A method and system for reducing w-type solidification-segregation phenomena in slabs

By building a nozzle testing system for the secondary cooling section and a coupled heat transfer-mass transfer-solidification model, the W-shaped solidification-segregation problem caused by uneven transverse cooling during slab continuous casting was solved, achieving efficient and accurate nozzle arrangement optimization and improving the quality of the cast slab.

CN116702565BActive Publication Date: 2026-07-21UNIV OF SCI & TECH BEIJING
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
UNIV OF SCI & TECH BEIJING
Filing Date
2023-07-20
Publication Date
2026-07-21

AI Technical Summary

Technical Problem

In the existing technology for continuous casting of slabs, uneven lateral cooling leads to differences in the solidification sequence of molten steel in the centerline region of the slab, resulting in a W-shaped solidification-segregation phenomenon. Furthermore, traditional trial-and-error methods are costly, slow to take effect, and cannot quantitatively control the quality of the cast slab.

Method used

A cold-state performance testing system for the nozzles in the second cooling section was built. The water flow density distribution was recorded, histograms were plotted and fitted, and a heat transfer-mass transfer-solidification coupling model was established based on the heat transfer coefficient formula. The appropriate nozzle arrangement was determined through model calculation to reduce segregation.

Benefits of technology

By predicting slab temperature and solute distribution through numerical models, accurate nozzle arrangement guidance can be provided, reducing slab W-type solidification-segregation and improving the efficiency of slab quality control.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present application belongs to the field of metallurgical continuous casting technology, and specifically relates to a method and system for reducing slab w-type solidification-segregation phenomenon based on transverse cooling non-uniformity, which tests the performance of nozzles arranged in different modes in the secondary cooling section, records the results of water flow density distribution, draws a water flow density distribution histogram using the results of water flow density distribution, and obtains a fitting curve through data fitting; in combination with the fitting curve, the cooling water volume of each zone in the secondary cooling section, the length of each zone, and an empirical formula of heat exchange coefficient, a correlation between the heat exchange coefficient of the wide face and the narrow face of the slab changing with position and time is established and loaded to the wide face and the narrow face of the established slab continuous casting full-process heat transfer-mass transfer-solidification coupling model for calculation; by comparing the temperature distribution, solute distribution, carbon segregation index and other information obtained by analyzing the calculation results of the model, a suitable nozzle arrangement mode in the secondary cooling section is determined, and the present application can reduce the slab w-type solidification-segregation phenomenon, which is of great significance to slab quality control.
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Description

Technical Field

[0001] This invention belongs to the field of metallurgical continuous casting technology, specifically relating to an optimized method and system for reducing the W-shaped solidification-segregation phenomenon in slabs, and more specifically, relating to a method and system for reducing the W-shaped solidification-segregation phenomenon in slabs based on lateral cooling non-uniformity. Background Technology

[0002] The uniformity of transverse cooling on the wide and narrow faces of a slab during continuous casting affects its solidification process, solidification structure, and solute transport. Due to the large cross-sectional dimensions of the slab and differences in the type and arrangement of nozzles in the secondary cooling section, transverse cooling on the wide and narrow faces is uneven. This leads to differences in the order of solidification of molten steel in the centerline region of the slab, with the transverse 1 / 8 of the slab solidifying last. The end of the liquid phase cavity in the slab is mostly "W"-shaped. Due to solidification shrinkage and lack of molten steel feeding, the last solidified area exhibits severe central porosity and central segregation. The type, arrangement, and atomization effect of the nozzles in the secondary cooling section directly affect the uniformity of transverse cooling on the wide and narrow faces of the slab. To improve the problem of W-shaped solidification and segregation in the slab, industrial tests are generally conducted by adjusting the nozzle arrangement and parameters. The effectiveness of the nozzle adjustment measures is then determined based on the final slab inspection results. This trial-and-error approach to industrial testing is costly, slow to produce results, and wastes a great deal of resources. Furthermore, it cannot quantify and combine information on the lateral cooling of the slab and the solidification process of the molten steel. Therefore, predicting and monitoring the relationship between lateral cooling non-uniformity and the solidification process and slab quality is of great significance for reducing the W-shaped solidification-segregation phenomenon in slabs and for controlling the quality of cast slabs. Summary of the Invention

[0003] To address the problems existing in the prior art, the main objective of this invention is to propose a method and system for reducing the W-shaped solidification-segregation phenomenon in slabs based on the non-uniformity of transverse cooling.

[0004] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0005] A method for reducing W-type solidification-segregation in slabs based on transverse cooling non-uniformity includes the following steps:

[0006] S1. Construct a cold-state performance testing system for the nozzles in the second cooling section;

[0007] S2. Test the nozzle performance of different arrangement methods in the secondary cooling section and record the results of water flow density distribution;

[0008] S3. Using the results of the water flow density distribution, draw a histogram of water flow density distribution and perform data fitting to obtain a fitted curve;

[0009] S4. By combining the fitted curve, the cooling water volume of each zone of the secondary cooling section, the length of each zone of the secondary cooling section, and the empirical formula for the heat transfer coefficient of the secondary cooling section, the correlation between the heat transfer coefficients of the wide and narrow sides of the slab and the changes in position and time is established.

[0010] S5. Establish a coupled heat transfer-mass transfer-solidification model for the entire process of slab continuous casting. After loading the correlation of the above heat transfer coefficients onto the wide and narrow planes of the model, start the model for calculation.

[0011] S6. Analyze the temperature distribution, solute distribution, carbon segregation index and other information in the continuous casting process using the results of model calculations. Compare the temperature distribution, solute distribution and carbon segregation index and other information in the continuous casting process to determine the appropriate nozzle arrangement in the secondary cooling section and reduce the solidification-segregation phenomenon of the slab W-type solidification.

[0012] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slab w-shaped solidification based on the lateral cooling non-uniformity described in this invention, in step S1, the testing system includes a water supply system, an air compression and conveying device, a testing platform, a control system, and a storage system.

[0013] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slabs based on transverse cooling non-uniformity according to the present invention, in step S2, the arrangement includes nozzle type and test parameters.

[0014] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slab w-shaped solidification based on the lateral cooling non-uniformity described in this invention, in step S2, the test system automatically records the result of water flow density distribution and transmits the result of water flow density distribution to the storage system.

[0015] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slab W-shaped based on the non-uniformity of transverse cooling described in this invention, in step S3, the result of water flow density distribution is exported from the storage system and imported into Origin software to draw a water flow density distribution histogram and perform data fitting to obtain a fitting curve, requiring a fitting degree R value greater than 0.95.

[0016] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slabs based on transverse cooling non-uniformity according to the present invention, in step S4, the correlation between the heat transfer coefficients of the wide and narrow faces of the slab as a function of position and time is established in Visual Studio software.

[0017] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slab w-type based on lateral cooling non-uniformity described in this invention, in step S5, a heat transfer-mass transfer-solidification coupling model of the entire continuous casting process of slab is established using Ansys software. The model is built using a Cartesian coordinate system, with X and Z corresponding to the wide and narrow faces of the slab, respectively, and Y being the casting direction. A hexahedral mesh is used for meshing. After loading the correlation of the heat transfer coefficients mentioned above onto the wide and narrow faces of the model through a subroutine of Ansys software, the model is started for calculation.

[0018] As a preferred embodiment of the method for reducing the solidification-segregation phenomenon of slab w-type based on the non-uniformity of transverse cooling described in this invention, in step S6, the results of the model calculation are imported into Tecplot software to analyze information including temperature distribution, solute distribution, and carbon segregation index during the continuous casting process.

[0019] To solve the above-mentioned technical problems, according to another aspect of the present invention, the present invention provides the following technical solution:

[0020] A control system for implementing the above-described method for reducing W-type solidification-segregation in slabs based on lateral cooling non-uniformity.

[0021] An information data processing terminal for implementing the above-mentioned method for reducing the W-type solidification-segregation phenomenon of slabs based on lateral cooling non-uniformity.

[0022] A computer-readable storage medium includes instructions that, when executed on a computer, cause the computer to perform the above-described method for reducing W-type solidification-segregation of slabs based on lateral cooling non-uniformity.

[0023] The beneficial effects of this invention are as follows:

[0024] This invention proposes a method and system for reducing W-shaped solidification-segregation in slabs based on lateral cooling non-uniformity. By constructing a cold-state performance testing system for the nozzles in the secondary cooling section, the performance of nozzles with different arrangements in the secondary cooling section is tested, and the water flow density distribution is recorded. A water flow density distribution histogram is plotted using the results, and data fitting is performed to obtain a fitting curve. Combining the fitting curve, the actual cooling water volume in each zone of the secondary cooling section, the actual length of each zone in the secondary cooling section, and the empirical formula for the heat transfer coefficient of the secondary cooling section, the correlation between the heat transfer coefficients of the wide and narrow faces of the slab and their changes with position and time is established. This correlation is then applied to the wide and narrow faces of the established slab continuous casting full-process heat transfer-mass transfer-solidification coupled model, and the model is started for calculation. By comparing and analyzing the temperature distribution, solute distribution, carbon segregation index, and other information obtained during the continuous casting process using the model calculation results, a suitable nozzle arrangement in the secondary cooling section is determined. This invention can reduce the W-shaped solidification-segregation phenomenon in slabs and is of great significance for controlling the quality of cast slabs. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the nozzle arrangement in the second cooling section according to arrangement method 1 of embodiment 1 of the present invention;

[0027] Figure 2 The histogram and fitted curve of water flow density distribution in arrangement mode 1 of Embodiment 1 of the present invention;

[0028] Figure 3 The carbon segregation index on the center line of the slab after solidification in arrangement method 1 of embodiment 1 of the present invention;

[0029] Figure 4 This is a schematic diagram of the nozzle arrangement in the second cooling section of embodiment 1 of the present invention;

[0030] Figure 5 The histogram and fitted curve of water flow density distribution in arrangement mode 2 of Embodiment 1 of the present invention;

[0031] Figure 6 The carbon segregation index on the center line of the slab after solidification in arrangement method 2 of embodiment 1 of the present invention;

[0032] Figure 7 This is a schematic diagram of the nozzle arrangement in the second cooling section of arrangement method 3 in Embodiment 1 of the present invention;

[0033] Figure 8 The histogram and fitted curve of water flow density distribution in arrangement mode 3 of Embodiment 1 of the present invention;

[0034] Figure 9 The carbon segregation index on the center line of the slab after solidification in arrangement method 3 of embodiment 1 of the present invention.

[0035] In the diagram, 1-secondary cooling section nozzle, 2-slab, 3-wide face, 4-narrow face.

[0036] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0037] The technical solutions described below in conjunction with the embodiments will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] The main objective of this invention is to propose a method and system for reducing the W-shaped solidification-segregation phenomenon in slabs based on the non-uniformity of transverse cooling. This addresses the problem that previous cold-state performance tests of nozzles in the secondary cooling section only provided quantitative information on the relationship between nozzle type, arrangement, atomization effect, and water flow density distribution. This invention establishes a heat transfer-mass transfer-solidification coupled model, combining nozzle performance, operating state, slab temperature distribution, and solute distribution. By integrating the aforementioned quantitative relationships with a numerical model and incorporating the actual water flow density distribution and heat transfer coefficient into the numerical model, the solidification process can be calculated, allowing for more accurate prediction of slab temperature and solute distribution. This provides guidance for adjusting the nozzle arrangement, which is beneficial for reducing the W-shaped solidification-segregation phenomenon in slabs and is of great significance for controlling the quality of cast slabs.

[0039] According to one aspect of the present invention, the present invention provides the following technical solution:

[0040] A method for reducing W-type solidification-segregation in slabs based on transverse cooling non-uniformity includes the following steps:

[0041] S1. Construct a cold-state performance testing system for the nozzles in the second cooling section;

[0042] S2. Test the nozzle performance of different arrangement methods in the secondary cooling section and record the results of water flow density distribution;

[0043] S3. Using the results of the water flow density distribution, draw a histogram of water flow density distribution and perform data fitting to obtain a fitted curve;

[0044] S4. By combining the fitted curve, the actual cooling water volume of each zone of the secondary cooling section, the actual length of each zone of the secondary cooling section, and the empirical formula for the heat transfer coefficient of the secondary cooling section, the correlation between the heat transfer coefficients of the slab wide and narrow surfaces as a function of position and time is established.

[0045] S5. Establish a coupled heat transfer-mass transfer-solidification model for the entire process of slab continuous casting. After loading the correlation of the above heat transfer coefficients onto the wide and narrow planes of the model, start the model for calculation.

[0046] S6. Analyze the temperature distribution, solute distribution, carbon segregation index and other information in the continuous casting process using the results of model calculations. Compare the temperature distribution, solute distribution and carbon segregation index and other information in the continuous casting process to determine the appropriate nozzle arrangement in the secondary cooling section and reduce the solidification-segregation phenomenon of the slab W-type solidification.

[0047] Preferably, in step S1, the testing system includes a water supply system, an air compression and delivery device, a testing platform, a control system, and a storage system.

[0048] Preferably, in step S2, the arrangement includes nozzle type and test parameters.

[0049] Preferably, in step S2, the testing system automatically records the results of the water flow density distribution and transmits the results of the water flow density distribution to the storage system.

[0050] Preferably, in step S3, the results of the water flow density distribution are exported from the storage system and imported into Origin software to draw a histogram of water flow density distribution, and the data is fitted to obtain a fitting curve, requiring a fitting degree R value greater than 0.95.

[0051] Preferably, in step S4, the correlation between the heat transfer coefficients of the wide and narrow surfaces of the slab as a function of position and time is established in Visual Studio software.

[0052] Preferably, in step S5, a heat transfer-mass transfer-solidification coupled model of the entire slab continuous casting process is established using Ansys software. The model is built using a Cartesian coordinate system, with X and Z corresponding to the wide and narrow faces of the slab, respectively, and Y representing the casting direction. A hexahedral mesh is used for meshing. The correlation of the heat transfer coefficients mentioned above is loaded into the wide and narrow faces of the model through a subroutine (User Defined Function, UDF) of Ansys software, and then the model is started for calculation.

[0053] Preferably, in step S6, the results of the model calculation are imported into Tecplot software to analyze information such as temperature distribution, solute distribution, and carbon segregation index during the continuous casting process.

[0054] According to another aspect of the present invention, the present invention provides the following technical solution:

[0055] A control system for implementing the above-described method for reducing W-type solidification-segregation in slabs based on lateral cooling non-uniformity.

[0056] An information data processing terminal for implementing the above-mentioned method for reducing the W-type solidification-segregation phenomenon of slabs based on lateral cooling non-uniformity.

[0057] A computer-readable storage medium includes instructions that, when executed on a computer, cause the computer to perform the above-described method for reducing W-type solidification-segregation of slabs based on lateral cooling non-uniformity.

[0058] The technical solution of the present invention will be further described below with reference to specific embodiments.

[0059] Example 1

[0060] A method for reducing W-type solidification-segregation in slabs based on lateral cooling non-uniformity, used in slab continuous casting machine production, with steel grade SQ700Z, casting speed 1.2 m / min, superheat 17℃, cross-section 1120 mm × 230 mm, and carbon content 0.0533 wt%; comprising the following steps:

[0061] S1. Construct a cold-state performance testing system for nozzle 1 in the second cooling section. The testing system includes a water supply system, an air compression and delivery device, a testing platform, a control system, and a storage system.

[0062] S2. The performance of nozzles with different arrangements in the secondary cooling section is tested. The testing system automatically records the water flow density distribution results and transmits them to the storage system. The arrangement methods include nozzle type and test parameters. Arrangements 1-3 for nozzle 1 in the secondary cooling section are as follows: Figure 1 , 4 As shown in Figure 7,

[0063] like Figure 1 As shown, arrangement method 1 uses a single nozzle, positioned at 1 / 2 of the width of the slab.

[0064] For example Figure 4 As shown, arrangement method 2 uses a dual-nozzle nozzle positioned at 1 / 2 of the width of the slab.

[0065] For example Figure 7 As shown, arrangement method 3 uses three single nozzles, which are respectively arranged at 1 / 4, 1 / 2, and 3 / 4 of the width of the slab.

[0066] The spray height for all three arrangement methods is set to 130mm, the air pressure to 0.37MPa, and the water pressure to 0.85MPa.

[0067] S3. After exporting the water flow density distribution results from the storage system, import them into Origin software, plot the water flow density distribution histogram, and perform data fitting to obtain the fitting curves. The fitting curves for layout methods 1-3 are shown below. Figure 2 , 5 As shown in Figures 1 and 8, the goodness-of-fit R values ​​for arrangement methods 1-3 are 0.997, 0.992, and 0.993, respectively.

[0068] S4. Combining the fitted curve, the actual cooling water volume of each zone of the secondary cooling section, the actual length of each zone of the secondary cooling section, and the empirical formula for the heat transfer coefficient of the secondary cooling section, establish the correlation between the heat transfer coefficients of the slab wide and narrow surfaces as a function of position and time in Visual Studio software.

[0069] S5. Use Ansys software to establish a coupled heat transfer-mass transfer-solidification model of the entire slab continuous casting process. Use Cartesian coordinate system for modeling. X and Z correspond to the wide face 3 and narrow face 4 of slab 2, respectively. Y is the pulling direction. Use hexahedral mesh for meshing. After loading the above heat transfer coefficient relationship into the wide face and narrow face of the model through the subroutine (User Defined Function, UDF) of Ansys software, start the model for calculation.

[0070] S6. Import the model calculation results into Tecplot software to analyze information such as temperature distribution, solute distribution, and carbon segregation index during the continuous casting process, and compare the information such as temperature distribution, solute distribution, and carbon segregation index during the continuous casting process.

[0071] The carbon segregation indices on the center line of the slab after solidification in arrangement methods 1-3 of Embodiment 1 of the present invention are respectively as follows: Figure 3 , 6 As shown in Figures 9 and 1, the maximum temperature difference from the transverse 1 / 8 to the center of the slab in arrangement 1 is 44.7℃, and the standard deviation of the carbon segregation index is 0.018; the maximum temperature difference from the transverse 1 / 8 to the center of the slab in arrangement 2 is 22.9℃, and the standard deviation of the carbon segregation index is 0.008; the maximum temperature difference from the transverse 1 / 8 to the center of the slab in arrangement 3 is 67.7℃, and the standard deviation of the carbon segregation index is 0.012. It can be seen that the temperature and solute uniformity of arrangement 2 are significantly better than those of arrangement 1 and 3. In summary, arrangement 2 is recommended for the nozzle arrangement in the secondary cooling section of SQ700Z steel during the continuous casting process.

[0072] As can be seen from the above embodiments, this invention, by constructing a cold-state performance testing system for the nozzles in the secondary cooling section, tests the performance of nozzles with different arrangements in the secondary cooling section and records the results of water flow density distribution. Using the results of the water flow density distribution, a water flow density distribution histogram is plotted, and data fitting is performed to obtain a fitting curve. Combining the fitting curve, the actual cooling water volume in each zone of the secondary cooling section, the actual length of each zone of the secondary cooling section, and the empirical formula for the heat transfer coefficient of the secondary cooling section, the correlation between the heat transfer coefficients of the slab's wide and narrow faces as a function of position and time is established. This correlation is then applied to the wide and narrow faces of the established slab continuous casting full-process heat transfer-mass transfer-solidification coupling model, and the model is started for calculation. By comparing and analyzing the temperature distribution, solute distribution, carbon segregation index, and other information obtained during the continuous casting process using the model calculation results, a suitable nozzle arrangement for the secondary cooling section is determined. This invention can reduce the W-shaped solidification-segregation phenomenon in slabs and is of great significance for controlling the quality of cast slabs.

[0073] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for reducing W-type solidification-segregation in slabs based on transverse cooling non-uniformity, characterized in that, Includes the following steps: S1. Construct a cold-state performance testing system for the nozzles in the second cooling section; S2. Test the nozzle performance of different arrangement methods in the secondary cooling section and record the results of water flow density distribution; S3. Using the results of the water flow density distribution, draw a histogram of water flow density distribution and perform data fitting to obtain a fitted curve; S4. By combining the fitted curve, the cooling water volume of each zone of the secondary cooling section, the length of each zone of the secondary cooling section, and the empirical formula for the heat transfer coefficient of the secondary cooling section, the correlation between the heat transfer coefficients of the slab wide and narrow surfaces and their changes with position and time is established. S5. Establish a coupled heat transfer-mass transfer-solidification model for the entire process of slab continuous casting. After loading the correlation of the above heat transfer coefficients onto the wide and narrow planes of the model, start the model for calculation. S6. Analyze the information on temperature distribution, solute distribution, and carbon segregation index in the continuous casting process using the results of model calculations. Compare the information on temperature distribution, solute distribution, and carbon segregation index in the continuous casting process to determine the appropriate nozzle arrangement in the secondary cooling section and reduce the solidification-segregation phenomenon of the slab in the W-shape.

2. The method for reducing W-shaped solidification-segregation in slabs based on transverse cooling non-uniformity according to claim 1, characterized in that, In step S1, the testing system includes a water supply system, an air compression and delivery device, a testing platform, a control system, and a storage system.

3. The method for reducing W-shaped solidification-segregation in slabs based on transverse cooling non-uniformity according to claim 1, characterized in that, In step S2, the arrangement includes nozzle type and test parameters; the test system automatically records the results of water flow density distribution and transmits the results of water flow density distribution to the storage system.

4. The method for reducing W-shaped solidification-segregation in slabs based on transverse cooling non-uniformity according to claim 1, characterized in that, In step S3, the results of the water flow density distribution are exported from the storage system and imported into Origin software to draw a histogram of water flow density distribution and perform data fitting to obtain a fitting curve. The fitting degree R value is required to be greater than 0.

95.

5. The method for reducing W-shaped solidification-segregation in slabs based on transverse cooling non-uniformity according to claim 1, characterized in that, In step S4, the correlation between the heat transfer coefficients of the wide and narrow sides of the slab as a function of position and time is established in Visual Studio software.

6. The method for reducing W-shaped solidification-segregation in slabs based on transverse cooling non-uniformity according to claim 1, characterized in that, In step S5, a heat transfer-mass transfer-solidification coupled model of the entire slab continuous casting process is established using Ansys software. The model is built using a Cartesian coordinate system, with X and Z corresponding to the wide and narrow faces of the slab, respectively, and Y representing the casting direction. A hexahedral mesh is used for meshing. After loading the relevant relationships of the heat transfer coefficients mentioned above onto the wide and narrow faces of the model through a subroutine of Ansys software, the model is started for calculation.

7. The method for reducing W-shaped solidification-segregation in slabs based on transverse cooling non-uniformity according to claim 1, characterized in that, In step S6, the results of the model calculation are imported into Tecplot software to analyze information including temperature distribution, solute distribution, and carbon segregation index during the continuous casting process.

8. A control system for implementing the method for reducing W-type solidification-segregation of slabs based on transverse cooling non-uniformity as described in any one of claims 1-7.

9. An information data processing terminal for implementing the method for reducing W-shaped solidification-segregation of slabs based on transverse cooling non-uniformity as described in any one of claims 1-7.

10. A computer-readable storage medium comprising instructions, when executed on a computer, causing the computer to perform the method for reducing W-type solidification-segregation of slabs based on lateral cooling nonuniformity as described in any one of claims 1-7.