ISIJ International, Vol. 58 (2018), ISIJ International, No. 5 Vol. 58 (2018), No. 5, pp

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1 ISIJ International, Vol. 58 (2018), ISIJ International, No. 5 Vol. 58 (2018), No. 5, pp Mechanism of Mil Cooling by Crystallisation of Moul Flux for Continuous Casting of Steel - A View from Apparent Thermal Conuctivity uner Steep Temperature Graient - Shunsuke TAKAHASHI, 1) Rie ENDO, 2) Takashi WATANABE, 2) Miyuki HAYASHI 2) an Masahiro SUSA 2) * 1) Department of Metallurgy an Ceramics Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan. 2) Department of Materials Science an Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan. (Receive on November 9, 2017; accepte on January 16, 2018) Effects of crystallisation on heat transfer across soli moul fluxes have been examine on the basis of apparent thermal conuctivities incluing raiative contribution. The apparent thermal conuctivities were measure on glassy an crystallise moul flux samples uner steep temperature graients using a parallel plate metho improve in the present work. Both surfaces of the samples were coate with silver paste to reuce contact thermal resistance. Thermal resistance except the sample itself was experimentally etermine to be m 2 KW 1 base upon measurements on Inconel 600. To confirm the reasonableness of this value, the metho was applie to fuse silica. Apparent thermal conuctivities were in goo agreement with reporte values. Apparent thermal conuctivities of moul fluxes were measure up to 900 C at the high temperature sie of the sample. The thermal conuctivity of the glassy sample was 1.25 Wm 1 K 1 below 300 C in the central temperature (T c ) of the sample, an was lower than those of the crystallise samples. With increasing egree of crystallinity, the thermal conuctivities increase aroun room temperature. Samples with higher egrees of crystallinity showe negative temperature epenence more remarkably an resultantly were close to that of the glassy sample where T c ~ C. Where T c > 500 C, the thermal conuctivity of the glassy sample was 1.54 Wm 1 K 1 an was greater than that of a crystallise sample, 1.32 Wm 1 K 1, which woul be ue to the raiation. Apparent thermal conuctivity at a practical temperature has also been estimate, which suggests that crystallisation enables raiative thermal conuctivity to be reuce. KEY WORDS: moul flux; continuous casting; mil cooling; thermal conuctivity; temperature graient; raiative heat transfer; crystallisation. 1. Introuction High-spee continuous casting is one of key technologies for improvements of steel prouctivity. Very fast casting, however, brings about surface efects calle longituinal cracking, especially for meium carbon (MC) peritectic steel. 1 3) Longituinal cracking is suppose to be ue to thermal stresses in the steel shell resulting from non-uniform soliification shrinkage uring the δ γ transformation occurring at the initial soliification stage. 4) To minimise suchlike efects, it is necessary to control the heat transfer across moul flux film ~ 1 mm thick consisting of liqui, partially crystallise an glassy layers, existing between the steel shell an the moul. For example, Kanazawa et al. 5) have reporte that the steel stran can be coole uniformly when the extracte heat flux is lower than about Wm 2. The cooling rate epens on the thermo-physical properties of the flux film an, thus, uniform cooling can * Corresponing author: susa.m.aa@m.titech.ac.jp DOI: be achieve by esigning moul flux compositions for mil cooling (or moerate cooling). In practice, moul flux is esigne to be partially crystallise, an thereby the heat transfer is reuce, leaing to improvement in homogeneity of soliification. 2,3,6) Thus, it is important to know how crystallisation of moul flux reuces the heat transfer for further improvements of moul flux. Against this backgroun, unerstaning of the mechanism of heat transfer reuction by crystallisation of moul flux has been one of the most commonly applie subjects in the research fiel on continuous casting. 7,8) The propositions in the previous stuies roughly fall into the following two mechanisms: (i) Reuction of raiative heat transfer by scattering: the crystal grains introuce by crystallisation scatter the raiation emitte from the steel shell an reuces raiative heat transfer. (ii) Reuction of conuctive heat transfer by an air gap: crystallisation introuces an air gap between the flux an the moul, which increases interfacial thermal resistance an reuces conuctive heat transfer ISIJ

2 With respect to the mechanism (i) - raiative heat transfer reuction -, Nakaa et al. 9) have reporte a heat transfer moel incluing the optical process, in which moel part of raiative energy emitte from steel shell is assume to be reflecte by crystalline phases in moul flux an returne to the steel again. This moel has further been progresse by some of the present authors, who have shown the possibilities of reucing raiative heat flux by (a) increasing the egree of crystallinity, 10 13) (b) ecreasing the iron oxie concentration, 11) (c) ajusting the crystalline grain sizes in 2 3 μm 14) an () increasing the concentration ratio of Fe 3+ /Fe 2+ in crystallise moul fluxes. 12) In these stuies, however, values of raiative heat flux have been estimate on the basis of a simple optical process moel using optical characteristic ata such as reflectivity an transmissivity measure at room temperature only. It is more important in practice to know how crystallisation of moul flux reuces the total heat flux incluing conuctive heat flux uner a temperature graient as steep as ~ K/mm forme in actual moul flux film. In contrast, there have been several stuies to attempt to evaluate the apparent thermal conuctivity or resistance incluing both conuctive an raiative contributions uner steep temperature graients ) For example, Yamauchi et al. 16) have measure to compare thermal resistances of moul fluxes with ifferent egrees of crystallinity using the parallel plate metho. They have reporte that raiative heat flux can be reuce by crystallisation, where the iscussion has been mae on the total heat resistance incluing the contributions from the air gap an the liqui phase. Accoringly, it is still uncertain whether crystallise moul flux itself reuces the total heat transfer. On the other han, Watanabe et al. 22) have ippe a water-coole copper sheet in a flux melt to conuct heat transfer analysis an surface observation. They have reporte that crystallisation increases surface roughness of moul flux, suggesting that mechanism (ii) - conuctive heat transfer reuction - is more preominant. In aition, Tsutsumi et al. 23) have measure surface roughnesses of glassy an crystalline flux samples prepare at various cooling rates an shown that more crystallise samples have rougher surfaces, suggesting that crystallisation reuces conuctive heat flux ue to the air gap on the basis of a moel calculation. As mentione above, the presence of the air gap has been suggeste experimentally; on the contrary, there is a report which oubts whether or not the air gap is forme uner static pressure exerte onto the moul flux film from the molten steel. 3) As escribe above, there have been many stuies which propose mechanisms (i) an/or (ii); however, further verification shoul be conucte on each stuy experimentally as well as theoretically. Hence, it is very important to remin: - Moul flux film is a very complex system consisting of three layers, i.e., basically liqui, partially crystallise an glassy layers; in aition, an air gap may join. - The total moul flux system is roughly 1 mm thick an exists uner a temperature graient as steep as ~ K/mm. Thus, it is very ifficult to examine how crystallisation reuces the total heat flux in experimental conitions which reprouce practical conitions satisfactorily. On the other han, there is also a fact that the partially crystallise layer comprises the major part of moul flux film. 2,4,5,16,18) As a first step, accoringly, it is strongly require to unerstan how crystallisation reuces the total heat flux across the partially crystallise layer, i.e., a soli flux layer uner steep temperature graients. Consequently, the present work focuses on the apparent thermal conuctivity of the soli flux layer only an aims: - to evelop an apparatus measuring the apparent thermal conuctivity of soli moul flux uner steep temperature graients, - to measure the apparent thermal conuctivity of soli moul flux as a function of egree of crystallinity, an finally - to propose a mechanism of how crystallisation reuces the total heat flux across soli moul flux film, from the perspectives of raiative an conuctive contributions. 2. Experimental 2.1. Apparatus an Principle Figure 1 shows a schematic iagram of the apparatus evelope in the present work for apparent thermal conuctivity measurement base on the parallel plate metho. A plate sample is sanwiche between two stainless (SUS304) plates. The lower stainless plate is place on a Ni-base super alloy (Inconel 600) plate 1 mm thick, which, in turn, is supporte by alumina ros (φ 6 mm). There are five rotype heating elements of SiC place about 30 mm below the alumina ros. The upper stainless plate has three holes for cooling water, each of which is solere to a stainless (SUS304) tube for water supply. There are also seven holes (10 mm in epth an 1 mm in iameter) in the two stainless plates as shown in Fig. 1, to measure temperatures at positions 1 7 (T 1 T 7, respectively) using K type thermocouples of 1 mm in iameter. On both surfaces of the sample, silver paste is applie to ecrease the contact thermal resistance. Figure 2 shows a schematic iagram of the temperature istribution along positions 2, 5 an 7. Where the system is in the steay state, the thermal resistance (R) between positions 5 an 7 is escribe as follows. R T 7 T 5 1 sample = = ri rii + q SUS sample 2 SUS... (1) where q is the heat flux, 1 is the istance (2.44 mm) from Fig. 1. Schematic iagram of experimental apparatus. (Online version in color.) 2018 ISIJ 906

3 Table 1. Chemical composition of moul flux sample (mass%). Basicity Contents CaO/SiO 2 SiO 2 CaO Al 2O 3 MgO Na 2O F Fig. 2. Schematic iagram of temperature istribution through positions 2, 5 an 7. (Online version in color.) position 7 to interface I, sample is the thickness of the sample, 2 is the istance (1.70 mm) from position 5 to interface II, λ sample an λ SUS are the thermal conuctivities of the sample an the stainless plate, respectively, an r I an r II are the contact thermal resistances at interfaces I an II, respectively. In this equation, ( 1 /λ sus ), r I, r II an ( 2 /λ sus ) are assume to be constants which epen on the apparatus, the reasonableness of which is iscusse later. Thus, Eq. (1) is simplifie as follows. sample R Rc... (2) sample where R c is the sum of the constant terms. Accoring to Eq. (2), R is in linear proportion to sample, an the graient of the linearity is the reciprocal of λ sample. Thus, the value of λ sample can be etermine by obtaining R for the same samples having ifferent thicknesses. The value of R can be erive from Eq. (1) in case the value of q is known. The value of q can be erive using temperatures T 2 an T 5 measure, on the basis of Fourier s law in the following. T 5 SUS T T2 q... (3) where 3 is the istance (4.79 mm) between positions 2 an 5, an λ SUS is consiere to be a function of temperature as follows SUS K K T T (4) Equation (4) is an approximate equation of reporte values for SUS304, 24) where T K is thermoynamic temperature in K, an can be applie in the temperature range between 60 C an 700 C Samples Samples use in the present work were Inconel 600, fuse silica, glassy moul flux an crystallise moul flux. Inconel 600 samples were use for etermining R c in Eq. (2). The imension of Inconel samples was mm 2 an the thickness was in the range of 1 5 mm. Fuse silica was use to confirm the accuracy of the apparatus as well as the reasonableness of the metho because there have been many reports 25 28) for its thermal conuctivity an the value is close to that of moul flux. The imension of fuse silica samples was the same as those of Inconel samples. Moul flux samples were mae so as to have the chemical compositions given in Table 1. Reagent powers of Al 2 O 3, MgO, Na 2 CO 3, CaF 2, CaO an SiO 2 were weighe so as to have esire compositions an mixe in an alumina motor, where CaO was prepare by thermal ecomposition of CaCO 3 reagent powers at C for 12 h. The mixe powers were melte in a platinum crucible in air at C for 300 s. The melt was cast into a brass moul size mm 3 to obtain homogeneous glassy samples. Some of the glassy samples were crystallise by heat treatment at 530 C, 550 C, 600 C, 660 C, 700 C, 800 C an 900 C in air for 10 h at T t 600 C an 2 h at 660 C T t, where T t represents the heat treatment temperature. The heat treatment time was ecie from the progress of crystallisation observe in preliminary experiments. The crystallise samples were analyse by scanning electron microscopy (SEM), an the egree of crystallinity was erive as the ratio of the area of the crystalline part to the total area using SEM images assuming that the sample is macroscopically uniform. The crystalline phases were ientifie by an electron probe micro analyser (EPMA) an X-ray iffraction (XRD) analysis. Moul flux samples were thinne to esire thicknesses (1 5 mm) by polishing both surfaces of the samples after each measurement was finishe Experimental Proceure The surfaces of the stainless plates, Inconel 600 samples an moul flux samples were polishe with emery papers up to #2000. The fuse silica samples were not polishe because the surfaces were smooth enough. Silver paste was applie onto both sies of the samples, an each sample was sanwiche in between the stainless plates. The silver paste was rie at room temperature for more than 2 h, after which thermocouples were inserte into the holes at positions 1 7, an water cooling as well as heating was starte. The water flow rate was fixe at 8.33 cm 3 s 1 i.e cm s 1 in each tube. The temperatures were recore every 5 s by a igital multimeter connecte with a PC. The sample was heate so that T 7 reache a esire temperature to obtain a steay state. Table 2 shows the range of T 7 applie to each sample. The maximum temperature of T 7 for crystallise samples was basically lower than T t to prevent further crystallisation of the samples uring the measurements; however, for the sample with T t = 660 C as well as the glassy sample, measurements were also taken at T 7 = 900 C. After the measurements, values of R were calculate from temperatures T 2, T 5 an T 7 measure to obtain apparent thermal conuctivities. Aitional experiments were also conucte to confirm the effect of silver paste. A fuse silica 2 mm thick was use as a sample, an silver paste was applie onto interface I only or onto both interfaces I an II, the latter conition being employe in the present work. The measurements were conucte for T 7 = 100 C an the values of R were calculate from the results ISIJ

4 Table 2. Range of T 7 for each sample. Sample (T t/ C) T 7/ C Inconel Silica glass Glassy flux , 900 Crystallise flux (530) Crystallise flux (550) Crystallise flux (660) , 900 Crystallise flux (800) Fig. 3. Temperature history for measurement on 3 mm-thick fuse silica sample. (Online version in color.) 3. Results an Discussion 3.1. Establishment of Experimental Conitions Confirmation of Steay State an Temperature Distribution in the Apparatus Figure 3 shows the temperature history use in a measurement for a fuse silica sample 3 mm thick. Temperatures T 1 T 7 are roughly constant in the time perios s an s, where T 7 = 800 C an 900 C were taken as esire temperatures, respectively. This figure confirms that steay states can be achieve in the present experimental apparatus. Figure 4 shows average temperatures of T 1 T 7 recore in the time perio s in Fig. 3 against istance. The horizontal temperature istribution is almost uniform although temperatures T 1 an T 4 are higher by about 16 C than the two corresponing temperatures. This result guarantees at least that there is no heat loss from the central part of the stainless plate to the outer part. In aition, the horizontal temperature graient is about 1.6 K/mm, whereas the vertical temperature graient is about 20.4 K/mm in the water-coole stainless plate. Comparison between these values suggests that the horizontal temperature istribution oes not consierably affect the etermination of heat flux Effect of Silver Paste Coating Figure 5 shows changes with time in R measure for two fuse silica samples 2 mm thick uner the conition of T 7 = 100 C: in one sample silver paste was applie only onto interface I (case 1), an in the other onto interfaces I an II (case 2). The average value of R an its stanar eviation are erive using the ata recore in the time perio s as (2.08 ± 0.65) 10 3 m 2 KW 1 for case 1 an (1.56 ± 0.02) 10 3 m 2 KW 1 for case 2. The value of R in case 2 becomes smaller an its uncertainty also ecreases. The ifference of R in these two cases is m 2 KW 1, which is roughly the same as reporte values of contact thermal resistance ue to an air gap ,20) As a consequence of this, silver paste was applie to both interfaces in the present work, except for this section Determination of Value of R c The value of R c is erive on the basis of Eq. (2): there is linearity between R an sample thickness, an the slope of the linearity is the reciprocal of thermal conuctivity an its intercept is the value of R c. Accoringly, values of R measure for Inconel samples are plotte against sample thickness ( Inconel ) to erive thermal conuctivity. Now a Fig. 4. Temperature istributions in sample an stainless plates recore in measurement on 3 mm-thick fuse silica sample where T 7 = 900 C. Fig. 5. Effect of silver paste on values of R for fuse silica sample 2 mm thick (T 7 = 100 C): silver paste was applie onto one interface only in case 1 an onto two interfaces in case 2. (Online version in color.) ifficulty is encountere with, that is, the thermal conuctivity of Inconel ecreases with increasing temperature an thereby is ifferent from position to position in the present sample with a consierable temperature graient. Thermal conuctivity iscusse in the present work is apparent thermal conuctivity of a sample uner a temperature graient, an thus the representative temperature of the sample is ecie to avoi this ifficulty. Hence, the temperature at the centre of the sample (T c ) is taken as the representative for convenience an is erive as an average of temperatures at interfaces I an II (T I an T II ), which in turn are erive from Eq. (5) using measure temperatures of T 5 an T 7, heat flux q an λ SUS as a function of temperature given by Eq. (4), where the presence of r I an r II is neglecte ISIJ 908

5 q T7 SUS TI T TII SUS T5 1 2 T... (5) Figure 6 shows values of R measure for Inconel samples in the range of C in T 7 against sample thickness, where measure values of T 5 were roughly constant an their stanar eviations were within ± 5% for each T 7, irrespective of sample thickness. The straight lines in this figure have been rawn by the metho of least squares so as to have slopes erive from reporte thermal conuctivity values of Inconel at T c. 29) There seem reasonable agreements between the experimental ata an the straight lines, except for a few ata. The slope ecreases progressively with increasing temperature, which reflects that the thermal conuctivity of Inconel has positive temperature coefficients. On the contrary, the intercept has no systematic change with temperature. The average an stanar eviation of the intercept (R c ) are erive as (2.27 ± 0.37) 10 4 m 2 KW 1. First, focus on the average value of R c. The term of R c consists of terms ( 1 /λ sus ), r I, r II an ( 2 /λ sus ) from comparison between Eqs. (1) an (2). Here the terms of ( 1 /λ sus ) an ( 2 /λ sus ) can be calculate using the experimental conitions an reporte thermal conuctivity values of SUS304, 23) an the sum has been erive as (2.29 ± 0.24) 10 4 m 2 KW 1. Comparison with the value of R c inicates that thermal resistance ue to the stainless plates ominates the value of R c within experimental uncertainty, which supports that the neglect of terms r I an r II is reasonable in the above iscussion on erivation of T c. Secon, focus on the stanar eviation of R c, m 2 WK 1. This magnitue may be consierable in the values of R measure for Inconel. As can be seen from Fig. 5, however, the values of R measure for silica are aroun m 2 WK 1, which is about two orers of magnitue greater than the stanar eviation of R c. In aition, the thermal conuctivity of silica is expecte to be almost equal or greater than that of moul flux. 7,9,10,15 17,19,20) Accoringly, the neglect of the uncertainty in R c woul not cause large error in the etermination of thermal conuctivity of moul flux because it may have greater thermal resistance. As a consequence of this, the value of R c has been etermine to be m 2 KW 1 in the present work. samples against sample thickness ( silica ). The values of R increase with increasing sample thickness at each T 7. The linearity seems better in ata obtaine at lower temperatures; in contrast, ata at higher temperatures seem to fall on convex curves. Nevertheless, the metho of least squares has been applie to these ata so as to pass the intercept, R c = m 2 KW 1 etermine in the above. From the slopes of the straight lines obtaine, thermal conuctivities of fuse silica samples (λ silica ) are calculate via Eq. (2). Figure 8 shows the thermal conuctivity of fuse silica as a function of T c. The values measure in the present work exhibit almost the same tren as reporte values 26 28) in the temperature range up to 350 C, above which the measure values increase with increasing temperature an show goo agreement with values reporte by Kingery 26) an Sugawara, 27) who have given comments that their values contain raiative contribution. Thus, the values of thermal conuctivity measure in the present work may also contain raiative contribution, which will be correcte in the following. Now it is assume that the value of q erive from Eq. (3) consists of conuctive (q conuctive ) an raiative (q raiative ) heat fluxes. q qconuctive qraiative... (6) The raiative heat flux can be estimate from Eq. (7) 9,19,30) Fig. 7. Values of R measure for fuse silica samples. (Online version in color.) 3.2. Thermal Conuctivity of Fuse Silica Figure 7 shows values of R measure for fuse silica Fig. 6. Values of R measure for Inconel samples against sample thickness. (Online version in color.) Fig. 8. Thermal conuctivities for fuse silica samples in comparison with reporte values; Wray an Connolly 25) by steay-state hot wire metho, Kingery 26) by spheroial envelop metho an parallel plate metho, Sugawara 27) by parallel plate metho an Abulagatov 28) by parallel plate metho. (Online version in color.) ISIJ

6 q raiative 2 n TI 4 TII 4... (7) silica I II where n an α are the refractive inex an absorption coefficient of fuse silica, respectively, σ is the Stefan- Boltzmann constant ( Wm 2 K 4 ), ε I an ε II are the emissivities at interfaces I an II. The value of refractive inex has been reporte to be ) for a wavelength range μm an a temperature range C, an the value of α to be higher than ~ 100 m 1 32) above room temperature for a wavelength of 2.5 μm which correspons to the wavelength of the strongest raiation at 900 C preicte from Wien s isplacement law. In aition, an emissivity value of silver paste of ) is employe as the emissivities at interfaces I an II. This value has been use for temperatures between 300 C an 600 C in the literature. Figure 9 shows heat fluxes q, q raiative an q conuctive across the fuse silica samples against sample thickness, where q has been obtaine in the measurement for T 7 = 900 C (T I = C an T II = C, epening on silica ), q raiative has been erive from Eq. (7), an q conuctive has been erive from Eq. (6) using q an q raiative. The value of q raiative is roughly Wm 2, irrespective of sample thickness, because the value of α for fuse silica is as small as 100 m 1. On the other han, the value of q ecreases with increasing sample thickness; as a result, the raiative contribution is relatively greater in thicker samples. This woul account for the ata at higher temperatures in Fig. 7 falling on convex curves. Now the value of q conuctive is use for Eq. (2) to correct thermal conuctivity values of the fuse silica samples. Figure 8 also inclues correcte thermal conuctivity values of the fuse silica samples, which show little temperature epenence at higher temperatures an are in goo agreement with reporte values without raiative contribution. 25) Thus, it has been confirme that the increase in thermal conuctivity of the fuse silica samples above 350 C is ue to raiative contribution an, in other wors, that the present measurement metho prouces the apparent thermal conuctivity incluing the effect of raiation. of crystallise moul flux samples. The types of precipitate vary epening on the heat treatment temperature for crystallisation. Crystal phases were analyse by EPMA an XRD resulting in: at 530 C, only CaF 2 precipitates, cuspiine (3CaO 2SiO 2 CaF 2 ) also appears at 550 C an 600 C, above which Na 2 O 2CaO 2SiO 2 is also observe. The brightness of the phase in the figure is in the orer; CaF 2 > Cuspiine > Na 2 O 2CaO 2SiO 2 > glassy phase. The shape an imension of crystalline phases also epen on temperature. It is note that the crystalline phases are uniformly isperse across the sample. Figure 11 shows the percentages of crystalline phases in the moul flux samples. All the samples contain about 1 vol% CaF 2. The percentage of cuspiine excees 60 vol% at 550 C an 600 C but ecreases to 50 vol% at higher temperatures. In contrast, the percentage of Na 2 O 2CaO 2SiO 2 lies aroun vol% above 700 C. The total percentage of all the crystalline phases is calle the egree of crystallinity in the present work Characterization of Moul Flux Samples Figure 10 shows backscattere electron (BE) images Fig. 9. Total (q), conuctive (q conuctive) an raiative (q raiative) heat fluxes for fuse silica with T 7 = 900 C against silica thickness. Fig. 10. Backscattere electron images of crystallise moul flux samples ISIJ 910

7 Fig. 11. Percentages of crystalline phases in samples. (Online version in color.) Fig. 12. Values of R measure for glassy an crystallise moul flux samples. (Online version in color.) 3.4. Thermal Conuctivity of Moul Flux Samples Thermal Conuctivity in the Range of 0 C < T c < 500 C Figure 12 shows values of R measure for glassy an crystallise moul flux samples, for the latter, heat treatment for crystallisation being conucte at T t = 660 C. The values of R for the glassy sample represente by ashe lines o not epen on temperature T 7 very much. In contrast, the values of R for the crystallise samples represente by soli lines increase more remarkably with increasing temperature T 7. Figure 13 shows apparent thermal conuctivity values (λ flux ) etermine for moul flux samples as functions of T c, where the percentage given represents the egree of crystallinity of each sample. It has been confirme that there are no changes in microstructure observe in the samples before an after the measurements at temperatures of T c < 500 C. The thermal conuctivity of the glassy sample is 1.25 Wm 1 K 1, almost inepenent of temperature, which is close to the feature of the thermal conuctivity of fuse silica shown in Fig. 8. The slight increase of thermal conuctivity aroun 350 C woul arise from raiative contribution. With increasing egree of crystallinity, the thermal conuctivity tens to increase at lower temperatures. In aition, the thermal conuctivities of crystallise moul fluxes ecrease with increasing temperature. These trens are too complicate to explain at the moment. In simple theory of soli state physics, thermal conuctivity of insulating materials (λ) is expresse as 1 Cvl... (8) 3 where C, v an l represent the specific heat per unit volume, the spee of soun an the mean free path of phonons, respectively. However, there is no enough information on C, v an l for moul flux for further iscussion. Nevertheless, it is suppose that the increase in thermal conuctivity with crystallisation is relevant to the increase in l ue to structural orering. In aition, the value of l for crystalline insulating materials generally ecreases accoring to a function of T 1 with increasing temperature ue to enhance phonon scattering. This woul be relevant to the ecrease in thermal conuctivity at higher temperatures observe in the samples with higher egrees of crystallinity. Fig. 13. Apparent thermal conuctivities measure for glassy an crystallise moul flux samples. (Online version in color.) Thermal Conuctivity in the Range of 500 C T c < 600 C Figure 13 also inclues ata marke by (A) an (B). These samples (A) an (B) use to be, respectively, a glassy sample an a crystallise sample with a egree of crystallinity of 84 vol%, the latter being heat-treate at T t = 660 C. It shoul be note that the thermal conuctivity of glassy sample (A) is greater than that of crystallise sample (B). Furthermore, it is also note that, in the measurements at T c = 550 C which correspons to T 7 = 900 C, parts of the samples were structurally change. Figure 14 shows crosssectional views of samples (A) an (B) after the measurements. Sample (A) is also crystallise in the portion expose to higher temperatures. Sample (B) looks unchange before an after the measurement; in actuality, there is a change in microstructure in the portion expose to higher temperatures, which microstructure correspons to those shown in Fig. 10. Apparent thermal conuctivities of these samples shown in Fig. 13 were etermine from the temperatures in steay states an shoul be equal to values of the samples after the structural changes. Inspection of Fig. 13 inicates that sample (A) has a larger thermal conuctivity than sample (B). This result, however, is inconsistent with a common view that thermal conuctivity of glassy substance is smaller than that of crystalline substance. This woul be because there is raiative contribution to the thermal conuctivity values of samples (A) an (B) measure at T 7 = 900 C, as ISIJ

8 Fig. 14. Cross-sectional views of samples after measurements at T 7 = 900 C, (A) glassy sample 5 mm thick an (B) crystallise sample 5 mm thick where T t = 660 C. (Online version in color.) Fig. 15. Thermal conuctivities of crystallise moul flux samples as functions of T c 1. (Online version in color.) seen for fuse silica at T c > 350 C. To examine the above inconsistency, conuctive an raiative contributions to the thermal conuctivities of samples (A) an (B) are examine as follows. First, thermal conuctivities without the effect of raiation (λ conuctive ) are estimate for samples (A) an (B) on the basis of the temperature epenence escribe in 3.4.1: thermal conuctivity of the glassy sample is roughly constant, irrespective of temperature, whereas thermal conuctivity of the crystallise samples ecreases with increasing temperature an, in theory, is in proportion to a function of T 1. Figure 15 shows apparent thermal conuctivities of the crystallise moul fluxes against T 1, in which the ata measure in the range of T c < 350 C are use where raiative contribution is negligibly small accoring to the result on fuse silica. There is goo linearity obtaine for each sample, an the slope is greater with increasing egree of crystallinity. This figure is use for the following iscussion. Figure 16 shows estimate temperature istributions in samples (A) an (B). Sample (A) is compose of glassy an crystallise layers which woul have ifferent thermal conuctivities. The temperature (T g/c ) at the interface between glassy an crystallise layers is assume to be 540 C because it is the lowest temperature at which cuspiine precipitates in the sample, as shown in Fig. 11. The mile temperatures (T m ) in the glassy an crystallise layers are estimate to be 413 C an 695 C, respectively, by taking the average of T I, T g/c an T II. The thermal conuctivity (λ conuctive-g ) of glassy layer is 1.25 Wm 1 K 1 at 413 C, as shown in Fig. 13. On the other han, the crystallise layer is assume to have the egree of crystallinity in the range of 80 90% from Fig. 11. Hence, the thermal conuctivity (λ conuctive-c ) is estimate to be 1.12 Wm 1 K 1 at T c = 695 C by averaging the values erive from Fig. 15 for crystallise samples with egrees of crystallinity of 84% an 86% at T c 1 = K 1. Using these values of λ conuctive-g an λ conuctive-c, the thermal conuctivity (λ conuctive ) of the entire sample (A) is calculate to be 1.19 Wm 1 K 1 from Eq. (9). conuctive fluxconuctivecconuctiveg gconuctivec c conuctive g... (9) which has been erive from a preictive equation of ther- Fig. 16. Schematic iagrams of temperature istribution in samples (A) an (B). mal conuctivity for composite material as follows: flux c g...(9 ) conuctive conuctivec conuctive g On the other han, T c of sample (B) is ca. 577 C an its thermal conuctivity is estimate to be 1.18 Wm 1 K 1 by averaging the values erive from Fig. 15 for crystallise samples with egrees of crystallinity of 84% an 86% at 1 T c = K 1. Secon, the raiative conuctivity (λ raiative ) is estimate from Eq. (10). flux raiative q raiative... (10) TI T II where q raiative is etermine from Eq. (7) assuming that samples (A) an (B) are homogeneous, where flux is use instea of silica. The refractive inices for samples (A) an (B) are assume to be ) an 1.59, 9) respectively. In aition, the apparent absorption coefficient of sample B (α B ) is assume to be m 1. 11) For sample (A), the transmissivity of the entire sample is assume to be etermine by the prouct between the transmissivities of crystallise an glassy layers, on which assumption the apparent absorption coefficient (α A ) is estimate from Eqs. (11) or (11 ) base on Lambert-Beer s law. expafluxexpccexp g g... (11) 2018 ISIJ 912

9 A c c g g flux... (11 ) where subscripts c an g represent crystallise an glassy layers, respectively. The apparent absorption coefficient (α A ) is erive as 521 m 1 using reporte values of α c (1 000 m 1 ) 11) an α g (100 m 1 ). 11) Finally, the apparent thermal conuctivity (λ flux ) incluing both conuctive an raiative contributions is calculate from Eq. (12). flux conuctive raiative... (12) Figure 17 compares between measure an calculate apparent thermal conuctivities for sample (A) an (B) an shows that there is goo agreement between them. It can also be seen that λ conuctive for sample (B) is roughly the same as for sample (A); meanwhile, the value of λ raiative for sample (B) is about a half of that of λ raiative for sample (A). As a consequence of this, the apparent thermal conuctivity of sample (B) is smaller than that of sample (A). This fining suggests that the reuction in raiative heat flux across the moul flux film contributes to mil cooling by crystallisaiton as well as the formation of an air gap Estimation of Thermal Conuctivities at Practical Temperature In the present work, the measurement of apparent thermal Fig. 17. Measure an calculate apparent thermal conuctivities of samples (A) an (B) along with conuctive an raiative contributions. conuctivity was conucte in the temperature range of 0 C < T c < 600 C which correspons to 100 C < T 7 < 900 C. Moul fluxes, however, are use at higher temperatures in actual operations where raiative contribution is expecte to be greater. In this section, apparent thermal conuctivities are calculate for moul fluxes at practical temperature above the present measurement temperature, an thereby raiative contribution to the thermal conuctivity is examine. Figure 18 shows schematic iagrams of three types of moul flux moel consiere here, which are name moels (A ), (A ) an (B ). The following assumptions are mae: - Moel (A ) is glassy across the entire flux film. Moel (A ) consists of glassy an crystallise layers with the same thickness, i.e. c = g, similar to sample (A). Moel (B ) is crystallise across the entire flux film. - All the moels have the same thicknesses of 2 mm. - Temperatures (T I an T II ) at both surfaces are C 9,10,14) an 227 C, 9) respectively. For these moels, values of λ conuctive an λ raiative are estimate as follows. The value of λ conuctive of moel (A ) is 1.25 Wm 1 K 1, irrespective of temperature. For moel (A ), T g/c is estimate to be 877 C assuming linear temperature graient. Temperature T m for the crystallise layer of moel (A ) is C. Hence, the value of λ conuctive-c is estimate to be 0.97 Wm 1 K 1 from Fig. 15. In contrast, the value of λ conuctive-g is 1.25 Wm 1 K 1, an thereby the value of λ conuctive for the entire moel (A ) is erive as 1.09 Wm 1 K 1 from Eq. (9). In aition, T c for moel (B ) is 877 C, an its value of λ conuctive is estimate to be 1.05 Wm 1 K 1 from Fig. 15. On the other han, values of λ raiative for moels (A ), (A ) an (B ) are estimate from Eq. (10), where raiative heat fluxes are calculate from Eq. (7). The apparent absorption coefficients of moels (A ), (A ) an (B ) are assume to be 100 m 1, 11) 550 m 1 an m 1, 11) respectively, where the value for moel (A ) has been estimate from Eq. (11) using values of α c = m 1 an α g = 100 m 1 in the same manner as in The refractive inices for moels (A ), (A ) an (B ) are assume to be 1.57, 7) 1.58 an 1.59, 9) respectively. Using these parameters, raiative conuctivities for moels (A ), (A ) an (B ) are erive as 0.61 Wm 1 K 1, 0.52 Wm 1 K 1 an 0.46 Wm 1 K 1, Fig. 18. Schematic iagrams of three types of moel for moul flux film where practical temperature istribution is assume ISIJ

10 Fig. 19. Apparent thermal conuctivities for moels (A ), (A ) an (B ) along with conuctive an raiative contributions. respectively. Figure 19 shows the values of λ flux consisting of the values of λ conuctive an λ raiative for the three moels in the above. Comparison between the values for the three moels inicates that the value of λ flux is the smallest in moel (B ) which has the highest egree of crystallisation. Thus, crystallisation is effective for mil cooling at practical temperature as well. At this temperature, the value of λ raiative for moel (B ) is the smallest; in aition, the value of λ conuctive is also the smallest by crystallisation, which is probably ue to negative temperature epenence of thermal conuctivity for crystalline substance. Thus, also at practical temperature, crystallisation of moul flux woul reuce not only raiative but also conuctive heat transfer, leaing to reuction in the total heat flux across the flux film, apart from the formation of an air gap. On the contrary, there is also a possibility that conuctive contribution in glassy flux is reuce to the same level as in crystallise flux at high temperatures. Even in that situation, crystallise flux woul be more effective for mil cooling ue to less raiative contribution. In aition, it woul be unrealistic for glassy moul flux to exist stably at practical temperature such as C; however, immeiately after the moul flux gets into between the moul an the shell to form a film, it is suppose that the film is in such a situation as moel (A ) until crystallisation starts. Consequently, moul flux esigne to crystallise as shortly as possible woul be more effective for mil cooling. 4. Conclusions An apparatus has been evelope for the measurement of the apparent thermal conuctivity incluing raiative contribution for soli moul flux uner a steep temperature graient base on the parallel plate metho. In this apparatus, the contact thermal resistance has been reuce as small as possible an has been etermine to be m 2 KW 1. This metho has been applie to measurements for fuse silica an the apparent thermal conuctivities obtaine are in goo agreement with reporte values. The measure values also reprouce the thermal conuctivity incluing raiative contribution where the central temperature (T c ) of the sample is above 350 C. Apparent thermal conuctivities of the glassy moul flux has been measure to be 1.25 Wm 1 K 1, almost inepenent of temperature. With increasing egree of crystallinity up to 86%, the thermal conuctivities increase to 1.8 Wm 1 K 1 where 0 C < T c < 350 C. Crystallise fluxes have thermal conuctivity values close to those of the glassy flux in the range of 350 C < T c < 500 C. Where 500 C < T c < 600 C, the apparent thermal conuctivity of the glassy sample has been measure to be 1.54 Wm 1 K 1, which is greater than that of an entirely crystallise flux, 1.32 Wm 1 K 1. The glassy sample was crystallise in the portion expose to high temperature uring the measurement. The ifference between the above apparent thermal conuctivities woul be ue to raiative contribution. Moel calculation consiering both raiative an conuctive contributions has suggeste that crystallisation of moul flux reuces raiative heat flux across the moul flux film, leaing to mil cooling, apart from the formation of an air gap. REFERENCES 1) K. Sorimachi, S. Sakai an T. Fujii: Tetsu-to-Hagané, 81 (1995), ) M. Hanao, M. Kawamoto, M. Hara, T. Murakami, H. Kikuchi an K. Hanazaki: Tetsu-to-Hagané, 88 (2002), 23. 3) M. Hanao an M. Kawamoto: ISIJ Int., 48 (2008), ) Y. Sugitani an M. Nakamura: Tetsu-to-Hagané, 65 (1979), ) T. Kanazawa, S. Hiraki, M. Kawamoto, K. Nakai, K. Hanazaki an T. Murakami: Tetsu-to-Hagané, 83 (1997), ) Y. Tsukaguchi, M. Hanao, M. Kawamoto, M. Aachi an H. Hayashi: Tetsu-to-Hagané, 97 (2011), ) K. C. Mills: ISIJ Int., 56 (2016), 1. 8) K. C. 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