Stability analysis of gravity-driven flow of a thermoviscous liquid on the exterior surface of a uniformly heated or cooled vertical cylinder is presented. The film evolution model derived using lubrication approximation consists of four dimensionless groups, namely, Marangoni number, Biot number, Bond number, and thermoviscosity number. The viscosity of the liquid is modeled as an exponentially varying function of temperature. The thermocapillary stress significantly affects the Rayleigh-Plateau instability for flow over a nonisothermal cylinder with intricate dependence on various parameters involved. For the temporally unstable system, spatiotemporal stability analysis is performed to delineate the parameter regions for convectively and absolutely unstable systems. Brigg's criterion is employed and the critical value of a composite parameter $\beta$ is evaluated to study the transition from convective to absolute instability. A proper rescaling of the dispersion relation shows that the condition on the composite parameter is $\beta <1.507$ for the existence of absolute instability, which is consistent with an earlier work on isothermal flows. Further, an expression is found for the critical composite Marangoni number beyond which the film is always absolutely unstable independent of the Bond number. This critical value is shown to be an increasing function of thermoviscosity number. Results from the nonlinear simulations are in agreement with the predictions of the linear temporal and spatiotemporal analyses.

中文翻译：

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重力驱动的热粘性液体薄膜在加热或冷却的垂直圆柱体中向下流动

提出了均匀加热或冷却的垂直圆柱体外表面上热粘性液体重力驱动流动的稳定性分析。使用润滑近似法得出的膜演化模型包括四个无因次组，即马兰哥尼数，比奥数，键数和热粘度数。液体的粘度被建模为温度的指数变化函数。热毛细管应力极大地影响了在非等温圆柱体上流动的瑞利-普拉多不稳定，这取决于所涉及的各种参数。对于时间不稳定的系统，进行时空稳定性分析以描绘对流和绝对不稳定系统的参数区域。布里格$\beta$进行了评估，以研究从对流到绝对不稳定的过渡。色散关系的适当重新定标表明，复合参数上的条件是$\beta <1.507$绝对不稳定性的存在，这与早期关于等温流的工作是一致的。此外，发现了临界复合Marangoni数的表达式，在该表达式中，薄膜始终绝对不稳定，与键数无关。该临界值显示为热粘度值的增加函数。非线性模拟的结果与线性时间和时空分析的预测一致。