The liquid frictional forces are operative in the upper part of the mold, because of the high temperature and fairly uniform pressure. In the lower mold region, solid-solid friction may arise from contact between the solidified flux, or the strand, and the mold. The total friction force is given by the sum of the liquid and solid frictional forces. Assuming the velocity gradient between the mold wall and the strand surface is linear, which is an approximation since the static pressure gradient and the transverse temperature gradient affect the velocity gradient, the liquid frictional force F, is given by the following equation.
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