Current Research Progress in Non-Classical Fourier Heat Conduction

Abstract

Classical Fourier law can accurately describe most heat conduction problems. But for ultrafast heat conduction process and micro/nanoscale heat conduction problems, non-classical Fourier (non-Fourier) effect may become dominated. The paper gives a review on the current progress on non-Fourier heat conduction in engineering. It includes basic concept, physical models, thermal relaxation effect, and related experiments. Also introduced are the solution methods of non-Fourier heat conduction equations, including closed-form solution, finite difference method, finite element method, molecular dynamics simulation, variational method, and other hybrid methods. Some challenging issues are discussed at the conclusion of the paper.

Nanoscale Heat Conduction in CNT-POLYMER Nanocomposites at Fast Thermal Perturbations

“…In any case, the thermal conductivity can be considered as an equilibrium parameter at Δt> 1 ns [13,14]. In fact, the characteristic time constants describing the heat flux lag and the temperature gradient lag in the Maxwell–Cattaneo approach [9,10] associated with nonequilibrium behavior of the thermal conductivity are much less than 1 ns in amorphous polymers; for details, see Reference [13]. Therefore, the effect of non-Fourier heat conduction can be neglected on nanosecond and longer time scales.…”

“…Technologically important polymer nanocomposites have been investigated recently by ultrafast nanocalorimetry [6,7,8]. However, the classical heat conduction theory is insufficient for ultrafast processes in nanocomposites if the local temperature is varying suddenly [9,10,11,12]. In addition, polymer-based nanocomposites have an interesting specificity for fast thermal perturbations [13,14].…”

Space–time Galerkin methods for simulation of laser heating using the generalized nonlinear model

“…Therefore, by the dissipation inequality (8), it follows that equation (25) leads to the required energy estimate; that is,…”

“…This model is commonly referred to as the Cattaneo-Vernotte-Maxwell equation: see [21], for example. For much of the historical development and theoretical justifications of the Cattaneo-Vernotte-Maxwell equation, see the review articles [16,17,22,23,[23][24][25]. Although the Cattaneo-Vernotte-Maxwell model has been used extensively in modelling wave-like thermal propagation in various applications [25][26][27][28][29], its validity and derivation have been the subject of considerable debate among researchers [30][31][32].…”

A Semi-explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model

“…heat conduction in biological tissues [3] and materials with non-homogeneous inner structure [4]) . For this reason, various linear and nonlinear generalizations of Fourier's law have been proposed by many researchers through the past two centuries (see books [5][6][7] and reviews [8][9][10][11]).…”