【正文】 slab in heating zone as shown in ,therefore,temperature rise of the slab is weakened and temperature is more evenly shows the 26th slab in the final soaking zone ,where temperature of the medium and furnace wall decreases than the previous heating ,one can notice the occurrence of the back heat flow from the slab surface into its surroundings and temperature of the slab decreases more or less pared with the slab in the previous heating zone.Further,displayed in are the predicted temperature profiles of the slan along the longitudinal direction of the furnace ,where Ts_u,Ts_c,and Ts_d denote the average temperature of the upper surface,centerline of the slab (2007)37403748 of the radiative heat flux vector on the slab surface and temperature contours in the slab :(a) 1st slab, ,(b) 3rd slab ,(c) 7th slab ,(d) 12th slab ,(e) 17th slab ,(f) 26th slab ,.. Predicted temperature profiles of the slab along the axial direction of the furnaceheight,and lower surface of the slab , can see that the centerline temperature of the slab charged into the furnace with increases through the first four zones from the final soaking zone,however,temperature slightly decreases and remains almost constant about for the upper and lower surface it is found that although the upper temperature is slightly lower than the lower one in the first nonfiring zone because of the lower cold furnace wall is more far from the slab,after charging zone the temperature reversal occurs and upper temperature is higher than lower one due to the furnace bottom the contrary ,in the final soaking zone ,lower surface is much lower than the (2007)37403748centerline temperature due to the above mentioned back heat flow. Effect of absorption coefficient and slab emissivity Radiative heat transfer from the flame and bustion gases and from the furnace wall to the slab is usually the dominant mode of heat transfer in high temperature reheating furnace .Here ,to find the effect of radiative properties,some parametric studies are performed . shows the effect of absorption coefficient of the medium on the longitudinal temperature profile of the centerline temperature of the slab .As shown,the slab centerline temperature increases as the absorption coefficient increases from to is because surrounding medium participates in thermal radiation more actively with the increase of the absorption coefficient .Next,the effect of slab emissivity on the temperature profile is introduced in ,where slab emissivity is varied from to ,while absorption coefficient and furnace wall emissivity are kept at and , expected ,temperature increases with the slab emissivity because the slab can receive more heat impinging on the surface as the surface bees black .However ,it is noted that although the effect of slab emissivity is more manifested within the furnace ,the final temperature near exit os relatively in the narrow limits. Comparison with the experimental dataFinally ,the predicted temperature history in the slab using the present model is pared with the experimental data conducted by POSCO ad shown in this figure,in situ measured average temperature in the upper and lower furnace zones,which is obtained by suing each five ktype thermocouples locations in the above and below the slab in the selected locations,is also presented with the centerline experimental data of the slab temperature .In order to predict the temperature of the slab ,in situ measured temperature shown in is used as medium temperature while furnace wall and slab emissivities are kept at . of absorption coefficient on the predicted longitudinal temperature profile of the slab . of slab emissivity on the predicted longitudinal profile of the slab.(2007)37403748 of the predicted and measured longitudinal temperature profile of the slab and ,respectively .Further,absorption coefficient of the mediun is obtained by using he WSGG nongray model[13]based on the experimentally obtained CO2 and H2O mole fractions ,which has similar value of the gray absorption coefficient of that although the uncertainty range of the measurements there exists a reasonable agreement between the predicted and measured temperature profiles .Especially,at the final soaking zone ,namely near the exit of the furnace,the predicted temperature bees to be in good agreement with the experimental means that the present heat transfer model can be successfully applied to the walking beam type reheating furnace for the prediction of slab temperature.4 ConclusionsA heat transfer model and applications have been presented for the prediction of thermal behavior in a five zone reheating model furnace resembling the POSCO on the given longitudinal furnace gas and wall temperature,the model can predict the radiative heat flux on the slab surface and the temperature distribution in the slab during the heating process by coupling the RTE and transient heat conduction equation. Although the numerical results are for the specific example under consideration ,the same methodology may be used to model any similar reheating furnace in the design phase or currently in operation .Further development of the present model will aim to include appropriate submodels for the analysis of skid mark formation ,gas and wall temperature distribution ,and ,finally ,full three dimensional heat transfer mosel.AcknowledgementsThe author gratefully acknowledges the financial support by the POSCO and Chonbuk National University,the author would like to tank ,POSCO technical Ramp。D center for his constructive ments and kind help.References [1] ,Threedimensional analysis of the walkingbeamtype slab reheating furnace in hot strip mills, Transfer,Part A 38(2000)589609.[2] ,Prediction of transient slab temperature distribution in the reheating furnace of a walkingbeam type for rolling of steel slabs,ISIJ (2000)1151123.[3] ,Numerical study of the