A Study of the Heat Transfer Behavior of Mold Fluxes with Different Amounts of Al₂O₃

Abstract

The element Al in molten aluminum containing steel reacts with the liquid mold flux and thus be transferred into the mold flux during the continuous casting process. Additionally, the increase in alumina in a mold flux changes its performance significantly. Thus, in this paper, the heat transfer properties of mold fluxes with the Al₂O₃ content ranging from 7 to 40 wt. % were studied with the Infrared Emitter Technique (IET). Results found that heat flux at the final steady state decreased from 423 kW·m⁻² to 372 kW·m⁻² with the increase in Al₂O₃ content from 7% to 30%, but it increased to 383 kW·m⁻² when the Al₂O₃ content was further increased to 40%. Both crystalline layer thickness and crystalline fraction first increased, then decreased with the further addition of A₂O₃ content. Moreover, it indicated that the heat transfer process inside the mold was dominated by both a crystallization of mold flux and the resulting interfacial thermal resistance. Further, the R_int increased from 9.2 × 10⁻⁴ m²·kW⁻¹ to 11.0 × 10⁻⁴ m²·kW⁻¹ and then to 16.0 × 10⁻⁴ m²·kW⁻¹ when the addition of Al₂O₃ content increased from 7% to 20% and then to 30%, respectively; however, it decreased to 13.6 × 10⁻⁴ m²·kW⁻¹ when the Al₂O₃ content reached 40%.

1. Introduction

Aluminum, as an effective additive, is widely used for the new generation of automotive steels (TRIP/TWIP, etc.) development, as it can lower the weight of an automotive body for a better fuel-efficiency without losing the safety through the improvement of the mechanical properties of steels. However, the containing aluminum in steels would tend to introduce problems for continuous casting processes, as partial dissolution of aluminum in the steels would transfer into a mold flux and lead to a dramatic interaction between silica and aluminum that would deteriorate the mold flux properties such as viscosity and crystallization, which would further degenerate the quality of the shell and consequently affect the smooth casting process. Basically, there are two ways for the pickup of Al₂O₃ in the mold flux during the continuous casting process. One is the absorption of Al₂O₃-based inclusions, which form in the steelmaking, refining, and casting processes [1,2]. The other is the direct reaction that occurs in the vicinity of the steel/slag interface between the Al contained molten steel and the SiO₂-contained liquid mold slag [3,4]. The experimental results reported by the ArcelorMittal [5] showed that the content of alumina in the mold flux can reach more than 30% during the TRIP steel continuous casting process.

The increase in Al₂O₃ content in the mold flux deteriorates the lubrication of shell. According to research by Zhang et al. [6], the viscosity increased sharply with the increase in Al₂O₃/SiO₂ in the mold flux, which is consistent with the results of Yu et al. [7] Further, Kim et al. [8] further investigated the effect of Al₂O₃ on the viscosity and suggested that the increase in viscosity was due to the change in the calcium silicate-based melt structure that was caused by the increase in Al₂O₃ content. Therefore, the increase in Al₂O₃ in the mold flux will lead to an increase in viscosity, which will lower the rheological ability of the mold flux that makes a mold flux infiltration harder and a lower mold flux consumption, consequently deteriorating the lubrication of shell.

Regarding the effect of Al₂O₃ content on the heat transfer behavior, the related reports are relatively rare. Cho et al. [9] observed a fade in mold heat transfer rate when the conventional lime-silica mold fluxes were used during casting the TRIP steel. Yu et al. [10] characterized the heat flux across the slag film when casting the high aluminum TRIP steel. Additionally, it was found that the heat flux decreased with the increase in the $w_{{\text{Al}}_2{\mathrm{O}}_3}/w_{{\text{SiO}}_2}$ ratio.

Although several works have been done, the impact of Al₂O₃ on the heat transfer performance of the mold flux is still not thoroughly clear; the importance of interfacial thermal resistance is especially ignored. Therefore, in this study, the effect of Al₂O₃ content (ranging from 7 to 40 wt. %) on heat transfer behavior of the mold flux, and interfacial thermal resistance between the mold/slag, were studied via an advanced Infrared Emitter Technique (IET).

2. Materials and Methods

2.1. Experimental Slags

A commercial mold flux (named as R0.8A7 in

Table 1. The chemical compositions of mold fluxes with different amounts of Al₂O₃ after pre-melted (in Mass Pct wt. %).

Sample	CaO	SiO2	Al2O3	MgO	F−	Na2O	Li2O	R
R0.8A7	33.53	42.05	7.02	2.00	5.88	9.02	0.50	0.8
R0.8A20	27.84	34.70	20.01	2.02	5.91	9.02	0.50	0.8
R0.8A30	23.37	29.16	30.01	2.01	5.94	9.01	0.50	0.8
R0.8A40	18.89	23.60	40.00	2.00	5.98	9.01	0.50	0.8

), with an R = CaO/SiO₂ (basicity) of 0.8 and Al₂O₃ content of 7 wt. %, for casting low carbon steel was chosen as the matrix flux in this study [11]. In order to investigate the influence of Al₂O₃ on the heat transfer behaviors of mold fluxes, different amounts of reagent grade chemicals, such as CaCO₃, SiO₂, Al₂O₃, MgCO₃, CaF₂, Na₂CO₃, and Li₂CO₃, were added into the matrix R0.8A7 to make the content of Al₂O₃ in the mold flux vary from 7 to 40 wt. %. The maximal amount of Al₂O₃ contained in the mold flux was chosen to be 40 wt. %, according to the CaO–SiO₂–Al₂O₃ ternary phase diagram [12], due to the fact that the maximal amount of precipitation of Al₂O₃ is about 40% when the basicity (CaO/SiO₂) is 0.8, as shown in Figure 1.

The samples were prepared via melting in an induction furnace with a graphite crucible at a temperature of 1773 K (1500 °C) for about 5 min in order to homogenize their chemical compositions. Then, they were poured onto a copper plate for quenching to fully obtain glass. Meanwhile, a new cylindrical tube copper mold was used to cast the slags before it solidified on the copper plate. After that, the cooled slag disks were ground and polished with SiC sandpaper to control their thickness and surface roughness. The glassy disks, after polished, were individually placed on the top surface of the copper mold during the heat transfer tests. Otherwise, a small amount of solidified glassy mold flux was crushed into powder samples for the Single Hot Thermocouple Technique (SHTT) tests. The final slags after pre-melting were also analyzed through X-Ray Fluoroscopy (XRF, Bruker, Karlsruhe, Germany). The main chemical compositions of those pre-melted slag are listed in Table 1 and marked as dots in Figure 1.

2.2. The Heat Transfer Test

The heat transfer tests of the mold flux with different amounts of Al₂O₃ were investigated by using the IET, which is schematically shown in Figure 2. Details about the IET have been illustrated in our previous paper [13,14]. The infrared radiant heater (CSU, Changsha, China) with the maximum emitting heat flux of 2.0 MW·m⁻², power controller, command/control unit, and data acquisition system were included in this experimental apparatus. Figure 3 shows the schematic figure of the copper mold system, which is simulated by a copper cylinder, cooled by water on one end. The cylindrical copper mold was covered by the slag disks before the application of radiation thermal energy from the infrared radiant heater. The response temperatures were obtained through the subsurface thermocouples.

The heat transfer tests were carried out by preheating the copper mold system with a single glassy disk under a thermal energy of 500 kW·m⁻² first. Then, the thermal energy was linearly increased to 800 kW·m⁻² with a rate of 1 kW·m⁻²·s⁻¹ and maintained for 2000 s, as shown in Figure 4.

Figure 5a shows the temperature time span when the heating profile, as shown in Figure 4, was applied to the bare copper mold without the slag disk. The temperature of T₁, T₂, T₃, and T₄ were obtained through the thermocouples, embedded 2 mm, 5 mm, 10 mm, and 18 mm below the surface copper mold (Figure 3), respectively. T_in and T_out are the temperatures of the inlet and outlet cooling water. The heat flux across the copper mold was calculated by using the one-dimensional inverse heat conduction model developed by Beck [15,16] based on Equation (1):

$$\frac{\partial }{\partial x}\left(k\frac{\partial T_i}{\partial x}\right)=\left(\mathsf{\rho }{c}_{\mathrm{p}}\right)\frac{\partial T_i}{\partial t}$$

(1)

where T is the temperature, x is the distance below the copper mold top surface, t is the time, k is the thermal conductivity, c_p is the heat capacity, and ρ is the mass density of copper.

Then, the calculated result of the heat flux time span across the bare copper system is shown in Figure 5b. It suggests that the measured heat flux linearly increased first with the increase in the output thermal energy; then, it comes into a relative steady state in a very short time.

2.3. The Initial Crystallization Temperature Test

The SHTT was utilized to obtain the initial crystallization temperatures in this study. Details about the SHTT apparatus have been illustrated by Prof. Kashiwaya [17] and our previous paper [18]. Figure 6 shows the schematic of the SHTT experimental apparatus. The precipitation of crystals can be directly observed and recorded by a DVD camera through a high-temperature microscope (DY Optical Instruments Co., Shanghai, China); meanwhile, the corresponding temperature was obtained by the temperature acquisition system. Figure 7 shows the temperature controlling profile for the glassy/crystalline phase transition temperature measurements of mold fluxes with different amounts of Al₂O₃. The samples were heated up to 1773 K (1500 °C) first, and then quenched to obtain a glassy phase; after that, they were heated up again at a heating rate of 0.5 K·s⁻¹ (0.5 °C·s⁻¹). The initial crystallization temperature was obtained by analyzing the recorded video and the corresponding temperature time span.

2.4. Phase Analysis

Those mold flux disks after heat transfer tests were crushed and ground into powders for phase analysis. The precipitated crystalline phases were analyzed with an X-Ray diffractometer (RIGAKU-TTR III, Rigaku Corporation, Tokyo, Japan) with the Cu–Kα (0.154, 184 nm). XRD data ranged from 2θ = 10° to 2θ = 80°, with a scanning speed of 10° min⁻¹.

3. Results and Discussion

3.1. The Heat Transfer Procedure

The prepared mold slag disks were individually placed on the top surface of the copper mold and subjected to the heating profile, as shown in Figure 4, for the heat transfer tests. Taking Sample R0.8A7, for example, there are four typical stages appearing during the heat transfer experiment as shown in Figure 8 and Figure 9. Among them, Figure 8 shows the heat flux time span of Sample R0.8A7 during the heat transfer test; Figure 9 shows the snapshots of the cross-section of those mold flux disks. It can be seen that, in the period of the pre-heating Stage I, the heat flux linearly increased with the increase in thermal energy, and the disk was remained as glassy without phase transition, as shown in Figure 9a. After that, the heat flux kept increasing, and the deviation occurred in the heat flux curve due to the initiation of mold flux crystallization, where the opaque crystals formed on the top of the mold slag disk, as shown in Figure 9b. At Stage III, the heat flux arrived to its peak value and then slightly decreased again due to the continuous crystallization. Finally, the heat flux remained constant when the crystallization completed and reached a steady state in Stage IV.

3.2. The Effect of Al₂O₃ Content on Heat Flux

In order to study the effect of Al₂O₃ content on the heat transfer performance of the mold flux, the heat flux of the four mold slags with the Al₂O₃ content ranging from 7% to 40% is combined and shown in Figure 10. It can be found that the final steady-state heat flux of Sample R0.8A7 (Al₂O₃, 7%) was 423 kW·m⁻², whereas it decreased to 419 kW·m⁻² (Sample R0.8A20) and to 372 kW·m⁻² (Sample R0.8A30) when the Al₂O₃ content increased from 7% to 20% and then to 30%, respectively. However, the final steady-state heat flux increased to 383 kW·m⁻² when the Al₂O₃ content increased to 40%. The reasons for the above results are mainly due to the variation in the mold flux crystallization and the corresponding interface thermal resistance caused by the change in Al₂O₃ content, which will be discussed in detail later.

Moreover, the snapshots of the cross-section of the mold flux disks, after the heat transfer tests, were obtained and shown in Figure 11. It can be observed that the opaque crystalline layer occurred on the top part of disks; however, on the bottom part of those disks, there was still a glassy layer. This is due to the temperature gradient that formed from the top to the bottom of the disks. The top part of the disk was close to the radiant heater, so it was heated to a higher temperature and became crystallized; meanwhile, the bottom part was close to the water-cooled cooper mold, so it remains in a glassy phase, as in a real continuous casting mold [19].

Although all the disks shown in Figure 11 are comprised of two layers—the crystalline and glassy layers—the specific thickness of each layer in the disk is different. Therefore, for a better comparison, the crystalline fraction and thickness of the crystalline layer of the mold flux disks with varying amounts of Al₂O₃ are shown in Figure 12. The crystalline layer thicknesses are 2.30 mm, 2.51 mm, 2.96 mm, and 2.68 mm for Samples R0.8A7, R0.8A20, R0.8A30, and R0.8A40, respectively, which corresponds to a 69.8%, 76%, 90%, and 81% crystalline fraction for those respective disks. Those values suggest that both crystalline layer thickness and crystalline fraction increased first, then decreased with the further addition of A₂O₃. In other words, the A₂O₃ can improve the crystallization ability of the mold flux when the Al₂O₃ content is less than 30%; however, it begins to inhibit crystallization when the Al₂O₃ content exceeds 30%. The amphoteric behavior of A₂O₃ on the crystallization of the mold flux obtained in the heat transfer test here is consistent with our previous study [20].

Thus, it is suggested that the change in Al₂O₃ content leads to the variation in mold flux crystallization ability, which results in different crystalline layer distribution in the disk and affects the heat flux. More specifically, when the Al₂O₃ content is less than 30%, the Al₂O₃ is added into the acidic matrix slag (the basicity is 0.8). Thus, it offers O²⁻ as a basic oxide. Then, the silicate structure is simplified by the addition of non-bridging oxygen, which makes the molten mold slag easier to become crystallized. Once the mold flux crystallizes, more incident thermal energy is scattered/reflected from the grain boundary, crystals surface, and defects, which leads to less thermal energy being transferred to the mold. Therefore, the final steady-state heat flux in the heat transfer tests decreases. On the contrary, in this case, the matrix itself turned into a basic slag when the Al₂O₃ content further increased from 30% to 40%. Therefore, the additional Al₂O₃ worked as acidic oxide, which made the silicate network of molten slag become an alumino-silicate structure, which is more complex and does not promote crystallization. Thus, less mold fluxes become crystallized, more incident radiation can be absorbed and transferred to the mold, and the final steady-state heat flux hence increases.

The XRD results of the mold fluxes with different amounts of Al₂O₃ after the heat transfer tests are shown in Figure 13. The main precipitated crystal in Sample R0.8A7 was cuspidine (Ca₄Si₂O₇F₂), which is quite common in mold fluxes. When the Al₂O₃ content increased to 20%, NaAlSiO₄ (nepheline) and CaF₂ appeared. When the Al₂O₃ content reached 30%, the compositions of the crystals were similar to the mold flux with 20% Al₂O₃ content; however, the content of CaF₂ increased, as the intensity of the characteristic peaks of CaF₂ of Sample R0.8A30 was higher than Sample R0.8A20, which suggests that the Al₂O₃ can enhance the precipitation of CaF₂ crystals. Finally, the Ca₂Al₂SiO₇ (gehlenite) precipitated when the content of Al₂O₃ continuously increased to 40%, as shown in Figure 13. According to Taylor’s observation [21,22], the thermal conductivity of the following several crystalline phases was given in the following order: CaSiO₃ > Ca₂Al₂SiO₇ > Ca₄Si₂O₇F₂ > NaAlSiO₄, which means that the heat flux of Sample R0.8A40 should be higher than both Sample R0.8A7 and Sample R0.8A20, as the precipitation crystals in Samples R0.8A40, R0.8A7, and R0.8A20 were Ca₂Al₂SiO₇, Ca₄Si₂O₇F₂, and NaAlSiO₄, respectively; however, the experimental result was different. Therefore, it was the mold flux crystallization that dominated the heat transfer process inside the mold flux instead of the specific precipitated crystal phase, as the crystal fraction of Sample R0.8A40 was larger than that of Samples R0.8A7 and R0.8A20, which let less incident energy be transferred to the water-cooled copper mold.

3.3. The Effect of Al₂O₃ Content on Interface Thermal Resistance

Except for the heat transfer performance of the mold flux, the interfacial thermal resistance between the mold wall and mold slag film is another very important factor that affects the heat flux, from solidified shell to mold. In order to investigate the impact of Al₂O₃ content on the interface thermal resistance of the mold wall/mold flux, a numerical calculation was conducted by assuming that (1) only a one-dimensional heat transfer occurred from the mold flux to the water-cooled copper mold and (2) the total heat flux across the mold flux consisted of conductive and radiative heat flux. The heat flux travels from the mold flux film to the mold wall and is schematically shown in Figure 14.

Therefore, the total heat flux q_tot across the mold flux disk, at the steady state, can be expressed as Equation (2):

q_tot = q_rad + q_cond

(2)

According to the Fourier’s law, the conductive heat flux at steady state could be expressed as Equation (3):

$$q_{\text{cond}}=K_{\text{cond}}\frac{T_{\mathrm{g}}-T_{\text{gs}}}{d}$$

(3)

where K_cond is the thermal conductivity of the glassy mold flux, its values employed as 1.0 to 1.2 Wm⁻¹·k⁻¹ as in previous study [23], T_gs is the bottom face temperature of the mold flux disk, d is the thickness of the glassy layer, and T_g is the temperature at the interface between the crystalline layer and the glassy layer, which was obtained as the temperature of the mold flux initial crystallization (glass/crystal transformation). Values were obtained by using SHTT tests as shown in Figure 15 and

Table 2. Conditions for R_int calculations of mold fluxes with different amounts of Al₂O₃.

Al2O3 Cont.	Tg/c (°C)	Tms (°C)	dcrystalline (mm)	dglassy (mm)
7%	830	103	2.30	1.00
20%	816	100	2.51	0.79
30%	791	96	2.96	0.34
40%	803	97	2.68	0.62

.

Thus, the T_gs can be calculated with Equation (4):

T_gs = T_gs + R_int × q_obs

(4)

where R_int is interface resistance, T_ms stands for the temperature of copper mold top face calculated by the in-mold temperature gradient, and q_obs is the measured steady-state heat flux.

For the transferred radiative heat flux from the mold slag into the copper mold, Fourier’s equation is used for convenience. Therefore, the radiative heat flux can be calculated as Equation (5):

$$q_{\text{rad}}=K_{\text{rad}}\frac{T_{\mathrm{g}}-T_{\text{gs}}}{d}$$

(5)

Additionally, the radiative thermal conductivity K_rad of the glassy mold slag can be obtained by Equations (6) and (7) through assuming the mold flux behaves like gray gas:

$$K_{\text{rad}}=\mathsf{\beta }\frac{(T_{\mathrm{g}}^4-T_{\text{gs}}^4)d}{T_{\mathrm{g}}-T_{\text{gs}}}$$

(6)

$$\mathsf{\beta }=\frac{n^2\mathsf{\sigma }}{0.75\mathsf{\alpha }d+{\mathsf{\epsilon }}_1^{-1}+{\mathsf{\epsilon }}_2^{-1}-1}$$

(7)

where σ is the Stefan–Boltzmann constant assumed to be 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴, n represents the refractive index, which is 1.6, ε is the emissivity—its value is 0.92 for the glassy mold slag, while it is 0.4 for the copper mold [24]—and α is the absorption coefficient of the glassy mold flux, which is 400 m⁻¹ [25].

Hence, the interface thermal resistance R_int can be computed with the above equations according to the flow chart in Figure 16 and parameters listed in Table 2.

The mold fluxes interface thermal resistances, R_int, with different amounts of Al₂O₃ are shown in Figure 17. It can be seen that the values of R_int ranged from 9.2 × 10⁻⁴ to 16.0 × 10⁻⁴ m²·kW⁻¹, which is close to other researchers’ results [26,27]. Further, the R_int increased from 9.2 × 10⁻⁴ (Sample R0.8A7) to 11.0 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A20) and then to 16.0 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A30) when the addition of Al₂O₃ content increased from 7% to 20% and then to 30%, respectively; however, it decreased to 13.6 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A40) when the Al₂O₃ content reached 40%. This is mainly due to the fact that the interface thermal resistance R_int was formed because of the deformation and shrinkage of the mold flux during the crystallization process that occurs in the heat transfer tests. Therefore, the variation tendency of the interface thermal resistance with the addition of Al₂O₃ content as shown in Figure 17 is proportional to the crystalline fraction of mold fluxes as shown in Figure 12 in Section 3.2. The crystalline fraction increase/decrease leads to more/less slag disk deformation and shrinkage; thus, the interface thermal resistance of mold fluxes tends to increase/decrease with the variation of Al₂O₃ content.

4. Conclusions

The heat transfer behavior of the mold fluxes with Al₂O₃ content ranging from 7% to 40% was studied through the IET, and the interfacial thermal resistance was estimated through numerical calculation. Some important results were summarized as following below:

• The final steady-state heat flux of Sample R0.8A7 (Al₂O₃, 7%) was 423 kW·m⁻², while it decreased to 419 kW·m⁻² (Sample R0.8A20) and then to 372 kW·m⁻² (Sample R0.8A30) when the Al₂O₃ content increased from 7% to 20% and then to 30%, respectively; however, it increased to 383 kW·m⁻² as the Al₂O₃ content was continuously increased to 40%.
• Both crystalline layer thickness and fraction increased first, then decreased with the further addition of Al₂O₃. Additionally, it was the mold flux crystallization, together with the resulted interfacial thermal resistance, that dominated the heat transfer performance of the mold flux—not the specific precipitated crystal phase.
• The R_int increased from 9.2 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A7) to 11.0 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A20) and then to 16.0 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A30) when the addition of Al₂O₃ content increased from 7% to 20% and then to 30%, respectively; however, it decreased to 13.6 × 10⁻⁴ m²·kW⁻¹ (Sample R0.8A40) when the Al₂O₃ content reached 40%.
• The variation in the interfacial thermal resistance R_int was proportional to crystalline fraction of the mold fluxes, as the interface thermal resistance was mainly caused by the deformation and shrinkage of the mold flux during its crystallization process.