FIELD OF THE INVENTION
The present invention relates to an improved method for determination of heat flux in a continuous casting billet mould.
BACKGROUND OF THE INVENTION:
In continuous casting process, a mould acts as the core component of the continuous caster. Heat transfer, solidification and mechanical behaviour in the mould are the key factors in determining the quality of the casted product and efficiency of the casting process. The uniformity of strand solidification and mould geometry also have great effect on the product quality and production stability. Understanding the status of these key factors within the mould becomes very important for optimisation of the casting process and quality control. Methods that are applied in prior art, to determine the state of mould heat transfer are the experimental monitoring and numerical simulation. The first one is to determine the average mould heat flux by monitoring the temperature of the thermocouples buried in the mould or monitoring temperature difference of cooling water. Measured data is used to reflect the variation of operation parameters of continuous casting, and heat transfer in the mould. On the other hand, the numerical method for calculating mould heat flux use mathematical models. This method is simple and convenient, and is helpful to investigate the strand solidification and heat transfer.
During the recent past, varieties of numerical methodologies have been developed to simulate heat transfer behaviour between the strand and the mould, most of which have heat flux empirical formula as boundary condition. However, these models can’t simulate the real non-uniform status inside the mould, and therefore bear less significance for optimising a continuous casting process. A mathematically rigorous technique of solving heat transfer problem is Indirect algorithm Heat Conduction approach, which involves estimation of time-or-spatial profile of a surface heat flux given one or more measured temperature inside a body.

OBJECTS OF THE INVENTION
It is therefore an object of the invention to propose a heat flux predicting system in the mold of the slab caster.
Another object of the present invention is to propose a heat flux predicting system in the mold of the slab caster.
A further object of the invention is to propose a heat flux predicting system in the mold of the slab caster, which is enabled to regularize the non-uniformity in heat transfer calculation in the billet mould.
SUMMARY OF THE INVENTION
Accordingly, in a first aspect of the invention, there is provided a heat flux predicting system(100) in the mold of the slab caster comprising: a plurality of measuring devices (M1, M2, M3………….Mn), the plurality of measuring devices being placed at various location in the billet caster, the plurality of measuring devices being configured to sense values corresponding to parameters of temperature (T), steel density (d), and thermal conductivity (k), and forward the sensed values to a data storage means (104); the data storage means (104) being coupled to the plurality of measuring devices (M1, M2, M3………….Mn), the data storage means (104) being configured to store and forward the sensed values to a calculating means (108); the calculating means (108) being coupled to the data storage means (104), the calculating means (108) being configured to receive and feed the sensed values in an equation ,
thereby determining the value of qs and forwarding the value of "qs” to a decision making means (112); and the decision making means (112) being coupled to the calculating means (108), the decision making means being configured to receive the output of “qs” and compare with the qt; the qt being threshold limit and deciding appropriate measurement.
Accordingly, there is provided a method to determine heat flux predict the variation of heat flux in a continuously-cast billet mould. According to the present invention, an improved method of determining heat-flux in continuous casting billet mould is provided

based on conjugate gradient -function and gradient-cross correlation technique while taking into consideration the intricate nature of heat transfer in the mould. Benchmark literature data are utilized to standardize the present results. Temperature data obtained from plant are used to calculate the heat flux in billet mould. Parametric data pertaining to different plant operation conditions and mould variables are determined and the heat transfer condition is established. Regularization technique is applied to reduce the non-uniformity in the estimation of the heat flux data.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
Figure 1 : shows a process flow-chart of the invention
Figure 2 : Schematic of heat transfer domain in mould.
Figure 3 : Calculated heat flux values without regularisation of solution
Figure 4 : Variation of heat flux
Figure 5 : shows a schematic of a heat flux predicting system in the mold of a slab caster according to the present system.
Figure 6 : shows the plurality of value buttons in predicting system of Figure 5.
DESCRIPTION OF THE PRESENT INVENTION:
In continuous casting process, solidification of liquid steel begins in a water-cooled copper mold. The steel shell which forms in the mould contains a core of liquid steel which gradually solidifies as the strand moves through the caster guided by a large number of roll pairs. In the above process, heat transfer plays a critical role and affects many of the quality and operational problems. The heat flow is complicated because it is controlled primarily by the formation of a gap which separates the mould from the billet, and the location and size of the gap are influenced simultaneously by shrinkage of the shell and ferrostatic pressure exerted by the liquid pool.

The coupled temperature distribution and mechanical behaviour of the mould wall are affected by many variables: wall thickness, thermal conductivity velocity and temperature of the mould water, and carbon content of the steel being cast. With these different variables and their effects, and considering the interactive nature of heat flow, thermal behaviour and mechanical distortion, the thermal and mechanical behaviour of the mould are not easily preidctable.
In order to develop a comprehensive understanding of mould thermal response and mould-related quality problem in billet casting, it is necessary to examine the heat transfer process, and thermal history in the mould and, based on these heat flux variation to be calculated in the mould as a function of casting variables.
For formulating the heat flow equation, using conservation of energy and Fourier's law of heat conduction, total energy in a domain oriented along the x-axis is written as,
where e(x,t) is the heat energy density function and the total energy is calculated
5 within the range a and b. In presence of a heat flux through x=a and x=b, the energy variation becomes,

Here ϕ (x , t) is the heat flux, and Q ( x , t ) is net heat effect from all heat sources (heat flux). Next, by using Leibniz’s rule, the derivative can be formulated as

Employing Fourier’s law, heat flux can be given as,


where T is temperature function and K0 ,is the thermal conductivity of the material, which is assumed to be constant. Combining above equations, following equation is obtained,
It may be mentioned here that, along with appropriate initial and boundary conditions, above equation forms the forward problem which can be integrated to form the inverse problem.
In presence of a single source, qs , at a known location, the effect on the resultant heat transfer can be predicted if the function f ( t ) is known,

Here 5 ( r ) is the Dirac delta function. Considering a number of nodes N located in the domain where the measurements of temperature at each point is assumed to be available, the problem of interest is the function estimation problem on the domain with a given boundary,

CALCULATION PROCEDURE
In the present approach, given an initial guess, the conjugate gradient method
minimizes a function J at each iteration, choosing a new guess term that pushes
the solution closer to the optimal one. The algorithm can be developed in the
following manner: Given an initial guess fk = f0, solve for the temperature, T(ri,t),
that result from f , at the measurement points
Calculate the residual error, i.e. the difference between the resultant temperature and
measured temperatures
Determine the heat source function which would account for the residual error

Adjustment of guess fk in the new iteration level to form fk in the new iteration level to
form fk+1
Set k=k+1 and repeat
Adopting a least square minimization problem, the source function is defined as

In order to determine the optimal step size ß, following expression is used in the present case based on the calculated and measured data,
where, Tk are the vectorized measurements from all measurement sensors across the time.

WE CLAIM
1. A heat flux predicting system(100) in the mold of the slab caster
comprising:
a plurality of measuring devices (M1, M2, M3………….Mn), the plurality of measuring devices being placed at various location in the billet caster, the plurality of measuring devices being configured to sense values corresponding to parameters of temperature (T), steel density (d), and thermal conductivity (k), and forward the sensed values to a data storage means (104);
the data storage means (104) being coupled to the plurality of measuring devices (M1, M2, M3………….Mn), the data storage means (104) being configured to store and forward the sensed values to a calculating means (108);
the calculating means (108) being coupled to the data storage means (104), the calculating means (108) being configured to receive and feed the sensed values in an equation thereby determining the
value of qs and forwarding the value of "qs” to a decision making means (112); and
the decision making means (112) being coupled to the calculating means (108), the decision making means being configured to receive the output of “qs” and compare with the qt; the qt beingthreshold limit and deciding appropriate measurement.
2. The heat flux predicting system (100) as claimed in claim 1, wherein the plurality of value buttons (124) are configured to do value alteration of the parameters.
3. The heat flux predicting system (100) as claimed in claim 1, wherein the heat flux prediction is donein real time operation.