A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

中文翻译：

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刚性固体的内部结构和热传导：两种温度方法

非傅立叶热传输机制表征了具有内部结构的固体中的热传导。几种热力学理论试图解释在这种系统中与傅里叶体系的分离。在这里，我们根据非平衡热力学原理开发了一个双温度模型来描述非傅立叶状态。基本假设是系统中存在两个分离良好的长度尺度，即一个与矩阵维数（体积）有关，另一个与内部结构的特征长度有关。对于描述每个长度尺度中的热传导的温度，获得了两个傅里叶类型的耦合传输方程。通过使用耦合参数作为拟合参数，最近几组关于不同结构材料的热响应的实验结果令人满意地再现了。讨论了现行形式主义与其他理论的异同。