Temperature calculation method, temperature calculation apparatus, heating control method, and heating control apparatus

1. A temperature calculation method, comprising:

dividing a cross section perpendicular to a longitudinal direction of a steel plate to be hot-rolled into a plurality of rectangular elements;

calculating a temperature of each of the rectangular elements using a finite difference method; and

controlling power of an edge heater that heats an edge part of the steel plate or an amount of applied heat by the edge heater, based on the calculated value of the temperature, wherein

a first region that includes the edge part of the cross section is divided such that a plurality of the rectangular elements are lined up in a plate-thickness direction and such that a plurality of the rectangular elements are lined up in a plate-width direction, and

a second region that includes a center of the cross section and is wider than the first region is divided such that a plurality of the rectangular elements are lined up in the plate-thickness direction but the second region is not divided in the plate-width direction.

2. The temperature calculation method according to claim 1 , wherein a length in the plate-width direction of each of the rectangular elements in the first region becomes smaller from a position close to the second region toward a side surface of the steel plate.

3. The temperature calculation method according to claim 1 , wherein in a calculation using the finite difference method when the steel plate is water-cooled, a value obtained by multiplying a value of a heat flux or a heat transfer coefficient due to water cooling for a top surface of the steel plate by an adjustment coefficient larger than 0 and smaller than 1 is used as a value of a heat flux or a heat transfer coefficient due to water cooling for a side surface of the steel plate.

4. A heating control method, comprising:

measuring a temperature difference between a representative temperature of the second region and a representative temperature of the first region at a position on a downstream of the edge heater;

calculating the temperature difference using the temperature calculation method according to claim 1 ; and

controlling power of the edge heater or an amount of applied heat by the edge heater, based on the measured value of the temperature difference, the calculated value of the temperature difference, and a target value of the temperature difference.

5. The heating control method according to claim 4 , further comprising:

learning a correction coefficient based on the measured value and the calculated value; and

correcting the calculated value with the correction coefficient.

6. A temperature calculation apparatus, comprising a controller to:

divide a cross section perpendicular to a longitudinal direction of a steel plate to be hot-rolled into a plurality of rectangular elements;

calculate a temperature of each of the rectangular elements using a finite difference method; and

control power of an edge heater that heats an edge part of the steel plate or an amount of applied heat by the edge heater, based on the calculated value of the temperature, wherein

a first region that includes the edge part of the cross section is divided such that a plurality of the rectangular elements are lined up in a plate-thickness direction and such that a plurality of the rectangular elements are lined up in a plate-width direction, and

a second region that includes a center of the cross section and is wider than the first region is divided such that a plurality of the rectangular elements are lined up in the plate-thickness direction but the second region is not divided in the plate-width direction.

7. The temperature calculation apparatus according to claim 6 , wherein a length in the plate-width direction of each of the rectangular elements in the first region becomes smaller from a position close to the second region toward a side surface of the steel plate.

8. The temperature calculation apparatus according to claim 6 , wherein in a calculation using the finite difference method when the steel plate is water-cooled, a value obtained by multiplying a value of a heat flux or a heat transfer coefficient due to water cooling for a top surface of the steel plate by an adjustment coefficient larger than 0 and smaller than 1 is used as a value of a heat flux or a heat transfer coefficient due to water cooling for a side surface of the steel plate.

9. A heating control apparatus, comprising:

the temperature calculation apparatus according to claim 6 ; and

a thermometer that measures a temperature difference between a representative temperature of the second region and a representative temperature of the first region at a position on a downstream the edge heater, wherein

the temperature calculation apparatus calculates the temperature difference, and

the controller controls power of the edge heater or an amount of applied heat by the edge heater, based on the measured value of the temperature difference, the calculated value of the temperature difference, and a target value of the temperature difference.

10. The heating control apparatus according to claim 9 , wherein the controller is to:

learn a correction coefficient, based on the measured value and the calculated value; and

correct the calculated value with the correction coefficient.