The lack of a practical mathematical model to simulate thermal behavior of the metal rolling process has forced mill operators and designers to rely on plant experience and testing, which is time consuming and expensive. An effective finite difference model has been developed to study the temperature profiles of the work roll and the strip. Several finite difference techniques have been successfully employed to cope with the special characteristics of the rolling process, such as very high velocity, high temperature variation in a very thin layer, curved boundary, and bimaterial interface. Typical rolling conditions were analyzed to provide temperature information on the roll and strip. Both cold and hot rollings were considered, and the effect of changing velocities was also studied. Good correspondence is found when present results are compared with either analytical solutions under simplified rolling conditions or measured data.

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