ABSTRACT

Thethree-dimensionalrollthermalcontourmodelthatwasdevelopedbytheU.S.SteelResearchLaboratory[4-7]isbasedonthefollowingassumptions:

•Meanrolltemperatureisconsideredtoplayamajorpartinradialexpansionoftheroll. •Axialconductionisconsideredsothatthevariationofrollexpansionalongtherollbarrelistaken

intoaccount. •Bothheatinputfromthehotslabandheatremovalbywaterspraysareassumedtoactuniformly

aroundtherollcircumferenceatanycircularcross-sectionoftheroll. •Constantvaluesoftheheattransfercoefficientsareadoptedbetweentheslabandtherollthroughout

theslabwidthaswellasbetweenthewatersprayandtheroll. •Heattransferfromtheslabtotherollisassumedtobebyconductionwiththecontactconductance

coefficientselectedasafunctionofmeanrolltemperature. Inthismodel,therollisdividedintotwoseparateregionsasshowninFig.19.3.Inregion1,bothslab

andwaterspraysparticipateintheheattransfer,whereasonlythewaterspraysactinregion2.Basedon thelawofconservationofenergy,thefollowingdifferentialequationsforaxiallysymmetrictime-varying temperatureT(z,t)havebeenderivedincylindricalcoordinates:

Fig. 19.3 Heat transfer in slab-roll-water spray system. Adapted from Pallone [4].