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.

中文翻译：

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热毛细管液桥自由表面传热的缩放和建模

目的

本文旨在推导出硅油的毫米级热毛细管液桥与周围环境气体之间界面传热的降阶模型。

设计/方法论/途径

双流体模型的数值解的计算涵盖了广泛的参数空间，总共进行了 2,800 次数值流动模拟。基于计算数据，设计了一个简化的液相单流体模型，其中液体和气体之间的传热由牛顿传热定律建模，尽管具有空间相关的毕奥函数 Bi(z) ，而不是常数毕奥数 Bi。

发现

Bi(z) 的显式稳健拟合涵盖了所考虑的整个参数范围。与二流体模型所需的相应两相全耦合模拟相比，单流体模型与导出的 Biot 函数一起以低得多的计算成本产生非常准确的结果。

实际影响

使用这种新颖的毕奥函数方法而不是恒定毕奥数，可以在单相线性稳定性求解器中更准确地预测临界雷诺数。

原创性/价值

热毛细管液桥的 Biot 函数是通过稳健的多级拟合程序从完整的多相问题导出的。导出的 Biot 函数很好地再现了理论边界层缩放。