4. Non-isothermal Newtonian model

In this case, the molten polymer is stretched in the air over a longer distance (of the order of a metre). In addition, draw-off velocities are significantly higher, which naturally leads to much higher draw-off ratios (in excess of 100). In conventional textile spinning processes, the filament is cooled and solidified by an air blower. The equations of equilibrium and conservation of matter are identical to those used previously. A new equation is the heat transfer equation, which describes the evolution of the average temperature over a section. A key problem is the uniformity of cooling between the different filaments leaving the spin pack. This problem will not be studied here, and we will consider, as before, the spinning of a unitary filament. The heat balance equation uses a heat transfer coefficient between the filament and the ambient air, which is difficult to estimate. This new...