Heat Transfer across the Free Surface of a Thermocapillary Liquid Bridge

Abstract

The heat transfer across the free surface of a millimetric thermocapillary liquid bridge is investigated for two dimensional axisymmetric flows, computed by Newton–Raphson iteration. The coupled multiphase flow in the silicone-oil liquid bridge and in the ambient gas (air) is considered for Marangoni and Prandtl numbers of interest for typical space experiments. Based on the space-resolved heat flux of the two-phase flow for a wide range of parameters, we derive a model for the heat flux in form of Newton’s heat transfer law for a surrogate single phase flow, in which a space-dependent Biot function is considered. A parametric study for a 2 St silicone-oil liquid bridge is conducted for 150 configurations to derive a reliable fit of the Biot function for a wide range of Reynolds numbers and aspect ratios. An explicit form of the parametric fit is provided which takes into account the hot- and cold-wall boundary layers in the liquid.