FIELD OF THE INVENTION
The present invention relates to a method for on-line prediction of slab core temperature
during heating of slab in pusher type reheating furnace using software based finite
element analysis/method . More particularly, the invention relates to developing a method
for providing on line temperature distribution inside slab using conduction heat transfer
equations with radiation heat transfer boundary condition. The method of the present
invention uses a Finite Element Method (FEM) program to solve the heat transfer
equations including considering the heat transfer to the skid pipes, by taking input data
automatically through a PLC system and predicts the slab core temperature. The method
also enable the operator decide on setting the zonal set point temperatures so that proper
soaking is done with minimum energy. The slab core temperature prediction is integrated
with the delay strategy model for automatic setting of the delay timings. The method of
the invention thus utilize input data relating to variables like each zonal temperature of the
reheat furnace, slab pushing time, slab dimension and steel grade and compute and
provide slab core temperature at the output. Advantageously, the method of online
prediction of slab core temperature also predicts the difference between the slab surface
and core temperature.
BACKGROUND ART
It has been experienced in conventional heating process of steel stock in reheat furnaces
of rolling mills that there occurs high specific fuel consumption. It is also observed that the
reason for higher fuel consumption is due to the fact that furnace temperature is not
reduced than what is required even if the slabs are completely soaked. As it is not possible
in the conventional practice to know the slab core temperature of each slab, it is not
possible to predict the soaking condition of slab in the existing process. Moreover, knowing
the zonal set point temperatures of reheat furnace is also not possible in absence of proper
information regarding slab temperature/soaking condition. As a consequence the reheat
furnace operation has not been energy efficient and cost of operation/product has been
high.
Conventional reheating comprise two preheating zones -an upper and a lower one , two
heating zones -an upper and a lower one, and one soaking zone are present. The burners

of each zone are controlled through thermocouple set points: a control loop regulates the
air and gas flow rates to match the set value with the temperature measured by a properly
placed zone thermocouple. Therefore, the problem of furnace temperature control is that
of specifying the set points that produce an adequate slab outlet temperature distribution.
An infrared pyrometer at the rougher is usually deployed to monitor the slab outlet
temperature which measures the slab longitudinal temperature profile on the upper side of
the slab.
In the conventional practice, slab tracking inside reheating furnace are done by
i) Laser barrier ELM/VRF, on the roll table with scanning HMD ROTA-SONDE DC.
(Make: M/s DELTA Sensors , M/s American sensors )
ii) CCTV system are in use for long for imaging of slab inside furnace and
consequent image analysis. The 1ST - Ventus II water cooled camera provides a
clear view of the steel slabs progression through the furnace and the burner
performance. The cameras are mounted preferably near the exit of the furnace
on opposite sides above the product. The combined view from 32 cameras
provides a full 360° view.
Conventional laser and CCTV system suffers from disadvantages and limitations, which
include:
(a) Installation of this system in existing pusher type furnaces is very difficult.
Maintenance of such systems is also troublesome.
(b) Generally, these systems are not directly connected to on-line heating module for
on-line correction of zonal temperatures to get required slab temperature for
rolling.
(c) There is no provision for storing of relevant information on pusher and extractor
operation, slab ID, last pushing time, entry time at heating zone, entry time at
soaking zone, time in furnace, no pushing in the shift, different zonal
temperatures.
(d) Cost implication for the system is also one of the major adverse factor.
There has thus been a need in the art to developing an online method for automatic
indication/prediction of core temperature of slab and means to determine zonal set point
temperatures of the reheat furnace so that the fuel consumption and entire furnace

operation can be optimized in order to save on energy and cost as well as to improve
quality of rolled product and minimize rejection as a result of uncontrolled heating of steel
stock at reheat furnace. A software based method is to be developed for prediction of core
temperature at different zones of reheat furnace so that soaking condition of slabs can be
visualized graphically enabling the operator to operate the delay strategy models and
generate set points for furnace zonal temperatures based on output of the software and
thus favour automatic controlled heating of slabs/billets/blooms to desired temperature to
suit steel plastic properties favoring flawless rolling/roughing downstream and on the other
hand ensure energy efficient furnace operation, eliminate wastage of fuel gas by
introducing means for programmed scheduling of furnace temperature, particularly during
shutdown/repair period and thus making the operation and maintenance of such systems
simple, cost effective, productive and reliable ensuring wide industrial application in steel
industry.
OBJECTS OF THE INVENTION
The basic object of the present invention is thus directed to providing a method for
online slab core temperatures ascertaining during heating of slabs in pusher type reheating
furnaces enabling energy efficient operation of the furnace.
Another object of the present invention is directed to providing a method for online
prediction/control of slab core temperature using finite element analysis/method for the
slab soaking conditions inside furnace.
Yet another object of the present invention is directed to providing a method for online
prediction/control of slab core temperature such that the method is implemented through
hardware comprising the PLC system, computers, and instrumentations/sensors deployed
in multiple levels and integrated through network for monitoring all zones of reheat
furnaces.
A further object of the present invention is directed to providing a method for online
prediction of slab core temperature enabling the operator to setting zonal set point
temperatures of furnace so that proper soaking is done with minimum energy.

A still further object of the present invention is directed to providing a method for online
prediction model for slab core temperature wherein out put of the model is integrated with
delay strategy models for automatic setting of delay timings.
A still further object of the present invention is directed to providing a method for online
prediction of slab core temperature wherein the operator can visualize graphically the
soaking condition of each slab.
A still further object of the present invention is directed to providing a method for online
prediction of slab core temperature wherein said model also predicts the difference
between the slab surface and the core temperatures so as to ensure proper soaking.
A still further object of the present invention is directed to providing a method for online
prediction of slab core temperature wherein the output of the prediction model favour
generation of set points for furnace zonal temperatures.
A still further object of the present invention is directed to providing a method for online
prediction of slab core temperature wherein the FEM analysis determines the temperature
distribution inside the slab using three dimensional conduction heat transfer
equations/expressions with radiation heat transfer boundary conditions.
A still further object of the present invention is directed to providing a method for online
prediction of slab core temperature wherein the shape factor(F) and the convection co-
efficient(h) used in heat transfer equations are considered as model tunning parameters
zonal values of which are determined based on minimizing the root mean square error by
comparing the measured and predicted slab exit temperatures for accuracy of prediction.
SUMMARY OF THE INVENTION
The basic aspect of the present invention is directed to a method for on-line prediction of
slab core temperature during heating of slab in reheat furnaces comprising
acquisition of input data relating to temperature of each zone of furnace, slab pushing
time, slab dimension and steel grade through PLC system;

online prediction of slab core temperature involving finite element method (FEM) in
supervisory computer;
computing temperature distribution inside the slab using conduction heat transfer
equations with radiation heat transfer boundary condition and auto tunning adapted to
calculate zonal shape factors and convention coefficient automatically ;
setting zonal set point temperatures of reheat furnace for proper soaking of slabs with
minimum energy based on slab core temperature prediction ;
automatic setting of delay timing through delay strategy model integrated to the slab core
temperature model for attaining desired slab temperature distribution and complete
soaking;
visual display of online soaking condition of any slab inside the furnace to the operator at
any point of time;
Another aspect of the present invention is directed to said method for on-line prediction of
slab core temperature during heating of slab in reheat furnaces wherein the method also
predicts the difference between slab surface and core temperatures.
A further aspect of the present invention is directed to said method for on-line prediction
of slab core temperature during heating of slab in reheat furnaces wherein the input data
to the prediction model comprise temperature of each zone of furnace, slab pushing time,
slab dimension and steel grade and output from the model is the slab core temperature.
Also in said method for on-line prediction of slab core temperature during heating of slab
in reheat furnaces the same is adapted to calculate the heat transfer to the skid pipes.
A still further aspect of the present invention is directed to a method for on-line prediction
of slab core temperature during heating of slab in reheat furnaces wherein auto tuning
involves finding the values for the zonal shape factors(F) and the convection
coefficients(h) used in the heat transfer equations which are computed such that the root

mean square error between the predicted and measured temperatures of slab at exit is
minimum applying a multivariate minimization program.
A still further aspect of the present invention is directed to said method for on-line
prediction of slab core temperature during heating of slab in reheat furnaces wherein the
values of the tuning parameters are updated automatically in successive stages so that the
values from one stage is used for slab core temperature prediction of next slab.
Advantageously also in said method for on-line prediction of slab core temperature during
heating of slab in reheat furnaces according to the present invention the model output of
temperature difference between surface and the core temperature is transmitted to PLC
for automatic operation of delay strategy model.
According to yet another aspect of the method for on-line prediction of slab core
temperature during heating of slab in reheat furnaces according to the present invention, a
driver software for communicating between PLCs and PCs favor smooth data transmission
between PLC and the model computer using said software.
A still further aspect of the present invention is directed to a hierarchical PLC based
automation/control system to carry out the above said method for online prediction of slab
core temperature comprising
tracking sensors of the furnace, thermocouples to measure zonal temperature of the
furnace, transmitters for zonal temperature, air-gas flow, air-gas pressure, I/P converter
and pneumatic actuators for controlling gas flow in the burners disposed at the lowest
level(level- 0);
PLC system with operator terminal disposed in the next higher level(Level I) comprising
PLCs, digital indicators, Input/Output and PCs;
supervisory computer in highest level(Level-2) adapted for finite element method (FEM)
for installation of slab core temperature prediction model therein with auto tunning
facilities to calculate zonal shape factors and convention coefficient automatically;

display means for displaying online slab soaking condition and temperature distribution to
the operator.
The present invention and its objects and advantages are described in greater details with
reference to the following accompanying non limiting illustrative drawings.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
Figure 1: is the schematic illustration of the multilevel hardware installation for
implementation of prediction model according to the invention.
Figure 2: is the schematic illustration of the hierarchical control system for model
implementation.
Figure 3: is the schematic diagram for the software and communication for model
implementation.
Figure 4: is the schematic illustration of typical model output showing the temperature
distribution inside slab.
Figure 5: is the illustration of typical partial output screen of the model showing the
predicted Surface and Core temperature of slab.
DETAILED DESCRIPTION OF THE INVENTION WITH REFERENCE TO THE
ACCOMPANYING DRAWINGS
The present invention relates to an on-line model for prediction of slab core temperature
during heating of slab in pusher type reheating furnace in plate mills using software based
finite element analysis/method. The invention relates in particular to a method for
providing on line temperature distribution inside slab using conduction heat transfer
equations with radiation heat transfer boundary condition directed to energy efficient
furnace operation and ensure appropriate soaking to deliver good quality of slab for further
rolling operation.

(a) Installation of hardware system:
Reference is first invited to the accompanying Figure 1 that schematically illustrates a
general embodiment of the PLC based multilevel hardware deployment for implementation
of the method of the invention. In the lowest level of automation (Level-0) there is the
furnace, thermocouples and tracking sensors. In the next higher level, there is PLC system
with operator terminal. In the level-2, there is the computer where the slab core
temperature prediction model is installed.
Reference is now invited to the accompanying Figure 2 that illustrates the details of
hardware of Level-0 and Level-l. In Level-0, there are thermocouples to measure zonal
temperature of the furnace, transmitters for zonal temperature, air-gas flow, air-gas
pressure, I/P converter and pneumatic actuators for controlling gas flow in the burners. In
level-l there are PLCs, digital indicators, Input/Output and PCs. The slab core temperature
prediction model has been installed in supervisory computer in Level-2.
Reference is now invited to the accompanying Figure 3 that schematically illustrates the
communication program between Level-l and Level-2. Driver software has been developed
for communicating between PLCs and PCs. This driver software is written in Visual C++
computer language based on Microsoft COM/DCOM technology. The data between PLC and
the model installed in computer are able to be transmitted smoothly with the use of this
software.
(b) Development of slab core temp prediction model
The method of the present invention uses a FEM program to solve the heat transfer
equations for providing on line temperature distribution inside slab using conduction heat
transfer equations with radiation heat transfer boundary condition, including considering
the heat transfer to the skid pipes, by taking input data automatically through a PLC
system and predicts the slab core temperature.
It is known that the absolute slab temperature (T) at any time t at any location (x,y,z) in a
slab is known by the differential equation

where, a is Stefan-Boltzman constant, K is the thermal conductivity of slab material, Tf is
the absolute zonal temperature of the furnace, θn is the absolute slab surface temperature,
θf is zonal temperature of the furnace (°C) , θn is slab surface temperature (°C) and θ is
the temperature (°C) inside slab at co-ordinate (x,y,z). Here, F is the shape factor and h
is the convection coefficient. F and h depend upon various conditions inside the furnace. It
is very difficult to calculate these two factors theoretically. For this reason, F and h have
been considered as model tunning parameters, the value of which are calculated by model
tunning method described in the following paragraphs.
(c) Development of model tunning method
The slab core temperature prediction model according to the present invention has two
tunning parameters namely, Shape factor (F) and convection coefficient (h) as described in
the preceding section. As there are usually five different zones in a typical reheating
furnace, five values of F and five values h have been chosen as tunning parameter
corresponding to each zone. Initial values of shape factors have been taken as unity and
convention coefficients have been chosen as 0.2 N/mm/s/C. Initial value of convection
coefficient has been chosen on the basis of the default values of convection in air. Slab exit
temperatures are predicted on the basis of these initial values. As a slab is pushed out of a
furnace, its temperature (θn) is measured by the mill pyrometer. The measured and
predicted temperature values are compared. The error for 100 slabs is recorded. The Root
Mean Square Error (RMSE) of all these 100 slabs is taken as the cost function to a
multivariable minimization program, which find the values of tunning parameters in such a
way that the value of RMSE is minimum. This process continues and tunning parameters
are updated automatically. The updated tunning parameters are used in the next slab for
prediction of core temperature.

(d) Model Output
Accompanying Figure 4 shows a typical model output where the temperature distribution
inside the slab surface has been shown. Operator can visually see the soaking condition of
any of slab inside the furnace at any point of time.
The FEM software runs for each slab and predicts the core temperature processed by the
software based prediction model according to the invention. Accompanying Figure 5
shows a partial output screen of the model predicting the Surface and Core temperature.
Temperature difference between surface and core temperature is also shown in the screen.
This output of the model is transmitted to PLC as an input for delay strategy model.
It is thus possible by way of the present invention to developing a method for predicting
slab core temperature as well as the temperature distribution of slab by applying FEM
technique with a software based approach so that the temperature at any point in slab is
determined by solving a heat transfer equation as a function of furnace zonal temperature
as well as the absolute slab surface temperature and wherein heat transfer by conduction
is defined along with radiation heat transfer boundary conditions . This method for finding
slab temperature at any zone of the reheat furnace at any point of time during heating
precisely predicts the slab core or surface temperatures. The method and system of the
invention also favor determining/setting automatically the delay timing by the operator.
The software based method of the invention also guides the operator for setting the zonal
set point temperature so that proper soaking is done with minimum energy consumption.

We Claim:
1. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces comprising
acquisition of input data relating to temperature of each zone of furnace, slab pushing
time, slab dimension and steel grade through PLC system;
online prediction of slab core temperature involving finite element method (FEM) in
supervisory computer;
computing temperature distribution inside the slab using conduction heat transfer
equations with radiation heat transfer boundary condition and auto tunning adapted to
calculate zonal shape factors and convention coefficient automatically ;
setting zonal set point temperatures of reheat furnace for proper soaking of slabs with
minimum energy based on slab core temperature prediction ;
automatic setting of delay timing through delay strategy model integrated to the slab core
temperature model for attaining desired slab temperature distribution and complete
soaking;
visual display of online soaking condition of any slab inside the furnace to the operator at
any point of time;
2. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claim 1 wherein the method also predicts the difference
between slab surface and core temperatures.
3. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claims 1 or 2 wherein the input data to the prediction model
comprise temperature of each zone of furnace, slab pushing time, slab dimension and steel
grade and output from the model is the slab core temperature.

4. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claims 1 to 3 wherein said method is adapted to calculate
the heat transfer to the skid pipes.
5. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claims 1 to 4 wherein auto tuning involves finding the values
for the zonal shape factors(F) and the convection coefficients(h) used in the heat transfer
equations which are computed such that the root mean square error between the
predicted and measured temperatures of slab at exit is minimum applying a multivariate
minimization program.
6. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claims 1 to 5 wherein the values of the tuning parameters
are updated automatically in successive stages so that the values from one stage is used
for slab core temperature prediction of next slab.
7. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claims 1 to 5 wherein the model output of temperature
difference between surface and the core temperature is transmitted to PLC for automatic
operation of delay strategy model.
8. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces as claimed in claims 1 to 5 wherein a driver software for communicating
between PLCs and PCs favor smooth data transmission between PLC and the model
computer using said software.
9. A hierarchical PLC based automation/control system to carry out the method for online
prediction of slab core temperature as claimed in claims 1 to 8 comprising
tracking sensors of the furnace, thermocouples to measure zonal temperature of the
furnace, transmitters for zonal temperature, air-gas flow, air-gas pressure, I/P converter
and pneumatic actuators for controlling gas flow in the burners disposed at the lowest
level(level- 0);

PLC system with operator terminal disposed in the next higher level(l_evel I) comprising
PLCs, digital indicators, Input/Output and PCs;
supervisory computer in highest level(Level-2) adapted for finite element method (FEM)
for installation of slab core temperature prediction model therein with auto tunning
facilities to calculate zonal shape factors and convention coefficient automatically;
display means for displaying online slab soaking condition and temperature distribution to
the operator.
10. A method for on-line prediction of slab core temperature during heating of slab in
reheat furnaces and a system to carry out such method substantially as herein described
with reference to the accompanying illustrative drawings.

The invention relates to a method for on-line model for prediction of slab core temperature
during heating of slab in pusher type reheating furnace using software based finite
element analysis/method. The method is adapted to providing on line temperature
distribution inside slab using conduction heat transfer equations with radiation heat
transfer boundary condition. The method of the present invention uses a FEM program to
solve the heat transfer equations including considering the heat transfer to the skid pipes,
by taking input data automatically through a PLC system and predicts the slab core
temperature. The method enables the operator to decide on setting the zonal set point
temperatures so that proper soaking is done with minimum energy. The slab core
temperature prediction model is integrated with the delay strategy model for automatic
setting of the delay timings.