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].