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
ISSN: 0961-5539
Article publication date: 29 January 2024
Issue publication date: 29 March 2024
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.
Keywords
Acknowledgements
Part of this work has been supported by FFG (ASAP 14, project number 866027) and by ESA (contract 4000121111/17/NL/PG/pt).
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
Publisher
:Emerald Publishing Limited
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