|Title of Invention||
A METHOD FOR PREDICTION OF TEMPERATURE PROFILE OVER THE LENGTH AS WELL AS OVER THE THICKNESS OF A STRIP IN A RUN-OUT TABLE OF A HOT STRIP MILL, AND VALIDATING THE SAME
|Abstract||A method for prediction of temperature profile over the length as well as over the thickness of a strip in a run-out table of a hot strip mill and its validation is disclosed. The prediction is done by first determining with a known heat conduction equation. Then the correlation between heat transfer coefficient 'h' and strip surface temperature 'Ts' at water-strip interface is determined by a third order polynomial. Finally, the correlation is validated for various grades of steel. The simulated cooling temperature of run-out table strip mill is predicted from the numerical solution.|
|Full Text||FIELD OF APPLICATION
The present invention relates to a method for prediction of temperature profile
over the length of run-out table (ROT) of a hot strip mill (HOT).
In particular, the invention relates to the developnnent of a new correlation of
heat transfer coefficient at water-strip surface in the run-out table of a hot strip
mill in steel plant. The correlation involves a third order polynomial of the strip
surface temperature for water-steel surface.
The polynomial correlation of heat transfer coefficient can be used in the nrnxlel
of heat transfer equation when the hot strip is coded over the bed of run-out
table in hot strip mill. With the use of this heat transfer coefficient the
temperature profile of the strip can be obtained which has tremendous
application in terms of grain size determination and mechanical properties of
BACKGROUND OF THE INVENTION
In hot strip mills, slabs are heated and soaked at elevated temperature (~ 1200°
C) in the furnace, and are subjected to subsequent reductions in the roughing
and finishing mill. The resultant strips coming out from the finishing mill are
then cooled on the run-out table using laminar water jets from the finish rolling
temperature (FRT) (~ 890° C) to the colling temperature (~ 600°" C).
The Coiling temperature (CT) and the cooling rate (CR) are important parameters
to determine final ferrite grain size at the end of the rolling and mechanical
properties in turn. Accurate prediction of coiling temperature depends on the
precise determination of heat loss from the strip segment and heat transfer
coefficient with water falling on the moving strip.
The cooling of strip in the hot strip mill exhibits a complete description of heat
transfer mechanism. The nature of heat transfer from the bed of run-out table Is
complex as it Involves several modes of heat transfer. The strip coming out of
the last finishing stand is exposed to air-cooling for a short distance (about 10
meter in the present steel plant) before it meets first water curtain. The water
jet (25o C) from each cooling bank Impinges on the surface of the running strip.
Once It hits the hot surface, the strip at a temperature of above 800° C meets
water at a temperature of 25° C. This gives rise to boiling heat transfer, which is
normally described by a boiling curve. Nukiyama glystudied first the
phenomenon of the boiling heat transfer which is heat transfer to water boiling
on submerged metal surface and then elucidate the idea of boiling phenomenon.
In case of water Impingement on hot strip, there are several views prevalent in
the literature as described earlier and the exact nature of heat transfer is not
known very precisely as the change of heat flux and the temperature change Is
very fast due to the boiling phenomenon and experimental studies for this case
are always performed with high speed camera.
It is very difficult to predict the amount of the heat flux or the heat transfer
coefficient associated with the transition boiling. In the literature there are
nearly as many number of heat transfer coefficients as the number of authors.
Most of the prior art is concentrated with experimental work on the cooling
model of run-out table of hot strip mill, which were performed in the laboratory
scale. In a flow visualization study, 50h and Yue  considered a stationary
strip with an initial temperature of 240oC DespiteTtTe fact that the study has
captured the images of the skirting jet on the plate, only splashing of the free
surface of the water followed by vapor bubbles from the boiling was observed.
No description of the determination of heat transfer coefficient has been made in
the study. The computational model developed by them has assumed nucleate
boiling and employed the correlations to evaluate the heat flux.. The
experimental results of a recent laboratory studyby Liu et al. indicates film
boiling on a stationary plate at an initial temperature of 900° C. Numerically,
two-dimensional heat conduction has been solved by finite element method to
calculate heat fluxes and heat transfer coefficient along the surface of the plate.
For colder cooling water, the area and growth rate of impingement zone
becomes larger. Outside the impingement area, boiling has been observed
where transition or stable, film boiling could not be differentiated.
Hernandez et. al.  "provided an insight into the fundamental evaporation
mechanism through a model for parallel flow boiling curves. For the modelling
purpose, most of the cooling in the run-out table has been assumed to be in the
transition-boiling regime. Colas et at.  have used a constant heat transfer
coefficient for the zone where the water flows parallel to the surface, whereas in
the jet impingement zone, another value was applied. By using the above
mentioned values of heat transfer coefficient, a reasonable good agreement with
observatior has been made in the study.
Guo  has developed a model with the correlation of heat transfer coefficient in
terfhs of a power law equation, which includes strip thickness, velocity, strip
surface temperature and water flow rate. The model determines heat transfer
coefficient by using operating data of a hot strip mill and an inverse method.
Plant data have allowed determining the powers, which are in the range of 0.8-
1.4. In the numerical model of Evans et al. [73,)the cooling for top header and
bottom cooling were treated independently and the average heat transfer
coefficient for the impingement zone has been calculated by using a correlation
involving Prandtl Number (Pr), Reynolds Number (Re)^ thermal conductivity of
the coolant and the width of impingement zone. The variation of the average
heat transfer coefficient with the change of strip surface temperature is shown to
have a parabolic distribution. The model of Hatta and Osakabe  has emerged
with a correlation of heat transfer coefficient with its validity in film boiling zone.
The correlation, given in Table 1, is a function of water temperature, saturation
temperature of coolant and the steel plate temperature. This model calculates
the temperature change of a moving steel plate cooled by a water curtain.
Similar to the work of Guo, power law (the powers of water flow density, strip
velocity, strip tempefatolfe) has been identified to represent the heat transfer
coefficient by using the plant data in the woric of/kato et al. . The dynamic
behaviour of heat transfer coefficient with the strip surface temperature has
been represented in ttie form of a boiling curve during the converagn from film
boiling to transition boiling. In anotiier recent study^ Sun et al.  have
employed different correlations at top and bottom surface of run-out table in the
form of a power law for heat transfer coefficients of water-coiling, whereby
powers of strip surface temperature and strip velocity have been considered.
A summary of different correlations for the determination of heat transfer
equation for spray cooling system has been provided in the Table 1. It can also
be inferred from the table and the above mentioned literature that the power
correlations for heat transfer coefficient are functions of many variables at the
same time. In most of the case, heat transfer coefficient value at strip-water
interface is based on the determined values at laboratory or a complex
correlation involving powers of details of plant data. In the laboratory scale, the
actual temperature of the strip of a hot strip is never reproduced. Most of
experimental studies are confined to a stationary plate and at a temperature of
250-350° C, whereas in reality a temperature drop from 890° C to 550° (near
down colter) for a moving strip is experienced.
The large amount of heat dissipation in the bed of run-out table becomes
possible owing to the boiling heat transfer mechanism. It is one of the areas of
fundamental research to obtain the heat transfer coefficient in the film boiling
and transition-boiling regime. The relevant literature indicates the existence of
correlation of heat transfer coefficient, which is dependent on the amount of
heat fluxes, water amount, and other variables. However, to estimate the
amount of heat transfer coefficient in run-out table is a challenging one when the
system is dynamic and the change of process parameters affects the heat
A need therefore, exists to estimate/obtain the heat transfer coefficient in run-
SUMMARY OF THE INVENTION
The main object of the present invention therefore, is to use the surface
temperature of the strip to obtain the heat transfer coefficient af the strip-water
Another object of the invention is to develop a correlation for heat transfer
coefficient at water-strip surface as a function of strip surface temperature.
Yet another object of the present invention is to develop an off-line model based
on numerical technique for prediction of through-thickness temperature of strip
in hot strip mill by predicting the temperature profile along the bed of the run-
Thus the present invention provided method for prediction of temiperature
profile over a length of a run-out table of a hot strip mill, comprising the steps
of: formulating an off-line mathematical model using heat conduction equation:
wnere p is oensiiy, c is specmc neau ana k is uiermal
conductivity; forming a correlation for heat transfer coefficient at water-strip
surface based on a single parameter third order polynomial of strip surface
temperature; determining the coefficients of said correlation; and using the
correlation in the numerical simulation to validate it for different grades of steel.
This invention can be applicable^'to other cases; proviaed similar parameters are
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The invention can now be described in detail with the help of the figures of the
accompanying drawings in which:
Rgure 1 shows schematic diagram of run-out table in hot strip mill.
Figure 2 shows schematic plot of heat flux with surface temperature (Ref.2):
I - Free convection regime, II - Nucleate boiling regime,
III - Transition boiling regime, IV - Film boiling regime.
Figures shows heat transfer regime close to the impinging zone.
Figure 4 shows computational domain of strip.
Figure 5 shows comparison of correlation of heat transfer coefficient.
Figure 1 illustrates the layout of run-out table of hot strip mill. The hot rolled
strip 3 coming out of the last finishing stand is first cooled by air before it meets
the water jets from cross sprays 4.
Pyrometers 1 and 2 are provided to determine the coiling temperature before
and after cooling. Accurate prediction of the coiling temperature depends on the
precise determination of heat loss from strip segment and heat transfer
coefficient with water falling on the moving strip.
Figure 2 shows the boiling curve which describes the boiling heat transfer when
the hot strip meets the water jets.
The different regimes of heat transfer are illustrated in Figure 3 for a water jet
impinging on a stationary strip. In zone I, just below the impinging jet, the
single phase convection prevails as the jet temperature is very low compared to
the high temperature of strip. Outside the stagnation region, the strip
temperature increases and boiling starts. Regime 11 is marked with start of
nucleate boiling. And this regime II separates the film^boiling region (regime III)
from the single phase forced convection. A situation occurs when the water jet
falling on the vapor layer coalesce to form agglomerated pool due to surface
tension and gives rise to regime IV. The pools are found to run away from the
strip in a random-walk fashion till they evaporate or lost from the edge of the
strip. Heat transfer outside these agglomerated pools takes place by radiation
and convection from the dry strip surface.
An off-line model has been developed for the prediction of the temperature
profile over the length of the run-out table so as to obtain correct CT prediction
from the model. In the development of the model for the strip cooling in the
run-out table, a transient one-dimensional heat conduction equation to obtain
the through thickness temperature has been used in the form of:
where P , c and K are density, specific heat and thermal conductivity
Assumptions for the numerical study:
1. The numerical simulation assumes constant temperature of properties of
the strip material over the change of temperature.
2. Heat transfer in the direction of strip movement and along the direction of
the strip width are substantially smaller or negligible.
The associated initial and boundary conditions are:
If t = 0, Ts = finish rolling temperature (FRT) Eq. (2)
where L is the strip thickness, h = Heat transfer coefficient, Ts and Ta, are strip
surface temperature and ambient temperature respectively.
The solution of the aix)ve equation gives the through thiclcness temperature of
the strip at different time during the travel of the strip from the last finishing
stand to the down coiler of hot strip mill. However, the same can be obtained,
once the value of heat transfer coefficient is known. The basic obstacle to solve
the above equation is the determination of the heat transfer coefficient. The
numerical study requires the formulation of the equation for heat transfer
coefficient or a correlation of heat transfer coefficient from different operating
parameters, as no correlation can be applied to find the heat flux for the boiling
The above model has been used to determine the heat transfer coefficient
between the water and strip interface. The heat transfer coefficient for air-strip
surface is available in the literature. However, the heat transfer coefficient value
for the water strip interface is different for different conditions of water flow,
strip velocity and strip thickness. In line with the literature, initial attempt for
estimation of the heat transfer coefficient for water-strip interface was made
with a parabolic distribution for heat transfer coefficient, similar to the work of
Evans et al. [7T Later on the correlations of Table 1 prompted the inventors of
tne present invention to develop a simpler form of the equation similar to the
correlations of the Table, which was still complicated as more than one variables
was involved. Further research led to devetopment of a simplified form of the
correlation. The developed correlation of heat transfer coefficient at water-strip
interface is a third order polynomial of instantaneous strip surface:
where a, b, c and d in the above equation are constants determined by the
plant data of the particular hot strip mill. A curve fitting method has been
adopted to determine the constants so as to match the measured value of coHing
temperature at the downcoiler with the value of coiling temperature from the
numerical solution of the heat-conduction equation.
The equation of the cubic polynomial for heat transfer coefficient has been used
for validation to determine the coefficients for different grades of steel like
grades D, DD and EDD (low carbon steel). The validation has been made for
strip thickness in the range of 1.6-6mm for the above grades of steel. However,
this may be used for other grades of steel as well.
The predicted values of heat transfer coefficient from the cubic correlation for a
3 mm thick strip have been compared with the values of heat transfer coefficient
from the correlation suggested by Hatta and Osakabe and Osakabe . The comparison has
been depicted in Figure 5. As shown in Figure 5, the suggested cubic correlation
for heat transfer coefficient for steel-water interface hais been found to be in
good agreement with the prediction of Hatta and Osakabe Osakabe [8p The proposed
cubic correlation only starts to deviate from the correlation of Ref. 8 when the
surface temperature is above 800° C. To our knowledge, there is no other
correlation of cubic polynomial to represent the film boiling in the run-out table
of hot strip mill.
The derived correlation has been used extensively for the strip of different
thickness from hot strip mill as mentioned above. The correlation ensures the
heat transfer coefficient value, which In turn provides the coiling temperature
from the numerical simulation. The simulated coiling temperature is very close
to the measured one. The derived correlation only needs the adjustment of its
coefficient for a particular thickness for the use of industrial application. The
determined heat transfer coefficient has solved one of the greatest challenges in
the industrial environment to determine its value.
Extensive validation has been made for different grades of steel like D,DD, EDD
of different thicknesses (1.6 mm to 6mm) with plant data from the hot strip mill
for different cooling patterns. The method can be used for other grades of steel
The off-line mathematical model is based on numerical technique for prediction
of through-thfckness temperature of strip in the hot strip mill, by predicting the
temperature profile along the bed of the run-out table.
 Nukiyama, S., 1934, "The Maximum and Minimum Values and Heat
Transmitted form Metal to Boiling Water under Atmospheric Pressure". 3. Japan
Soc. Mech. Engg., 37, pp. 367-374 (Translation: Int. J. Heat Mass Transfer, 9,
 W.K. Soh and W.Y.D. Yuen, "Flow Visualization of the Boiling Heat Transfer
at the Run-Out Table", 41^ Mechanical Working and Steel Processing
Conference, ISS, 1999, Vol./XXXVII, pp. 707-715.
 Liu, Z.D., Fraser, D., and Samarsekera, IV., 2002, "Experimental Study and
Calculation of Boiling Heat Transfer on Steel Plates during Run-out Table
Operation", Canadian Metallurgical Quarterly, Vol. 41, No. 1, pp. 63-74.
 Hernandez, V.H.., Samarasekera, I.V., and Brimacombe J.K., 1994, "Heat
Transfer Model of Run-out Table Cooling: A Fundamental Approach", 36*
Mechanical Working and Steel Processing Conference, Vol./XXXIl, pp. 345-356.
 Colas, r., and Sellars, 1987, CM., "Computed Temperature Profiles of Hot
Rolled Plate and Strip during accelerated Cooling", Proceedings of the
International Symposium on Accelerated cooling of Rolled Steel. Winnipeg,
Canada, Eds. G.E. Ruddle and A.F. Crawley, pergamon Press, London, Vol. 3, pp.
 Guo, R.M., August 1993, "Heat Transfer of Laminar Flow Coofing during Strip
Acceleration on Hot Strip Mill Run out Tables", Iron and Steelmaker, pp. 49-59.
 Evans, J.F., Roebuck, I.D., and Watkins, H.R., 1993, "Numerical Modelling of
Hot Strip Mill Run out Table Cooling", Iron and Steel Engineer, Vol. 70, No. 1, pp.
 Hatta, N., and Osakabe, H., 1989, "Numerical Modelling for Cooling Process
of a Moving Hot Plate by a Laminar Water Curtain", ISU International, Vol. 29,
No. 11, pp. 919-925.
 Kato, T., Hayasi, Y., Kuraishi, T., Ayano, S., and Kashiwazaki, T., 1994, "New
temperature Control System of Hot Strip Mill Run Out Table", 35the Mechanical
Working and Steel Processing Conference, ISS-AIME, Vol. XXXI, pp. 311-316.
 Sun, CG., Han, H.N., Jin, Y.S., and Hwang, S.M., 2002, "A Finite Element
Model for the Prediction of Thermal and Metallurgical Behaviour of Strip on the
Run out Table in Hot Rolling", ISD International, Vol. 42, No. 4 No. 4, pp 392-
 MItsutsuka, M., 1983, "Heat Transfer Coefficients in the Surface^
Temperature Range of 400 to 800 C during water - spray Cooling of Hot Sted
Product", Tetsu-to Hagane, Vol. 69, pp. 268.
1. A method for prediction of temperature profile over the length as well as over
the thickness of a strip in a run-out table of a hot strip mill comprising the steps
- determining offline through thickness temperature with the aid of heat
where p, is density, C is specific heat and k is thermal conductivity;
- determining the correlation between heat transfer coefficient h and strip
surface temperature Ts at water-strip interface based on a third order polynomial
of strip surface temperature with the following equation:
h = a Ts3 + bTs2 + CTs + d,
where a, b, c and d are plant constants and
validating said correlation between said heat transfer coefficient and said surface
temperature at water-strip interface for various grades of steel,
characterized in that the simulated cooling temperature of a length of run-out
table strip mill is predicted from the numerical solution.
2. The method as claimed in claim 1, wherein said validation is made for
different grades of steel like D, DD, EDD, etc.
A method for prediction of temperature profile over the length as well as over the thickness of a strip in a run-out table of a hot strip mill and its validation is disclosed. The prediction is done by first determining with a known heat
conduction equation. Then the correlation between heat transfer coefficient 'h' and strip surface temperature 'Ts' at water-strip interface is determined by a third order
polynomial. Finally, the correlation is validated for various grades of steel. The simulated cooling temperature of run-out table strip mill is predicted from the numerical solution.
|Indian Patent Application Number||865/KOL/2006|
|PG Journal Number||19/2010|
|Date of Filing||25-Aug-2006|
|Name of Patentee||TATA STEEL LIMITED.|
|Applicant Address||RESEARCH AND DEVELOPMENT DIVISION JAMSHEDPUR-831001|
|PCT International Classification Number||B21B 28/00|
|PCT International Application Number||N/A|
|PCT International Filing date|