Real-Time Temperature Prediction Model for Online Continuous Casting Control Using Simplified Boundary Condition Computing Method

Abstract

Numerical process modeling of continuous casting is increasingly applied to optimize production practices for higher product quality guarantees, in which real-time temperature prediction is the key factor that makes it possible to observe and optimize the solidification behavior of the continuous casting process. For offline simulations, the completeness of boundary conditions and accuracy of calculation are core concerns; as for online control, the stability of the model calculation and the correctness are equally important. This study demonstrates a process tracking and online control model of continuous casting based on IoT technology and proposes a simplified calculation method for secondary cooling boundary conditions. The proposed method calculates a comprehensive heat transfer coefficient based on offline simulated parameters and computes the total heat flux of a secondary cooling zone. The experimental results show that the temperature field calculated by this method is stable, and the difference between the actual measured temperature is within an acceptable range of 15 °C. The proposed method no longer requires an online model to consider four types of heat transfer boundary conditions, improving the versatility of the online model. The smoother surface temperature curve is beneficial for dynamic control of secondary cooling water. It can be an alternative method for implementing a more conducive online continuous casting model.

1. Introduction

Continuous casting (CC) is the most important process for steelmaking, accounting for more than 96% of steel products. It also reduces production costs and energy consumption and offers flexible operation [1]. The function of CC is to solidify liquid steel into solid slabs, providing intermediate materials for the next rolling. Due to the solidification process’s mechanical, thermal, and chemical nature and the metallurgical rules [2,3,4], the CC process is pretty complex. To indicate this, the main components of a CC process, shown in Figure 1, will be briefly introduced.

At the beginning of the process, molten steel in ladles is injected into an intermediate vessel (tundish). The tundish can be a buffer container for cast speed adjustment and floating inclusions in the steel, making multi-stand casting possible. The molten steel flows from the tundish, controlled by a stopper and enters the mold through the submerged nozzle (SEN). The mold consists of a water-cooling copper plate, which can quickly cool the molten steel and form a solidified shell, ensuring that the strand does not fracture after leaving the mold and can continue to be withdrawn downwards [5,6]. This process is also called primary cooling. Secondary cooling is carried out by applying water/air sprays to strands in several secondary cooling zones. It must be performed extremely carefully to ensure the cooling is smooth and prevent cracks.

For producing high-quality steel products, temperature control is crucial. Maintaining the temperature within a reasonable range is crucial for achieving constant temperature pouring and preventing issues like steel leakage [7,8]. Efficient and stable cooling, facilitated by proper temperature control, is key to ensuring the quality of slab formation and promoting the overall efficiency of the steelmaking process [9,10,11]. Moreover, temperature control is vital for preventing defects such as corner cracks in slabs, highlighting the significance of temperature management in quality control [12,13].

Due to the secondary cooling zone being a steam-filled spray chamber, the harsh environment makes it impossible to measure the casting strand’s temperature reliably. Models to predict temperature distribution and growth of the solidifying steel shell are necessary to optimize the production process for better quality steel casting products [14]. This study uses IoT technology to collect real-time production data, including the initial molten steel temperature, the casting speed, the cooling water volume of each cooling zone, cross-sectional dimensions, the molten steel composition, and other production data, to establish a heat transfer model to predict the surface and internal temperature distribution of the CC strand in real-time.

2. Related Work

Many models based on solidification heat transfer calculations have been proposed in recent decades. The main idea of these models is to establish a heat balance equation, calculate the heat removal of the mold and the secondary cooling zone, and compute the temperature distribution of the strand through finite difference and other methods [14,15]. The development of heat transfer models has provided valuable insights into the complex phenomena occurring in the CC process, enabling the optimization of process parameters and the mitigation of defects [16,17,18,19,20]. Ji et al. introduced a heat transfer model that considers distributed thermophysical properties to predict the solidification end accurately in wide/thick CC slabs [21]. Yang et al. and Ding et al. focused on transient thermo-fluid and solidification behaviors in the mold, incorporating heat transfer, multiphase flow, and mold oscillation phenomena, making the heat removal process more definable [22,23]. Bernhard et al. and Preuler, Lukas et al. analyzed various heat transfers during the mold and secondary cooling zone and simulated the boundary conditions of the cooling process [24,25]. However, due to the complexity of the boundary conditions in the model, if the calculation is strictly carried out according to the various types of boundary conditions, the temperature prediction data of the online model will fluctuate, which will cause fluctuations in the secondary cooling water, which may lead to surface cracks. Kong, Yiwen et al. proposed a method to average multiple heat transfer boundary conditions in the secondary cooling zone and achieve stable temperature prediction [26]. Liu, Daiwei et al. analyzed how the roll contact heat transfer calculation method influences the results of predicted slab surface temperature and shell thickness [27]. The above research reveals how to use models to simulate the solidification process and optimize the continuous casting process parameters, especially how to improve the accuracy of temperature prediction by accurately simulating different types of boundary conditions, as well as the heat transfer boundary condition averaging method used by the online model to avoid temperature fluctuations. This study proposes an alternative boundary condition calculation method using a nonlinear programming algorithm based on offline simulated cooling parameters, which can eliminate the fluctuations in temperature calculation and is more suitable for application in online control circumstances.

3. Methods

3.1. On-Site Data Perception

To create an online control system, the model was connected to a Level 1 automation control system [28] which was mainly composed of programmable controllers (PLCs) and several kinds of sensors. The model mainly needed pipeline electromagnetic flowmeters to measure the flow of mold cooling water and each secondary cooling water circuit, a continuous temperature measurement device for molten steel in tundish to observe the change in the temperature during the casting process as the initial condition for the model calculation, position coders to track the casting length and casting speed, and water flow regulating valves to control the cooling water flow of each circuit according to the model optimization. Then, these parameters’ sensors, position encoders, and temperature sensors were connected to PLCs with IO modules, and the PLC was connected to the model system through an OPC server. Therefore, the model could obtain on-site data, which mainly included casting speed, cast length, liquid steel temperature, and cooling water volume for each circuit, making online calculation of the process possible, and could also send an optimized data set to the PLCs. The architecture of the online control model system is shown in Figure 2 and the main parameters of the sensors are listed in

Table 1. Main parameters of the sensors.

Sensors/Devices	Accuracy	Signal/Parameter Range	Reading Frequency	Writing Frequency
Electromagnetic flowmeters for cooling water	±0.5%	4~20 mA DC	1 s
Temperature sensor for cooling water	±0.05 °C	10–65 °C	1 s
Temperature measurement device for molten steel	±2 °C	800–1650 °C	1 s
Position coders	-	-	1 s
Water flow regulating valves	±0.5%	4~20 mA DC		3 s

.

3.2. Heat Transfer Model

A heat transfer model was the basis for online temperature field prediction, and an “equal thickness slice unit” was used to calculate the temperature field of the casting strand. The whole strand was discretized in time and space for the needs of finite element calculations, as shown in Figure 3. The numerical discrete solution was performed dynamically for each slice in the computational space, and the temperature information of all slice units was periodically tracked to achieve online simulation of the three-dimensional temperature field.

3.2.1. Heat Conduction Equation

The heat transfer behavior with the phase change of the model was determined by the heat conduction control equation:

$$\rho \cdot c_{eff}\cdot {\displaystyle \frac{\partial T}{\partial t}}={\displaystyle \frac{\partial }{\partial x}}\left({\lambda }_{eff}\cdot {\displaystyle \frac{\partial T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left({\lambda }_{eff}\cdot {\displaystyle \frac{\partial T}{\partial y}}\right)$$

(1)

where $\rho$ is the steel’s density, kg/m³; T is the temperature, °C; $x$ is the distance from the slab center along the width direction, m; $y$ is the distance from the slab center from the thickness direction, m; $c_{eff}$ is the effective specific heat, J/(kg·°C); and ${\lambda }_{eff}$ is the effective thermal conductivity, J/(m·S·°C).

The equation’s solution should specify the strand surface’s boundary conditions. Next, we will discuss the initial and boundary conditions of the cooling strand.

3.2.2. Initial Condition

When new molten steel is poured into the mold, we can consider that a new slice is generated in the slice space. At the moment τ = 0, the heat flux at both the width and thickness directions is zero. The initial condition of the slice unit of the strand is just the temperature of the molten steel. We can obtain

$${T\left(x,y,\tau \right)|}_{\tau =0}=T_m$$

(2)

where $T_m$ is the temperature of molten steel, °C and τ is time, s.

During the calculation process, the slice unit is assumed to move with the casting speed, and the corresponding cooling boundary conditions are determined according to the slice position.

3.2.3. Boundary Condition

• Boundary conditions in mold

The high-temperature molten steel gradually solidifies to form a slab shell with a certain thickness under the intense cooling of the water-cooled copper plate in the mold. The study uses a square root formula to determine the distribution of heat in a mold [29]:

$$q_m=k\left(A-B\cdot \sqrt{t}\right)$$

(3)

where $q_m$ is the heat flux between the strand shell and mold, w/m²; $k$ is the heat flow density correction coefficient, which is generally 0.8~1.2 based on different steel grades; $A$ and $B$ are coefficients determined by the characteristics of the CC machine; and $t$ is the duration time in the mold, s.

2.

Boundary conditions in secondary cooling zones

Heat removal in secondary cooling occurs through spray water impact, roller contact, radiation, and water accumulation evaporation. These four types of heat transfer can be distinguished between two support rollers on the slab’s surface. Due to the different intensities of each cooling method, the surface of the ingot usually experiences rapid cooling and a temperature increase, as shown in Figure 4a. The distribution of these four cooling types in the width and casting directions is related to factors such as nozzle arrangement, casting machine structure, roller array, and differences in the area between the two gap rollers, as shown in Figure 4b. Spray water impact cooling is also related to the nozzle performance and cooling intensity. The amount of heat withdrawal of each cooling type is calculated as listed in

Table 2. Calculation of heat transfer in secondary cooling zone.

Type	Heat Transfer by	Calculation Method
1	Roll contact	$\mathrm{11,513.7}{T_{surf}}^{-0.76}{V_c}^{-0.20}(\alpha {)}^{-0.17}$
2	Radiation	$a\cdot \delta \cdot \left[{\left(T_{surf}+273.15\right)}^4-{\left(T_{envi}+273.15\right)}^4\right]$
3	Spray water	$f_{sp}\cdot 1570\cdot W^{0.55}\cdot \left(1-0.0075\cdot Tw\right)$
4	water accumulation evaporation	$(1+F)q_{rad}$

.

where $T_{surf}$ is the surface temperature of the slab, °C; $V_c$ is the casting speed, m/min; α is the angle corresponding to the arc length of the contact part between the roller and the slab surface$;T_{envi}$ is the ambient temperature, °C; a is the blackness coefficient of the slab surface, which is taken as 0.85 in this article; δ is the Stefan Boltzmann constant, which is 5.67 × 10⁻⁸ W/(m²·K⁴); $f_{sp}$ is the spray coefficient describing the cooling effect of the secondary cooling water, where its specific value depends on the structural characteristics of the secondary cooling zone; W is the water flow density, L/(m²$\cdot$s), where the formula is based on the empirical model of Nozaki [30]; $Tw$ is the cooling water temperature, °C; and the value of the adjustment factor $F$ is related to the accumulation and evaporation of the nozzle water.

For the offline model, simulation of the above four boundary heat transfers is necessary to help the model make accurate temperature predictions. But for the online model, there are two consequences if we strictly follow these four cooling methods to calculate the heat transfer boundary conditions. Firstly, it increases the difficulty of calculation and reduces the model’s versatility; numerous geographic parameters need to be inputted, such as the parameters of each row of nozzles, their installation position, their distance from the strand, and the distance of each roller from the meniscus; and numerous cooling parameters need to be determined, making the online model too difficult to implement. Secondly, the calculated surface temperature fluctuates. The simulation calculation of the four cooling methods acting alternately on the surface of the strand will cause uneven cooling, which leads to surface temperature fluctuates and can be seen in the surface temperature curves of many simulation models [25,27]. For the online control model, since the calculation of the secondary cooling water volume is based on the difference between the calculated surface temperature and the set temperature, the fluctuation in surface temperature will cause frequent fluctuations in the cooling water volume; this will cause unexpected frequent thermal state changes in the strand, which is very harmful to the quality of products.

In actual production, the cooling intensity is often adjusted according to the needs of different steel grades. Among the above four cooling methods, the most prominent change in cooling state is caused by the change in cooling water, while the other three cooling factors are relatively small. This study proposes a comprehensive thermal heat transfer coefficient based on cooling spray water, considering the heat transfer of the other three methods and applying the effects of those methods to the spray water flow rate in a parameter manner. If we consider the comprehensive cooling coefficient as a function of water flow density, we can obtain:

$${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i=f\left(W^i\right)$$

(4)

where ${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i$ is the target value of comprehensive coefficient of secondary cooling zone $i$, and $W^i$ is the cooling water flow density of secondary cooling zone $i$.

To simplify this, this study employs a quadratic function as the following regression formula to calculate the ${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i$:

$${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i=A_h\cdot {\left(W^i\right)}^2+B_h\cdot W^i+C_h$$

(5)

In order to determine the values of parameters $A_h$, $B_h$, and $C_h$ in the online control model, we can simulate the four boundary heat transfers in Table 1 under main working casting speeds (0.8–1.5 m/min) in the offline model, calculate the total amount of heat flux of each secondary cooling zone at each speed, and then calculate the comprehensive thermal heat transfer coefficient of each casting speed of each secondary cooling zone based on the total heat transfer and water flow density, as follows:

$${CompS}_j^i=h_j^i\cdot {1570}^{-1}\cdot {w_j^i}^{-0.55}\cdot {(1-0.0075Tw)}^{-1}$$

(6)

where ${CompS}_j^i$ is the simulated value of the comprehensive coefficient of secondary cooling zone $i$ under casting speed j, $h_j^i$ is the total amount of heat flux of zone $i$ under casting speed j, $w_j^i$ is the cooling water flow density of secondary cooling zone $i$ under casting speed j, and $Tw$ is the temperature of cooling water.

For each comprehensive heat transfer coefficient ${CompS}_j^i$ obtained by simulation under typical casting speed j of zone $i$, a set of parameters $A_h$, $B_h$, and $C_h$ needs to be found to minimize the difference between ${CompT}_j^i$ and ${CompS}_j^i$. The objective function is

$$\sum _{j=1\dots n}\left[A_h\cdot {\left(W_j^i\right)}^2+B_h\cdot W_j^i+C_h-{CompS}_j^i\right]=0$$

(7)

To generalize the problem of solving linear programming to problems with nonlinear objective functions, the Generalized Reduced Gradient (GRG) is one of the most popular methods used to solve problems of nonlinear optimization [31]. The method uses gradient-based optimization, where derivatives of the objective function with respect to decision variables are computed to find the direction that improves the objective function. We will use experimental data as an example to demonstrate the solving process.

Given the $A_h$, $B_h$, and $C_h$ coefficient of each zone, we can calculate the heat flux of each zone in the online model as

$$h_{tot}^i=\left[A_h\cdot {\left(W^i\right)}^2+B_h\cdot W^i+C_h\right]\cdot 1570\cdot {W^i}^{0.55}\left(1-0.0075\cdot Tw\right)$$

(8)

where $h_{tot}^i$ is the heat flux of zone $i$, w/(m²·°C); ${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^i$ is the comprehensive thermal heat transfer coefficient of zone $i;$ $W^i$ is the cooling water flow density of secondary cooling zone $i$; and $Tw$ is the cooling water temperature, °C.

Since $A_h$, $B_h$, and $C_h$ are calculated by fitting the comprehensive heat transfer coefficient under several typical casting speeds, the total heat flux calculated by these parameters in the online model is at the same level as the total heat flux calculated using the four heat transfer boundaries when the offline model is used. After this simplification, the online model no longer needs to consider the specific four boundary heat transfers, which is more conducive to the online implementation.

3.2.4. Solution of the Model

From the meniscus of the mold to the end of the model tracking position (the exit of secondary cooling), the strand is discretized into n slice units of limited thickness that move synchronously with the casting strand. Taking 1/4 of the area of the slice unit as the research object, this area of each slice unit is divided into uniform grids, as shown in Figure 5. A limited number of grid discrete nodes are used to replace the continuous points in the entire area. Then, each node is numerically solved to obtain the temperature field information.

We adopt the explicit finite difference method to discretize the differential equation of the heat transfer model. According to the Taylor series, we have

$${\displaystyle \frac{\partial T_{i,j}^k}{\partial x}}\approx {\displaystyle \frac{∆T_{i,j}^k}{∆x}}={\displaystyle \frac{T_{i+1,j}^k-T_{i,j}^k}{∆x}}$$

(9)

$${\displaystyle \frac{\partial T_{i,j}^k}{\partial y}}\approx {\displaystyle \frac{∆T_{i,j}^k}{∆y}}={\displaystyle \frac{T_{i+1,j}^k-T_{i,j}^k}{∆y}}$$

(10)

$${\displaystyle \frac{{\partial }^2{T}_{i,j}^k}{\partial x^2}}\approx {\displaystyle \frac{\partial }{\partial x}}\left({\displaystyle \frac{T_{i+1,j}^k-T_{i,j}^k}{∆x}}\right)\approx {\displaystyle \frac{T_{i+1,j}^k-{2T}_{i,j}^k+T_{i-1,j}^k}{∆x^2}}$$

(11)

$${\displaystyle \frac{{\partial }^2{T}_{i,j}^k}{\partial y^2}}\approx {\displaystyle \frac{\partial }{\partial y}}\left({\displaystyle \frac{T_{i,j+1}^k-T_{i,j}^k}{∆y}}\right)\approx {\displaystyle \frac{T_{i,j+1}^k-{2T}_{i,j}^k+T_{i,j-1}^k}{∆y^2}}$$

(12)

$${\displaystyle \frac{\partial T_{i,j}^k}{\partial \tau }}\approx {\displaystyle \frac{∆T_{i,j}^k}{∆\tau }}={\displaystyle \frac{T_{i+1,j}^k-T_{i,j}^k}{∆\tau }}$$

(13)

Substituting Formulas (11)–(13) into Formula (1) and discretizing them, ignoring the truncation error, we can obtain the differential equation corresponding to the internal nodes of labels (i, j) in Figure 5 as

$$\begin{gathered} T_{i,j}^{k+1}=T_{i,j}^k+{\displaystyle \frac{{\lambda }_{eff}∆\tau }{c_{eff}\rho }}\left[{\displaystyle \frac{{(T}_{i+1,j}^k-T_{i,j}^k)-(T_{i,j}^k-T_{i-1,j}^k)}{∆x^2}} \\ +{\displaystyle \frac{{(T}_{i,j+1}^k-T_{i,j}^k)-(T_{i,j}^k-T_{i,j-1}^k)}{∆y^2}}\right] \end{gathered}$$

(14)

where $T_{i,j}^k$ is the temperature of node (i, j) at time k; ∆x is the space step in the width direction of the slab.

During the dynamic tracking process of the entire slice unit, each grid node in every slice unit needs to be numerically solved in every tracking cycle. The temperature field calculation results of the entire casting machine are obtained by integrating the dynamically updated and tracked temperature of all slice units.

4. Experimentation and Field Application

The model is applied to a CC production line of a steel manufacturing company. The CC machine has 10 secondary cooling zones; its main parameters are shown in

Table 3. The parameters of the casting machine.

Items	Unit	Values
Radius of the machine	m	9.5
Number of strands		2
Slab width	mm	1200–1800
Slab thickness	mm	230
Length of caster	m	34.545
Length of each secondary cooling zone	mm	Zone 1: 540; Zone 2: 948; Zone 3: 2208; Zone 4: 1855; Zone 5: 1855; Zone 6: 3871; Zone 7: 4017; Zone 8: 4215; Zone 9: 6300; Zone 10: 7666
Casting speed	m/min	0.7–1.5

. We tested the model when producing Q345B steel; the composition data are shown in

Table 4. Chemical composition of the Q345B steel.

Composition	C	S1	Mn	P	S	Ni	Cr	N	Ti
Mass fraction (%)	0.15	0.30	1.35	0.02	0.003	0.02	0.06	0.004	0.012

. The real-time data of molten steel temperature, casting speed, cooling water of the mold, and cooling water volume of each cooling zone were connected from the site. We first used four boundary heat transfer methods in the offline simulation program to calculate the water flow density and total heat flux of each zone (zone1–zone10) at different casting speeds (0.8 m/min, 1.0 m/min, 1.2 m/min, 1.4 m/min). Then, according to Formula (6), the comprehensive heat transfer coefficient of each secondary cooling zone at four casting speeds was calculated. The water flow density and comprehensive cooling parameters of zones 1–10 under different cast speeds are shown in Figure 6. Then, according to the objective function of Formula (6), the GRG algorithm in Excel was used to calculate the $A_h$, $B_h$, and $C_h$, so that the comprehensive heat transfer coefficient ${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i$ calculated by these parameters at various casting speeds in secondary cooling zone $i$ can be very close to the offline simulated ${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{S}}^i$. The $A_h$, $B_h$, and $C_h$ parameters of the comprehensive thermal heat transfer coefficient, as well as the error between the comprehensive heat transfer coefficient calculated by the offline simulation and calculated online in each cooling zone (${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{S}}^i$-${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i$), are listed in

Table 5. The $A_h$, $B_h$, and $C_h$ parameters of comprehensive thermal heat transfer coefficient in each cooling zone.

Zone	1	2	3	4	5	6	7	8	9	10
$A_h$	−0.0004	0	0.0001	−0.0003	−0.0004	−0.0013	−0.0094	−0.0102	−0.0197	0.1373
$B_h$	0.038	0.0114	0.0131	0.0570	0.0397	0.0647	0.1697	0.2190	0.2319	0.1995
$C_h$	−0.3208	−0.1799	−0.1484	−0.2383	−0.1870	−0.2016	−0.3245	−0.0557	−0.2741	−0.5919
${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{S}}^i$-${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{T}}^i$	0.071	0.049	0.015	0.003	0.006	0.003	0.029	0.016	0.018	0.021

.

The model predicted the temperature distribution inside the strand and its solidification thickness in real-time, as shown in Figure 7. A comparison of the surface temperature of the strand calculated by the comprehensive heat transfer coefficient calculation method and the surface temperature calculated by the four boundary heat transfer methods in the offline simulation is shown in Figure 8. We can learn that the surface temperature curves computed using the four boundary heat transfer methods rapidly drop in temperature due to rapid heat transfer near the roller and in the water spray coverage area, and the surface temperature rises quickly in the rest of the area. There have been significant fluctuations in the temperature curve, while the comprehensive heat transfer coefficient calculation method ignores these cooling change details and eliminates surface temperature fluctuations. Since the total heat flux of each zone calculated by the two methods is consistent, the temperature drop trend of the two curves is consistent. The calculation method using a comprehensive heat transfer coefficient is very beneficial for the dynamic control of secondary cooling water because the water volume is calculated based on this smooth surface temperature.

We used an Optris P20 portable non-contact infrared thermometer (Berlin, Germany) to measure the temperature of five different positions selected in the width direction of the slab at the exit of the secondary cooling zone. The temperature measuring range of the thermometer is 650–1800 °C, the measuring accuracy is ±(0.3%$\cdot T_{measure}$+ 2 °C), and the resolution is 1 °C. Each measurement position is measured 6 times, and each time will detect 30 s continuously. The maximum value during the period is taken as the measurement result to reduce the impact of the iron oxide scale on the surface of the slab. The measurement data for each time are shown in

Table 6. The measured temperature of each time and the model-predicted temperature.

Item	Pos 1	Pos 2	Pos 3	Pos 4	Pos 5
Distance from center (mm)	0	100	350	630	750
Test time1 (°C)	861	866	862	866	817
Test time2 (°C)	860	870	853	857	814
Test time3 (°C)	866	862	858	860	810
Test time4 (°C)	865	864	860	871	820
Test time5 (°C)	871	867	868	869	813
Test time6 (°C)	868	872	861	858	814
Average of tested (°C)	865	867	860	864	815
Model-predicted temperature (°C)	879	875	869	871	820

. The average value of the six measurements is used as the final test temperature of each position and compared with the model calculation results. As shown in Figure 9, the deviation between the model calculation and the actual measurement data is less than ±15 °C.

5. Conclusions

This work presents a temperature prediction model by solving the heat transfer model using a simplified boundary condition computing method. It proposes a method to improve the stability of temperature calculation in an online continuous slab casting model. An online process tracking control model of CC was achieved based on IoT technology. The calculation of heat removal of different heat transfer types in the mold and secondary cooling zones is analyzed. A simplified comprehensive heat transfer coefficient is proposed and calculated based on offline simulated parameters to meet the online control’s requirements for temperature calculation stability and improve the versatility of the online model. The experimental results show that the temperature field calculated by this method is stable, and the difference between the actual measured temperature is within an acceptable range of 15 °C. Although this boundary calculation method in the online model simplifies the boundary condition calculation, it should be based on offline simulation parameters. The final accuracy of the model is limited by the accuracy of the physical property parameters related to the steel grade simulated in the online model. The set of parameters ($A_h$, $B_h$, and $C_h$) in the study applies to the steel grade group; if the steel grade group changes, the parameters need to be refitted based on the calculation of the offline simulation. Different steel grades in the same steel grade group do not require one to recalculate the parameters because their thermal and physical properties are similar. Future research may focus on the following: (1) Optimizing the heat transfer calculation of the mold and reduce strand temperature fluctuations at the exit of the mold. The mold heat removal calculation method adopted in this study was empirical Formula (3), which resulted in a fluctuation of about 25 °C in some calculation circles, which affected the temperature calculation of second cooling zone 1 and zone 2. The method of calculating heat flux based on the volume and temperature difference in the mold cooling water may be more reliable. (2) Machine learning-based heat transfer boundary condition calculations for various steel types to replace the GRG algorithm in this study. (3) Other averaging methods for these four heat transfer types in secondary cooling zones to make the online calculation of temperature more accurate and stable.