Temporal linear instability of viscous coaxial jets under a radial thermal field is carried out by considering axisymmetric and non-axisymmetric disturbances. The interfacial tensions of different fluids are taken to be temperature dependent. The para-sinuous, para-varicose, and helical unstable modes are identified in the Rayleigh regime. The energy budget is also employed to explore the relative importance of thermal-induced stresses on the jet instability at the most unstable wavenumber by changing the dimensionless parameters. It is shown that decreasing the temperature ratio of inner fluid to surrounding fluid (T₁₃) promotes the jet instability. For coaxial jets at T₁₃ > 1, the Marangoni flow makes coaxial jets more stable, and increasing the fluid thermal conductivity suppresses the jet instability. For coaxial jets at T₁₃ < 1, however, their influences on the jet instability are opposite. Compared with the thermal-induced stresses at the inner and outer interfaces, the inner interfacial tension is the main factor dominating the flow. Increasing either inner interfacial tension or outer surface tension and decreasing viscosity of any fluid can promote the instability of coaxial jets. The variations of thermal conductivity and specific heat capacity of either inner or surrounding fluids apparently influence the jet instability of the para-varicose mode, but hardly influence that of the para-sinuous mode. This work would provide great insight into the physical mechanism of thermal jet instability in various applications.

中文翻译：

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径向热场下粘性同轴射流的不稳定性和能量收支分析

通过考虑轴对称和非轴对称扰动来实现粘性同轴射流在径向热场下的时间线性不稳定性。不同流体的界面张力被认为是温度依赖性的。在瑞利政权中确定了顺正，顺静脉和螺旋不稳定模式。能量预算还用于通过更改无量纲参数来探索最不稳定波数下热诱导应力对射流不稳定性的相对重要性。结果表明，降低内部流体与周围流体的温度比（T ₁₃）会导致射流不稳定。用于T ₁₃处的同轴射流> 1，Marangoni流动使同轴射流更加稳定，而增加流体的导热率可以抑制射流的不稳定性。用于T ₁₃处的同轴射流<1，但是，它们对射流不稳定的影响是相反的。与内部和外部界面处的热应力相比，内部界面张力是控制流动的主要因素。增加内部界面张力或外部表面张力并降低任何流体的粘度都可能会促进同轴射流的不稳定性。内部或周围流体的热导率和比热容的变化显然会影响准静脉曲张模式的射流不稳定性，但几乎不会影响准正弦波模式的射流不稳定性。这项工作将为各种应用中的热射流不稳定性的物理机理提供深刻的见解。