Studies on melt spinning. I. Fundamental equations on the dynamics of melt spinning

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<jats:title>Abstract</jats:title><jats:p>The dynamics of melt spinning was analyzed by deriving a set of simultaneous partial differential equations.</jats:p><jats:p>Equation of heat balance: <jats:disp-formula> </jats:disp-formula></jats:p><jats:p>Equation of force balance: <jats:disp-formula> </jats:disp-formula></jats:p><jats:p>Equation of material balance: <jats:disp-formula> </jats:disp-formula> In the above equations, the distance <jats:italic>x</jats:italic> from the spinneret and time τ are the independent variables; temperature <jats:italic>t</jats:italic>, local velocity <jats:italic>v</jats:italic>, and cross‐sectional area <jats:italic>A</jats:italic> are the dependent variables. It is assumed that tensile viscosity β is a function of temperature <jats:italic>t</jats:italic> alone, and the spinning tension <jats:italic>F</jats:italic> is a pure time function. Steady‐state (∂/∂τ = 0) solutions of the above equations showed a fairly good agreement with the experimentally measured values of temperature <jats:italic>t(x)</jats:italic> and thickness <jats:italic>A(x)</jats:italic>.</jats:p>

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