Abstract

This study aims to analyze the stability of a gravity-driven thin film flow in the heated/cooled interior surface of a vertical hollow cylinder. The model development involves simplifying the flow and energy equations using the usual thin-film approximation, where the average film thickness is considered to be much smaller than the radius of cylinder. A dispersion relation is then derived to study the temporal stability of the system in order to quantify the effect of various non-dimensional parameters present in the model, such as the thermoviscous number, Marangoni number, Biot number, and Bond number. Another non-dimensional parameter is introduced by considering an opposing suction pressure in the annulus region. The thermocapillary stress and the thermoviscous effect are shown to strongly affect the temporal stability of the flow. It is shown that although the suction pressure affects the velocity profile of the flow, it does not affect the temporal stability results. The suction pressure is then shown to have some effect on the spatiotemporal stability. Critical condition is presented for the transition between absolutely and convectively unstable systems, and parameter regimes are presented to quantify the effect of the above-mentioned parameters.

Graphic abstract

中文翻译：

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吸入压力在重力驱动的热粘性液膜流下气缸内表面的稳定性中的作用

摘要

本研究旨在分析垂直空心圆柱体加热/冷却内表面中重力驱动的薄膜流的稳定性。模型开发涉及使用通常的薄膜近似简化流动和能量方程，其中平均薄膜厚度被认为远小于圆柱半径。然后导出色散关系来研究系统的时间稳定性，以量化模型中存在的各种无量纲参数的影响，例如热粘性数、马兰戈尼数、毕奥数和邦德数。另一个无量纲参数是通过考虑环空区域中的反向吸入压力引入的。热毛细应力和热粘性效应显示出强烈影响流动的时间稳定性。结果表明，虽然吸入压力影响流动的速度剖面，但不影响时间稳定性结果。然后表明吸入压力对时空稳定性有一些影响。提出了绝对不稳定系统和对流不稳定系统之间过渡的临界条件，并提出了参数制度来量化上述参数的影响。

图形摘要