate the applicability to mould flux, Ni-based super alloy (Inconel 600), alumina and PTFE (Teflon) with know thermal conductivity values were employed as samples; [9] silica glass sheets were also measured because SiO2 is a major component of mould flux [4]. Two samples with different thicknesses were prepared: 20×20×0.5 mm3 and 20×20×0.1 mm3 for Inconel; 20×20×0.5 mm3 and 20×20×0.2 mm3 for alumina and Teflon; 20×20×1.0 mm3 and 20×20×0.5 mm3 for silica glass. The surface
roughness was measured by a laser microscope at ten different places for each sample.
In experiment, silver paste or heat conductive grease was applied to both surfaces of a sample to reduce interfacial heat resistance, then the sample was placed upon the copper lid, and finally the heat source heated at 873 K was placed upon the sample at 100 s after the sample setting-up. The liquid height in the pipe was measured by a laser displacement meter where a plastic disc was placed on the water surface to make laser reflection stronger.
Figure 1. Schematic diagram of measurement apparatus. Figure 2. Conceptual diagram of simulation geometry.
Applicability to Mould Flux Film
In order to examine the applicability of the measurement to mould flux film, a two-dimensional model is used with COMSOL simulation software, as shown in Figure 2. The top rectangle is a heat source 20×10 mm2, the next rectangle is a block 20×10 mm2, which is placed between the heat source and the mould flux film to accommodate a thermocouple. The top two rectangles are made of aluminum. The next thin layer is a mould flux film 20×0.5 mm2, and the assumed composition of the mould flux film is shown in Table 1, which composition is typical of practical mould flux used in the continuous casting of steel. [4] The thermal conductivity value of this mould flux is 1.11 Wm-1K-1 at 573 K. [4] The bottom rectangle is a container 54×150 mm2, which is filled with an ice/water mixture. The container is sealed with a lid 54×1 mm2, which is made of copper. It should be noted that there are no fins and stirrer provided in this simulation system. The thermophysical properties of the materials except mould flux used were obtained from the COMSOL Multiphysics Material Library. [10] The whole system is governed by transient heat transport in each part is described by the following equation.
𝑑𝑧𝜌𝐶P𝜕𝑇
𝜕𝑡+ 𝑑𝑧𝜌𝐶P𝒖 ∙ 𝛻𝑇 + 𝛻 ∙ 𝒒 = 𝑑𝑧𝑄 + 𝑞0+ 𝑑𝑧𝑄ted (5) where 𝑑𝑧, 𝜌, 𝐶P, 𝑇, 𝒖 and 𝑄 denote the distance in z direction, density, specific heat,
temperature, fluid velocity and heat with respect to each part, respectively. In the simulation system, well-insulation, no fins and stirrer are considered so that convection and radiation are negligible in this system. Therefore, the heat flux 𝒒 is derived from the following:
𝒒 = −𝑑𝑧𝑘∇𝑇 (6)
The initial temperature of the heat source is set at 873.15 K, whereas the other parts are set at 273.15 K; the top boundary is in contact with air at 298.15 K. The boundary condition in the bottom contacted with the ice/water mixture is set at 273.15 K.
Table 1 Chemical compositions of the mould flux (wt.%) [4]
SiO2 CaO Al2O3 Na2O F C-free
34.4 33.0 6.1 13.4 8.1 2.9
Results and Discussion Thermal Conductivity of Silica Glass
Figure 3 shows the temperature changes (𝑇up and 𝑇down) with time obtained in experiments for silica glass samples. It can be seen that 𝑇up values increase significantly and rapidly just after the heat source is placed and then start to decrease after reaching the maxima. The maximum of 𝑇up for the thinner sample is higher than that for the thicker sample, which is because the thicker sample has larger thermal resistance. It is also noted that 𝑇down is not kept at 273.15 K, which might affect the thermal conductivity value. However, the increase in 𝑇down is less than 10 K.
Figure 4 shows the liquid height change with time obtained for the glass samples. It can be seen that the liquid height decreases slowly before the heat source is placed but drastically immediately after the heat source is placed and then slowly again.
Figure 5 compares values of 𝑞ice determined from the liquid height decrease via Eq. (2) for the glass samples. The values of 𝑞ice increase quickly at about 100 s, namely, just after the heat source is placed, and then decrease after reaching the maxima. There can be seen a difference between the values of 𝑞ice for the two samples with different thicknesses.
The results by a laser scanning microscope indicate that the same material samples with different thicknesses have almost the same average roughness values. Thus, Figure 6 is obtained on the basis of Eq. (4), showing the relation between the heat flux and the temperature difference for glass, using 𝑞ice data having the same value of (𝑇up - 𝑇down) in Figure 5. It is considered that before the calculation region the sample is just heated up by the heat source and the system has not yet reached a quasi-steady state. On the other hand, after the calculation region the temperature difference is too small for analysis. There can be seen a linear portion in Figure 6, which
corresponds to the data within the calculation region. The slope of the linearity provides the thermal conductivity of glass, and the intercept might be due to the heat loss but is small enough to be neglected. Table 2 gives the experimental values derived for the four kinds of sample with their standard deviations, along with the respective reported values. [9] The experimental scatter of thermal conductivity values is less than 5%, and all the experimental values are in good agreement with the reported values. Consequently, this apparatus can be applied to sheet samples with thermal conductivity ranging between 0.25 Wm-1K-1 and 30 Wm-1K-1.
Figure 3. Change with time in temperatures for silica. Figure 4. Change with time in liquid height for silica.
Figure 5. Comparison between heat flux changes with time for silica. Figure 6. Plots based upon Eq.(5) for silica.
Table 2 Experimental thermal conductivities in comparison with reported data
Literature Data (Wm-1K-1) [9] Experimental Data (Wm-1K-1)
Inconel 14.8 14.7±0.4
Alumina 23-30 24.8±0.7
Teflon 0.25 0.313±0.04
Silica 1.38 1.34±0.03
Applicability of the present method to thermal conductivity measurements of oxide scales Figure 7 shows the heat flux changes in the block and the mixture (𝑞block and 𝑞ice) with time,
0 200 400 600 800
300 350
400 Tup (silica glass 1.0 mm) Tdown (silica glass 1.0 mm) Tup (silica glass 0.5 mm) Tdown (silica glass 0.5 mm)
t / s
T / K
where the negative sign means that heat flows downwards. The numerical results predict that heat is mainly transferred from the heat source to the ice/water mixture across the sample and 𝑞block equals 𝑞ice in 20 s, indicating that the system approaches a quasi-steady state in 20 s. Figure 8 shows temperatures of 𝑇up and 𝑇down as a function of time. It can be seen that 𝑇up and 𝑇down increase first and reach the maxima and then start to decrease. These tendencies are the same as obtained in the present work. However, it should be noted that the maximum of 𝑇up is 550 K when the calculation time region starts, and the steepest temperature gradient is only 160 Kmm-1. A heat source with higher temperature should be applied if the temperature gradient close to that in the actual mould flux is required. It should also be noted that 𝑇down increases by about 140 K, which is greater than the increase of 𝑇down obtained for the present work. Thus, another key factor to apply the present method to mould flux at higher temperatures is to control the temperature of the ice/water mixture as close to 273.15 K as possible by optimizing the fin design.
In addition, as mentioned above, the simulation system provides no fins, the use of which would be of help to improve this situation.
According to the above, it has been confirmed that the present method can be applied to mould flux film. However, there is a key factor to prepare mould flux films with different thicknesses in the range 0.5 – 1.0 mm and with the same surface roughness; and the measurement system should be improved in the following aspects: (i) the increase in the initial temperature of heat source, (ii) the use of high heat capacity material as heat source and (iii) the increase in the mass of heat source.
Figure 7. Change with time in heat flux in 0 ~50 s. Figure 8 Change with time in temperatures of Tup and Tdown
Conclusions
A new quasi-steady state hot plate method has been developed and the procedure to derive the thermal conductivity has also been established for future measurements of apparent thermal conductivities of mould flux film.
The method proposed has been applied to sheet samples of Inconel, alumina, Teflon, and silica glass, and the thermal conductivity values have been obtained as 14.7 ± 0.4 Wm-1K-1 for Inconel
at 281 K – 287 K, 24.8 ± 0.7 Wm-1K-1 for alumina at 281 K – 287 K, 0.313 ± 0.004 Wm-1K-1 for Teflon at 286 K - 412 K, and 1.34 ± 0.03 Wm-1K-1 for glass at 293 K – 303 K under a temperature gradient of 20 Kmm-1, which results are in good agreement with the respective reported values.
Simulation study has also been made to discuss the applicability of the present method to mould flux film at higher temperature under a steeper temperature gradient and concludes that the method would be applicable to the mould flux.
ACKNOWLEDGEMENTS
Parts of this paper have been reprinted from the article ‘ISIJ Int., 56 (2016), p366-p375’, by permission of the Iron and Steel Institute of Japan.
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