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.

Citation

Romanò, F., Stojanović, M. and Kuhlmann, H.C. (2024), "Scaling and modeling of the heat transfer across the free surface of a thermocapillary liquid bridge", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 4, pp. 1528-1566. https://doi.org/10.1108/HFF-04-2023-0164