Numerical investigation of the flow of a glass melt through a long circular pipe

This work is concerned with the comparison between a two-dimensional axisymmetric simulation of glass melt flowing through a pipe with a circular cross-section and a one-dimensional model studied by Gießler et al. [Gießler, C., Lange, U., Thess, A., 2007. Nonlinear laminar pipe flow of fluids with strongly temperature-dependent material properties. Phys. Fluids 19, 043602]. The fluid is supposed to be heated by internal electromagnetic (Joule) heating and cooled at the wall by convection. The exponential temperature dependence of the viscosity and the electrical conductivity are fully taken into account. The two models are being compared over a range of values of two different parameters. We find a very good agreement for moderate and high thermal conductivities or in the case of dominating heating. For strong cooling and low thermal conductivities, differences between the one-dimensional model and the two-dimensional axisymmetric simulation occur. The comparison shows that in the latter case the formation of strong radial temperature variations and the resulting radial variation of the viscosity lead to a divergence between the two-dimensional simulation and the one-dimensional model.