Current research progress in non-classical Fourier heat conduction

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.