Determination of Thermal Diffusivity/conductivity of Oxide Scale Formed on Steel Plate by Laser Flash Method through Thermal Effusivity Measurement by Transient Hot-strip Method

Abstract

Thermal diffusivity and conductivity were determined for oxide scale formed on steel plate by the laser flash method in combination with thermal effusivity measurement by the transient hot-strip method. The thermal effusivity measurement technique was confirmed by measurement of silica glass, and the value was determined to be 2.52 kJ m⁻² s^−1/2 K⁻¹ for the oxide scale formed on an ultra-low-carbon steel plate by oxidation in air at 900°C for 3600 s. Thermal diffusivity measurements were also conducted for 1 mm-thick steel plates oxidized in air at 900°C for 770–3600 s by the laser flash method. The apparent thermal diffusivity of samples provided the thermal diffusivity of the oxide scale based on three-layered analysis by inputting the measured value of the thermal effusivity. The measured values suggested that no significant boundary resistance exists between the oxide scale and the steel plate. The thermal conductivity and diffusivity of the oxide scale were calculated to be 1.6 W m⁻¹ K⁻¹ and 4.0 × 10⁻⁷ m² s⁻¹, respectively.

1. Introduction

In the hot-rolling process of steelmaking, a steel slab is processed at high temperature and then cooled after being rolled into a plate. The steel plate is easily oxidized at high temperatures to form an oxide scale layer with several tens of micrometers thick. The thermal conductivity of the oxide scale is lower than that of steel, suggesting that the scale acts as a heat-resistant layer during the cooling process. Given this background, the thermophysical properties of oxide scale have attracted much attention for temperature control of steel plates.^1,2,3,4,5,6) A measurement technique for thermal diffusivity has recently been reported; the measurement was conducted for a sample consisting of oxide scale formed on steel by the laser flash method, and a multilayer model was applied to derive the thermal diffusivity of the oxide scale from that of the sample. Thermal diffusivities have been measured for Fe_1−xO and oxide scales using this technique.^7,8,9,10) The thermal conductivity (λ) can be calculated as the product of the measured thermal diffusivity (α), heat capacity (C_p) and density (ρ):   

$$\lambda =C_p\rho \alpha$$(1)

In the previously reported papers, the oxide scale was treated as dense samples with a layered structure, especially for oxide scale; this structure was confirmed by cross-sectional imaging of the scale.^7,8,9,10) However, applying this measurement technique to scales that exhibit complex structures is difficult; voids or pores are present, and the scales comprise not only simple iron oxides but also mixed oxides such as fayalite (Fe₂SiO₄).^11,12,13) In this case, the density and heat capacity values input into Eq. (1) must be the apparent/average value for the oxide scale. Determining such values for ρ and C_p in Eq. (1) is not straightforward because the oxide scale is too thin for a representative sample to be obtained. In addition, another equation expresses the relation between thermal conductivity and thermal diffusivity (e):   

$$\lambda =e\sqrt{\alpha }$$(2)

The apparent value of thermal effusivity for an oxide scale, in combination with thermal diffusivity, can provide the thermal conductivity. However, a measurement technique for the thermal effusivity of oxide scales has not been established.

Susa et al.¹⁴⁾ proposed a thermal effusivity measurement technique for molten silicates based on the transient hot-strip method. A constant heat flux is supplied to the sample from a heater, and the thermal effusivity and conductivity of the sample are determined on the basis of the temperature ramp rate of the heater over short and long time periods, respectively. The thermal effusivity value of the oxide scale is estimated to be of the same order as that for molten silicate because both are oxides. From the perspective of an objective sample for the thermal effusivity measurement, the oxide scale and silicate differ in size: the oxide scale is 10–100 μm thick and solid. Therefore, the aim of the present study is to measure the thermal effusivity based on the transient hot-strip method for the oxide scale formed on the steel plate and to determine the thermal conductivity of the oxide scale including the thermal diffusivity measurement by the laser flash method.

2. Experimental

2.1. Samples

Samples used were steel plates with an oxide scale. Ultra-low-carbon steels were cut into 1 × 20 × 40 mm³ specimens for thermal effusivity measurements and into 1 × 10 × 10 mm³ specimens for thermal diffusivity measurements. Table 1 shows the chemical composition of the ultra-low-carbon steel used in this study. The steel plates were oxidized in air at 900°C for 770–3600 s followed by air cooling. The volume ratio of iron oxides formed at 900°C in air is known to be F_1−xO:Fe₃O₄:Fe₂O₃ = 95:4:1.¹⁵⁾ Plates of fused silica (20 × 40 × 10 mm³) were also used as samples to validate the transient hot-strip method applied in this study.

Table 1. Chemical composition of ultra-low-carbon steel used in the present study (in mass%).

Fe	C	Si	Mn	P	S
Bal.	0.001	0.01	0.14	0.019	0.007

2.2. Thermal Effusivity Measurements

Figures 1(a) and 1(b) show a schematic of the transient hot-strip method used in this study. A strip heater of Pt-13%Rh (40 mm long, 2 mm wide, and 20 μm thick) was placed between the two sample plates. Thermal grease was spread between the heater and the sample, and samples were pressed with a mini-vise as shown Fig. 1(b) to reduce the thermal resistance. The thermal grease used had the properties as follows: thermal conductivity was 8.5 Wm⁻¹K⁻¹, density was 2.5 gcm⁻³ and viscosity was 87 Pa·s. A constant current (3–4.5 A) was applied to the hot-strip by a galvanostat. The temperature rise (ΔT) of the hot-strip was recorded continuously by two potential leads: the hot-strip served as both a heating element and a temperature sensor. The thermal effusivity (e) of the sample was calculated from the equation   

$$e=\frac{Q/2a{\pi }^{1/2}}{d\mathrm{\Delta }T/d{t}^{1/2}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(\sqrt{\alpha t}/a<0.5\right)$$(3)

where Q, t, and a are the heat generation rate per unit length of the heater, the time, and the half-width of the strip heater, respectively. The condition in parentheses indicates that the analysis was applied only for the initial time range. In practice, the heat flux was supplied by the constant current and the temperature rise was recorded as the voltage change (ΔV) of the hot-strip measured by an oscilloscope using the four-terminal method. Here, samples that contacted the heater were silica glass and an Fe₂O₃ layer, both of which are insulators;^16,17) thus, the supplied current did not leak to the sample and was assumed to be converted into heat. The thermal effusivity was calculated from the equation   

$$e=\frac{I^3{\beta }_T{R}_{0}X/2a{\pi }^{1/2}}{d\mathrm{\Delta }V/d{t}^{1/2}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\left(\sqrt{\alpha t}/a<0.5\right)$$(4)

where I, β_T, R₀, and X are the supplied current, temperature coefficient of the resistance for the heater at temperature T, the electric resistance of the heater at 0°C and the electric resistance for a unit length of the heater, respectively. The measurement of dΔV/dt^1/2 gives the thermal effusivity.

Fig. 1.

Schematic of the transient hot-strip method: (a) samples with strip heater and (b) samples with vise and electric circuit. (Online version in color.)

2.3. Thermal Diffusivity Measurement

Thermal diffusivity measurement was conducted by the laser flash method for the oxidized steel plate with dimensions of 1 × 10 × 10 mm³, as illustrated in Fig. 2. A pulse laser was applied to one oxidized surface, and the temperature increase of the rear surface was monitored using a radiation thermometer.^7,8,9,10) The apparent thermal diffusivity of the sample was determined on the basis of the half-time analysis.¹⁸⁾ The thermal diffusivity measurement was also performed for the steel plate with no oxide scale.

Fig. 2.

Schematic of the laser flash method used in the present study.

2.4. Sample Analysis

After the measurements, scanning electron microscopy (SEM) was used to analyze the structure and thickness of the oxide scale. X-ray diffraction (XRD) was used to analyze the phase of the oxide scale. The density of the steel plate was measured by the Archimedean method.

3. Results

3.1. Thermal Effusivity Measurement for Silica Glass

Figure 3 shows the results of the thermal effusivity measurement for the fused silica under the supplied current of 3.0 A. The curve represents the average of 10 measurements. The measured voltage initially increases to the value corresponding to the electrical resistance of the heater. A linear relationship exists between the measured voltage change and t^1/2 for the time range 0.01 < (t/s)^1/2 < 0.4. From the slope in Fig. 3, the thermal effusivity was calculated to be 1.57 kJ m⁻² s^−1/2 K⁻¹ using Eq. (4). To derive the thermal effusivity from the linearity, the analysis time has the conditions described in Eq. (4). The thermal diffusivity reported for silica glass is 8.66 × 10⁻⁷ m² s^{−1 19)} at room temperature, producing the analysis condition as (t/s)^1/2 < 0.4, which is the same as that used in the present study. The obtained thermal effusivity also agrees well with the value of 1.52 kJ m⁻² s^−1/2 K⁻¹ obtained using Eq. (2) by substituting recommended values¹⁹⁾ (thermal conductivity: 1.42 W m⁻¹ K⁻¹ and thermal diffusivity: 8.66 × 10⁻⁷ m² s⁻¹ at 273 K).

Fig. 3.

Voltage change with time for the thermal effusivity measurement of silica glass; the supplied current was 3.0 A. (Online version in color.)

3.2. Thermal Effusivity Measurement of Oxide Scale

Figure 4 shows the measurement results for the oxide scale formed on the steel plate by the transient hot-strip method with the applied current of 4.5 A. The values plotted were averaged from 16 measurements. As in the case of the measurement of silica glass, the measured voltage initially increases to the value corresponding to the electrical resistance of the heater and then gradually increases with time. A linear relationship is observed between the square root of time and the voltage change in the range t^1/2< 0.17; in the range t^1/2 > 0.17, the slope changes more gradually because of heat penetration into the steel substrate. The thermal effusivity value was calculated to be 2.48 ± 0.06 kJ m⁻² s^−1/2 K⁻¹ from the initial slope in Fig. 4. The uncertainty was obtained from the slope determination by the least-squares method. The oxide scale has a limited thickness; thus, this limitation must be considered when deriving the thermal effusivity. The validity for the determination will be discussed later, in conjunction with the thickness values of the oxide scale and the thermal diffusivity. Table 2 shows the thermal effusivity data derived for each current supply; the average value was 2.52 ± 0.08 kJ m⁻² s^−1/2 K⁻¹.

Fig. 4.

Voltage change with time for the thermal effusivity measurement of oxide scale; the supplied current was 4.5 A. (Online version in color.)

Table 2. Measured thermal effusivity of oxide scale.

Current, I/A	e/kJs1/2m2K
3.0	2.58 ± 0.08
4.0	2.50 ± 0.10
4.5	2.48 ± 0.06
Average	2.52 ± 0.08

Figures 5(a) and 5(b) shows cross-sectional SEM images of the sample after the thermal effusivity measurement. A homogeneous oxide scale layer was observed on the steel substrate (Fig. 5(a)). The average thickness of the oxide scale layer is 220 μm. Figure 5(b) suggests that the main component of the oxide scale is Fe_1−xO; however, there is an 11 μm-thick Fe₃O₄ scale near the surface and Fe₃O₄ particles are dispersed in the Fe_1−xO layer just below the Fe₃O₄ layer as indicated by closed triangle. The latter Fe₃O₄ dispersion was likely formed by the decomposition of Fe_1−xO during the cooling process of sample preparation. As a result, the thickness of the oxide scale consists of 86%FeO layer, 9%FeO with the dispersion of Fe₃O₄ and Fe, and 5% Fe₃O₄. Cracks were also observed in the oxide scale layer, i.e., at the steel substrate/Fe_1−xO interface, and in Fe₃O₄ because the samples were pressed together by the mini-vise to reduce the thermal resistance as shown in Fig. 1(b).

Fig. 5.

Cross-sectional SEM images of the sample after thermal effusivity measurement: (a) oxide scale with steel substrate and (b) oxide scale near surface.

Figure 6 shows the XRD results for the sample after the thermal effusivity measurement. Fe_1−xO and Fe₃O₄ were found in the sample, as suggested by the results in Fig. 5.

Fig. 6.

XRD profile for oxide scale formed on ultra-low-carbon steel used for thermal effusivity measurement. (Online version in color.)

3.3. Thermal Diffusivity Measurement and Sample Analysis

Figure 7 shows a typical temperature profile derived for the thermal diffusivity measurement for the sample oxidized for 770 s. The half-time analysis¹⁸⁾ gave the apparent thermal diffusivity of the sample (α_s) consisting of three layers (oxide scale/steel/oxide scale). Table 3 lists the thermal diffusivity of the sample measured in this study. The value of α_s decreases with increasing oxidation time. Figure 8 shows the cross-section of the sample after the thermal diffusivity measurement. Good adhesion is observed between the steel substrate and the oxide scale. The thicknesses of the oxide scale and the steel layer (d_oxide and d_steel, respectively) were measured from the figure; the results are also listed in Table 3.

Fig. 7.

Measurement result for laser flash method for oxidized steel with 97.8 μm scale.

Table 3. Thickness, thermal diffusivity, and thermal conductivity of sample and oxide scale measured in the present study.

Oxidation time/s	Thickness/mm			Thermal diffusivity/10−6 m2s−1		Thermal conductivity/Wm−1 K−1
	Total, ds	Oxide scale, doxide	Steel, dsteel	Sample, αs	Oxide scale, αoxide,m	Oxide scale, λoxide,m
770	1.099	0.0978	0.903	6.97	0.478	1.74
1650	1.131	0.133	0.865	4.56	0.450	1.69
3600	1.204	0.206	0.792	2.14	0.376	1.55

Fig. 8.

Cross-section of the sample after the thermal diffusivity measurement.

3.4. Thermophysical Properties of the Steel

Table 4 lists the measured thermal diffusivity (α_steel) and density (ρ_steel) values obtained for the steel plate. The values show good agreement with reported values for mild steel.²⁰⁾

Table 4. Comparison of thermophysical properties of steel measured in the present study with reported values.

	This study	Mild steel20) Fe-0.23%C-0.6%Mn
Thermal diffusivity, αsteel/10−5m2s−1	1.91	1.5
Heat capacity, Cp, steel/JK−1mkg−1	–	469
Density, ρsteel/kgm−3	7880	7860

4. Discussion

4.1. Calculation of the Thermal Diffusivity of Oxide Scale

The thermal diffusivity of oxide scale (α_oxide,m) can be calculated from the following equations:^21,22)   

$$\begin{array}{l}{\displaystyle \frac{d_s^2}{6{\alpha }_s}}=\\ {\displaystyle \frac{\left({\mathrm{\Gamma }}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}+3{\displaystyle \frac{e_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}}{\sqrt{{\alpha }_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e},\mathrm{m}}}}}{d}_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}\right){\displaystyle \frac{d_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}{}^2}{{\alpha }_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}}}+\left({\displaystyle \frac{e_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}}{\sqrt{{\alpha }_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e},\mathrm{m}}}}}{d}_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}+3{\mathrm{\Gamma }}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}\right){\displaystyle \frac{d_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}{}^2}{{\alpha }_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e},\mathrm{m}}}}}{6\left({\mathrm{\Gamma }}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}+{\displaystyle \frac{e_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}}{\sqrt{{\alpha }_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e},\mathrm{m}}}}}{d}_{\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{d}\mathrm{e}}\right)}}\\ {\mathrm{\Gamma }}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}={\rho }_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}{C}_{p,\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}{d}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}\end{array}$$(5)

where subscripts of steel and oxide represent steel and oxide scale, respectively. The value of α_oxide,m was obtained from the values for the steel listed in Table 4 (where the heat capacity value used was that for mild steel²⁰⁾), the thermal effusivity of the oxide scale (e_oxide), the apparent thermal diffusivity of the sample (α_s) and the thickness of layers, as listed in Table 3. The derived values of α_oxide,m are also listed in Table 3. The thermal conductivity of the oxide scale (λ_oxide,m)was calculated from λ_oxide,m = e_oxide(α_oxide,m)^½; the results are also listed in Table 3.

The measured thermal diffusivity of oxide scale (α_oxide,m) would include the effect of boundary resistance between the oxide scale and the steel substrate, as suggested by Li et al.^7,10) The total heat resistance (R_total) is the sum of the heat resistance of the oxide scale itself and the boundary resistance, which can be expressed by   

$$\begin{array}{l}{R}_{\text{total}}=\frac{d_{\text{oxide}}}{{\lambda }_{\text{oxide},\text{m}}}\\ \mathrm{\hspace{1em}\hspace{1em}\hspace{0.17em}}=\frac{d_{\text{oxide}}}{{\lambda }_{\text{oxide}}}+R\end{array}$$(6)

where λ_oxide,m, λ_oxide, and R represent measured thermal conductivity of the oxide scale, the actual thermal conductivity of oxide scale, and the boundary resistance, respectively. Figure 9 shows the total heat resistance (R_total) derived from the measured thermal conductivity as a function of the oxide scale thickness based on Eq. (6). There is a good linear relation between the total heat resistance and the thickness of the oxide scale. A simple least-squares method shows the intercept to be a negative value, which is unreasonable for the heat resistance. Thus, the boundary resistance was considered to be negligibly small in the present study because the heat resistance of the oxide scales was substantially larger. Li et al.^7,10) reported the existence of boundary resistance from thermal diffusivity measurements for FeO and oxide scales formed on iron plates; their measurement conditions were almost the same as those used in the present study. However, Li et al.^7,10) used density data corresponding to perfectly stoichiometric FeO; they did not consider the nonstoichiometry of Fe_1−xO. By contrast, present study used the measured thermal effusivity for the oxide scale to derive the thermal diffusivity on the basis of Eq. (5). Thus, the thermal diffusivity and conductivity calculated in the present study are considered more reasonable, although estimating the effect of density on the thermal diffusivity/conductivity calculation in the study by Li et al.^7,10) is difficult. Further investigations will be required to elucidate the effect of density and the boundary resistance on the determination of thermal diffusivity. The average thermal conductivity of the oxide scale (λ_oxide) can be calculated to be 1.6 W m⁻¹ K⁻¹ from Fig. 9 by the least-squares method under the assumption that there is no boundary resistance and that the average thermal diffusivity of the oxide scale (α_oxide) is 4.0 × 10⁻⁷ m² s⁻¹.

Fig. 9.

Relation between the total heat resistance of oxide scale and the scale thickness.

4.2. Validity of Thermophysical Values Determination

As described in section 3.2, the sample used for the thermal effusivity measurement exhibited a limited thickness of the oxide scale, about 220 μm, and the analysis to obtain the thermal effusivity must use the data corresponding to heat diffusion only in the oxide scale layer. The heat diffusion distance (l_heat) is calculated as follows:   

$$l_{heat}=2\sqrt{{\alpha }_{\text{oxide}}t}$$(7)

The condition that the value of l_heat is equal to the thickness of the oxide scale layer gives a t^1/2 value of 0.17 s^1/2 with the thermal diffusivity value of 4.0 × 10⁻⁷ m² s⁻¹. This case is the same as that used in the determination of thermal effusivity (e.g., the results in Fig. 4). Thus, the values of the thermal effusivity/diffusivity are confirmed to be self-consistently determined in the present study.

The validity of the thermophysical properties derived in this study can also be discussed from the viewpoint of Fe_1−xO scale composition. Assuming that the oxide scale consisting only of Fe_1−xO (even though 5% of the oxide scale is actually Fe₃O₄), the density is determined to be 5720 kg m⁻³ from thermal conductivity and effusivity using the following equation:   

$$e_{\text{oxide}}=\sqrt{{\rho }_{\text{oxide}}{C}_{p,\text{oxide}}{\lambda }_{\text{oxide}}}$$(8)

where the value of C_p,oxide is 699 J kg⁻¹ K⁻¹.²³⁾ Given that Fe_1−xO has the rocksalt-type structure, the obtained density value indicates that the composition of Fe_1−xO is x = 0.051,²⁴⁾ which corresponds to Fe-51.5at%O. This composition confirms that the average composition was in the Fe_1−xO stable region at 900°C,²⁵⁾ which was the oxidation temperature used in this study.

4.3. Comparison with Reported Data

Table 5 compares the thermal diffusivity measured in the present study with those reported for Fe_1−xO and oxide scales at room temperature. The thermal diffusivity for the Fe_1−xO scale⁷⁾ and oxide scales^9,10) shows agreement with each other. The thermal diffusivity value measured for a bulk sample prepared from a melt²⁷⁾ and that estimated for no porosity²⁸⁾ also agree with the values obtained for scales. The thermal diffusivity calculated in the present study is the smallest among those for scales but is of the same order. The difference is caused by (i) the density of Fe_1−xO used in the calculation to derive the thermal diffusivity of Fe_1−xO or oxide scales via Eq. (5), where e_oxide was replaced by ${\rho }_{\text{oxide}}{C}_{p,\text{oxide}}\sqrt{{\alpha }_{\text{oxide},\text{m}}}$, (ii) the boundary resistance, which was discussed in section 4.1, and (iii) the constitution of the oxide scale; the larger ratio of the Fe₃O₄ layer resulted in greater thermal diffusivity because Fe₃O₄ has a greater thermal diffusivity. Also, the value in this study shows good agreement with those reported by Ohta et al.,²⁷⁾ who considers the nonstoichiometry of Fe_1−xO. As evident from the results in Figs. 5 and 8, the oxide scale in this study is dense; thus, the measured thermal diffusivity values are reasonably similar to that for the sample without porosity, whereas almost all of the sintered samples have smaller values because of their porosity.

Table 5. Thermal diffusivity of Fe_1−xO and oxide scale.

	α/10−7m2s−1	Sample	Authors
Fe1−xO	5.5	Scale formed on iron plate	Li et al.7)
	14	Sinter, 99.9% purity, porosity < 0.1%	Akiyama et al.26)
	1.8–2.3	Fired pellet produced from hematite ore with porosity = 51%
	1.5–2.3	Nonfired pellet produced from limestone ore with porosity = 44%
	1.0–2.0	Sinter prepared from mixed iron ore with porosity = 42%
		Melt and equilibrated under CO/CO2 mixture	Ohta et al.27)
	5.11±0.37	Fe0.89O
	3.31±0.09	Fe0.92O
	3.70±0.25	Fe0.95O
	6.7	Sinterd, after correction of porosity to be 0.	Slowik et al.28)
	26.9	Sinter	Takeda et al.29)
Oxide scale	5.9	Formed on iron by oxidation in air at 1173 K	Li et al.10)
	7.3	30%Fe3O4–70%FeO scale formed on heavy steel	Endo et al.9)
	4.0	Scale formed on ultra-low carbon steel	This study

From the aforementioned comparison, it could conclude that the method proposed in this study, i.e., where thermal diffusivity is determined both from the thermal effusivity of the oxide scale and from the apparent thermal diffusivity of the sample on the basis of Eq. (5), is valid for deriving the thermal diffusivity/conductivity of the oxide scale. This method also has advantages in that the Fe_1−xO composition and density do not need to be determined; by contrast, these values are required to estimate the thermal diffusivity more accurately by the previously applied method.^7,9,10) Furthermore, the method proposed in this study is considered to be applicable to more complex oxide scales because the required values are only the average value of thermal effusivity of the oxide scale, the apparent thermal diffusivity of the sample, and thicknesses of the oxide scale; analysis of the oxide scale structure is not necessary.

5. Conclusions

Thermal effusivity was measured for oxide scale formed on a steel plate by the transient hot-strip method for the determination of thermal diffusivity/conductivity of the oxide scale. The transient hot-strip method was confirmed by the measurement of silica glass; the measured value was 1.57 kJ m⁻² s^−1/2 K⁻¹ at room temperature, showing good agreement with that calculated using literature values corresponding room temperature. The thermal effusivity measurement was applied for the oxide scale, which was produced by the oxidation of ultra-low-carbon steel plate in air at 900°C for 3600 s. The determined thermal effusivity was 2.52 kJ m⁻² s^−1/2 K⁻¹.

The thermal diffusivity measurements were also conducted for steel plates oxidized in air at 900°C for 770–3600 s. The three-layered analysis for the apparent thermal diffusivity of a sample gave the thermal diffusivity of the oxide scale by inputting the measured value of the thermal effusivity. The thermal conductivity and the heat resistance of the oxide scale in the sample were also calculated, and no significant boundary resistance was found between the oxide scale and the steel plate. Finally, the thermal conductivity and diffusivity of the oxide scale were calculated to be 1.6 W m⁻¹ K⁻¹ and 4.0 × 10⁻⁷ m² s⁻¹, respectively, from the slope between the heat resistance and the thickness of the oxide scale.

The determined values suggested the oxide scale consists of Fe_0.949O as an average. This composition is in the Fe_1−xO stable region at 900°C, suggesting that a reasonable value was obtained with self-consistency. The measured value also shows good agreement with previously reported values for Fe_1−xO scale, oxide scales, and bulk nonporous Fe_1−xO.

Acknowledgments

This work has been conducted as one of the projects in Research Group II for “Investigation on Factors Controlling Heat Transfer Characteristics of Scales” in Rolling Theory Committee, The Iron and Steel Institute of Japan. The authors would like to express their appreciation to the members for useful advice. Grant for General Research and Development of Grant by the Amada foundation is also acknowledged, and the corresponding author thanks the foundation. The authors would like to thank enago (www.enago.jp) for the English language review.

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