An asymptotic model of work roll heat transfer in strip rolling

An asymptotic model of work roll heat transfer is developed using a multiple time scale approach. The model is appropriate under typical high Peclet number rolling conditions and provides a unified framework for relating previous roll heat transfer models. The solution consists of a fast time scale thermal boundary layer near the roll surface, along with a slow time scale core heat transfer problem. Several features of the model are illustrated. First, boundary layer behavior is examined under steady and dynamic conditions. Here, the decay rate for boundary layer transients is determined and theoretical steady-state temperature distributions are compared against previously reported experimental data. Heat transfer within the core is then considered under relatively general surface heating conditions. In the special case where the surface heat flux is constant, core temperatures are shown to increase linearly with time. In the last illustration, the model is used to obtain inverse estimates of circumferentially varying roll surface heat flux and temperature distributions. In this case, comparisons are made with the finite difference-based inverse estimates recently reported by Huang et al., International Journal of Heat and Mass Transfer, 1995, 38, 1019–1031.