Scaling and modeling of the heat transfer across the free surface of a thermocapillary liquid bridge

Abstract

Purpose – This paper aims to derive a reduced-order model for the heat transfer across the interface between a millimetric thermocapillary liquid bridge from silicone oil and the surrounding ambient gas. Design/methodology/approach – Numerical solutions for the two-fluid model are computed covering a wide parametric space, making a total of 2,800 numerical flow simulations. Based on the computed data, a reduced single-fluid model for the liquid phase is devised, in which the heat transfer between the liquid and the gas is modeled by Newton’s heat transfer law, albeit with a space-dependent Biot function Bi(z), instead of a constant Biot number Bi. Findings – An explicit robust fit of Bi(z) is obtained covering the whole range of parameters considered. The single-fluid model together with the Biot function derived yields very accurate results at much lesser computational cost than the corresponding two-phase fully-coupled simulation required for the two-fluid model. Practical implications – Using this novel Biot function approach instead of a constant Biot number, the critical Reynolds number can be predicted much more accurately within single-phase linear stability solvers. Originality/value – The Biot function for thermocapillary liquid bridges is derived from the full multiphase problem by a robust multi-stage fit procedure. The derived Biot function reproduces very well the theoretical boundary layer scalings.