Non-isothermal flows of Newtonian slender glass fibers (Q1367325)

We perform a non-isothermal analysis of axisymmetric Newtonian slender fibers. Lubrication scaling with a small slenderness ratio \(\varepsilon\) along with restrictions on other dimensionless parameters systematically provides one-dimensional approximations by using the full Navier-Stokes equations. At leading order, we formally obtain the equations of previous analyses when the parameter range is appropriate. Higher-order analyses show the effects of weak two-dimensionality when all appropriate parameters are not sufficiently small. We have also established limitations on the one-dimensional approach of previous analyses. We consider a variable heat transfer coefficient and show its importance in accurate predictions of fiber diameter.