Title of Invention  A METHOD FOR PREDICTION OF TEMPERATURE PROFILE OVER THE LENGTH AS WELL AS OVER THE THICKNESS OF A STRIP IN A RUNOUT 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 runout 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 waterstrip interface is determined by a third order polynomial. Finally, the correlation is validated for various grades of steel. The simulated cooling temperature of runout 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 runout 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 waterstrip surface in the runout table of a hot strip mill in steel plant. The correlation involves a third order polynomial of the strip surface temperature for watersteel 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 runout 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 strip produced. 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 runout 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 runout table Is complex as it Involves several modes of heat transfer. The strip coming out of the last finishing stand is exposed to aircooling 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 runout table of hot strip mill, which were performed in the laboratory scale. In a flow visualization study, 50h and Yue [2] 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.[3] indicates film boiling on a stationary plate at an initial temperature of 900° C. Numerically, twodimensional 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. [4] "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 runout table has been assumed to be in the transitionboiling regime. Colas et at. [5] 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 [6] 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 [8] 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. [9]. 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. [10] have employed different correlations at top and bottom surface of runout table in the form of a power law for heat transfer coefficients of watercoiling, 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 stripwater 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 250350° 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 runout 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 transitionboiling 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 runout table is a challenging one when the system is dynamic and the change of process parameters affects the heat transfer coefficient. A need therefore, exists to estimate/obtain the heat transfer coefficient in run out table. 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 stripwater surface. Another object of the invention is to develop a correlation for heat transfer coefficient at waterstrip surface as a function of strip surface temperature. Yet another object of the present invention is to develop an offline model based on numerical technique for prediction of throughthickness temperature of strip in hot strip mill by predicting the temperature profile along the bed of the run out table. Thus the present invention provided method for prediction of temiperature profile over a length of a runout table of a hot strip mill, comprising the steps of: formulating an offline 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 waterstrip 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 used. BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS V 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 runout 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. DETAILED DESCRIPTION Figure 1 illustrates the layout of runout 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 randomwalk 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 offline model has been developed for the prediction of the temperature profile over the length of the runout table so as to obtain correct CT prediction from the model. In the development of the model for the strip cooling in the runout table, a transient onedimensional 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 respectively. 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: Initial Condition: If t = 0, Ts = finish rolling temperature (FRT) Eq. (2) Boundary Condition: Eq. (3) 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 transfer. The above model has been used to determine the heat transfer coefficient between the water and strip interface. The heat transfer coefficient for airstrip 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 waterstrip 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 waterstrip interface is a third order polynomial of instantaneous strip surface: Eq(4) 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 heatconduction 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 1.66mm 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 [8]. The comparison has been depicted in Figure 5. As shown in Figure 5, the suggested cubic correlation for heat transfer coefficient for steelwater 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 runout 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 also. The offline mathematical model is based on numerical technique for prediction of throughthfckness temperature of strip in the hot strip mill, by predicting the temperature profile along the bed of the runout table. REFERENCES: [1] 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. 367374 (Translation: Int. J. Heat Mass Transfer, 9, 1419, 19%) [2] W.K. Soh and W.Y.D. Yuen, "Flow Visualization of the Boiling Heat Transfer at the RunOut Table", 41^ Mechanical Working and Steel Processing Conference, ISS, 1999, Vol./XXXVII, pp. 707715. [3] Liu, Z.D., Fraser, D., and Samarsekera, IV., 2002, "Experimental Study and Calculation of Boiling Heat Transfer on Steel Plates during Runout Table Operation", Canadian Metallurgical Quarterly, Vol. 41, No. 1, pp. 6374. [4] Hernandez, V.H.., Samarasekera, I.V., and Brimacombe J.K., 1994, "Heat Transfer Model of Runout Table Cooling: A Fundamental Approach", 36* Mechanical Working and Steel Processing Conference, Vol./XXXIl, pp. 345356. [5] 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. 121130. [6] 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. 4959. [7] 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. 5055. [8] 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. 919925. [9] 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, ISSAIME, Vol. XXXI, pp. 311316. [10] 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 392 400. [11] MItsutsuka, M., 1983, "Heat Transfer Coefficients in the Surface^ Temperature Range of 400 to 800 C during water  spray Cooling of Hot Sted Product", Tetsuto Hagane, Vol. 69, pp. 268. We Claim; 1. A method for prediction of temperature profile over the length as well as over the thickness of a strip in a runout table of a hot strip mill comprising the steps of:  determining offline through thickness temperature with the aid of heat conduction equation: 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 waterstrip 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 waterstrip interface for various grades of steel, characterized in that the simulated cooling temperature of a length of runout 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 runout 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 waterstrip interface is determined by a third order polynomial. Finally, the correlation is validated for various grades of steel. The simulated cooling temperature of runout table strip mill is predicted from the numerical solution. 

00865kol2006 correspondence1.2.pdf
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00865kol2006description(complete).pdf
865KOL2006(05122011)FORM27.pdf
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865KOL2006CANCELLED DOCUMENTS.pdf
865kol2006correspondence1.1.pdf
865KOL2006DESCRIPTION COMPLETE.pdf
865kol2006grantedabstract.pdf
865kol2006grantedclaims.pdf
865kol2006grantedcorrespondence.pdf
865kol2006granteddescription (complete).pdf
865kol2006granteddrawings.pdf
865kol2006grantedexamination report.pdf
865kol2006grantedform 1.pdf
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865kol2006grantedreply to examination report.pdf
865kol2006grantedspecification.pdf
865KOL2006REPLY TO EXAMINATION REPORT1.1.pdf
865KOL2006REPLY TO EXAMINATION REPORT.pdf
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Patent Number  235723  

Indian Patent Application Number  865/KOL/2006  
PG Journal Number  19/2010  
Publication Date  07May2010  
Grant Date  07May2010  
Date of Filing  25Aug2006  
Name of Patentee  TATA STEEL LIMITED.  
Applicant Address  RESEARCH AND DEVELOPMENT DIVISION JAMSHEDPUR831001  
Inventors:


PCT International Classification Number  B21B 28/00  
PCT International Application Number  N/A  
PCT International Filing date  
PCT Conventions:
