A numerical strategy to determine an estimate to the optimal initial distribution of temperature for industrial processes requiring coiling of bars in hot metal rolling operations based on a three-dimensional mathematical model for the evolution of temperature in a shape changing domain is presented. The corresponding numerical solution is presented as well. The solution integrates a two dimensional geometrically adaptive finite element solution in the coiling plane for a shape changing domain with a finite difference one-dimensional solution in the widthwise direction of the bar using a novel numerical separation of variables strategy. Time is discretized according to a Crank-Nicolson type scheme. The results of a specific numerical study for the coiling of hot steel between the roughing stands and the finishing stands are presented.

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