论文标题
非四车传导模型的动物园
The Zoo of Non-Fourier Heat Conduction Models
论文作者
论文摘要
傅立叶热传导模型对于大多数宏观问题有效。然而，当热传播或时间滞后的波性质变得占主导地位时，它会失败，并且在超快加热（脉冲激光加热和融化）中，液体金属的快速固化，在玻璃聚合物中的玻璃聚合物中的快速固体，在Nansoscale的玻璃转移中，在热量的速溶体中，液体金属的过程快速固化，在玻璃聚合物附近的玻璃聚合物中，液体金属的过程快速固化，在热量脉冲中，液压液的速度升温，并在热量的速溶体中，液体金属的过程很快持续时间，在包括多硅烷在内的颗粒和多孔材料中，在热通量的极高值中，在生物组织中的传热中。 在通用材料中，放松时间范围从$ 10^{ - 8} $到$ 10^{ - 14} $ sec，但是，在衰老恒星的退化核心中，它可能高达1秒，并且在颗粒和生物学物体中报告的值可能变化为30秒。该论文考虑了许多非峰热传导模型，这些模型包含具有记忆（遗传材料，包括分数遗传材料）的材料的时间非本地性或空间非局部性，即具有非均匀内部结构的材料。
The Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation or time lags become dominant and the memory or/and spatial non-local effects significant -- in ultrafast heating (pulsed laser heating and melting), rapid solidification of liquid metals, processes in glassy polymers near the glass transition temperature, in heat transfer at nanoscale, in heat transfer in a solid state laser medium at the high pump density or under the ultra-short pulse duration, in granular and porous materials including polysilicon, at extremely high values of the heat flux, in heat transfer in biological tissues. In common materials the relaxation time ranges from $10^{-8}$ to $10^{-14}$ sec, however, it could be as high as 1 sec in the degenerate cores of aged stars and its reported values in granular and biological objects varies up to 30 sec. The paper considers numerous non-Fourier heat conduction models that incorporate time non-locality for materials with memory (hereditary materials, including fractional hereditary materials) or/and spatial non-locality, i.e. materials with non-homogeneous inner structure.
