A three-dimensional heat transfer model considering various skid button heights for the prediction of the temperature history of steel slabs was performed in order to obtain the optimal heating pattern of these slabs with minimum energy consumption in a walking-beam type reheating furnace. An algorithm was developed using a simplified conjugated-gradient method combined with a shooting method and was used as an optimiser to design the furnace temperature distribution. The effect of the skid button heights on the design requirements, such as the energy consumption necessary for heating a slab, skid-mark temperature uniformity at the furnace exit and slab discharging temperature, was investigated. The parametric study results indicated that the skid-mark temperatures significantly decrease with increases in the skid button heights. In addition, the optimal designs suggested lower energy consumption for heating a slab and improved skid-mark temperature uniformity as compared to the original operating conditions in a steel plant.
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