The 3w method may be used to estimate the thermal conductivity of an electric conducting wire. In this method, an alternating voltage with an angular frequency w is applied to the wire. The resulting low tension 3 of angular frequency 3w that appears in the total tension is extracted by a lock-in amplifier. The amplitude of 3w is directly linked to the thermal conductivity of the wire and enables its estimation. All authors using the 3w method for the determination of the thermal conductivity of an electric conducting wire considered that the heat flux produced by Joule effect in the wire is constant. This hypothesis leads to a linear form of the heat transfer equation. In this paper, an analytical model taking into account the dependence of the heat flux on the temperature is developed, it leads to a non-linear form of the heat transfer equation. The importance of the non-linearity in certain cases is demonstrated and the analytical solution is used to define a unique criterion that must be verified to ensure the validity of the linear solution.

中文翻译：

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瞬态热源情况下传热方程的非线性分析：应用于 $$3\omega $$3ω 方法

3w 方法可用于估计导电线的热导率。在该方法中，向导线施加角频率为 w 的交流电压。出现在总张力中的角频率为 3w 的低张力 3 由锁相放大器提取。3w 的幅度与导线的热导率直接相关，并且可以对其进行估计。所有使用 3w 法测定导线导热系数的作者都认为导线中由焦耳效应产生的热通量是恒定的。这个假设导致传热方程的线性形式。在本文中，考虑到热通量对温度的依赖性的分析模型被开发，它导致传热方程的非线性形式。