Abstract Positive temperature coefficient (PTC) material is widely used in the field of thermal control due to its unique temperature sensitive characteristics. However, there is no general criterion about PTC material thermal control at present due to the lack of theoretical analysis in the previous works. Thus, in this paper, the dimensionless method is used to study PTC material adaptive thermal control and finally, a fitting formula is obtained to estimate the equilibrium temperature of controlled device. First, a one-dimensional and steady-state heat transfer model was proposed to calculate the equilibrium temperature of controlled device under thermal control of PTC materials, and it was verified by experiment. Then, the model has been nondimensionalized and four dimensionless numbers are introduced by Buckingham theorem, in which the Wr number is presented to represent the heating characteristics of PTC materials. Finally, by fitting all the data, a form of fitting equation of equilibrium temperature of controlled device is obtained. The results show that this form proposed in this paper can be applied to the widely used ceramic PTC materials. The criterion equation fitted by this form can effectively estimate the equilibrium temperature of the controlled devices with good accuracy and wide application.

中文翻译：

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正温度系数（PTC）材料热控制的无量纲研究

摘要 正温度系数（PTC）材料由于其独特的温度敏感特性而广泛应用于热控制领域。然而，由于以往工作缺乏理论分析，目前还没有关于PTC材料热控制的通用标准。因此，本文采用无量纲方法对PTC材料自适应热控制进行研究，最终得到了估计受控器件平衡温度的拟合公式。首先，提出了一种一维稳态传热模型来计算PTC材料热控制下受控器件的平衡温度，并通过实验验证。然后，模型被无量纲化，并由白金汉定理引入四个无量纲数，其中 Wr 数表示 PTC 材料的加热特性。最后，通过对所有数据进行拟合，得到受控装置平衡温度拟合方程的形式。结果表明，本文提出的这种形式可以应用于广泛使用的陶瓷PTC材料。这种形式拟合的判据方程可以有效地估计被控装置的平衡温度，精度好，应用广泛。