Abstract

The Fourier law correctly describes heat transport in most practical macroscopic problems. However, for heat transfer in rapid processes, heat transport on micro- and nanoscales, and heat transfer in materials with an internal structure (porous media and biological tissues), other models are required that take into account nonlinear effects, as well as temporal (memory) and spatial nonlocality. Such models are considered in this review, including models with time lag, phonon and thermodynamic models, as well as models based on differential equations in fractional derivatives.

中文翻译：

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傅立叶定律以外的热传导

摘要

傅立叶定律正确地描述了大多数实际宏观问题中的热传递。但是，对于快速过程中的热传递，微米和纳米级的热传递以及具有内部结构的材料（多孔介质和生物组织）的热传递，还需要考虑到非线性效应以及时间（记忆）和空间非局部性。本文中考虑了此类模型，包括具有时滞的模型，声子模型和热力学模型，以及基于分数导数中微分方程的模型。