Multi-dimensional nonclassical heat conduction analysis with multiple spatial and temporal scales analysis method

A spatial and temporal multiple scale method used to simulate the phenomenon of non-Fourier heat conduction in multi-dimensional periodic heterogeneous materials was systematically studied. The model was derived from the high-order homogenization theory with multiple spatial and temporal scales. Amplified spatial and reduced temporal scales were respectively int roduced to account for fluctuations of non-Fourier heat conduction due to material heterogeneity and nonlocal effect of the homogenized solution. By combining various orders of homogenized non-Fourier heat conduction equations，the reduced time dependence was eliminated，the homogenized coefficients were solved by the numerical method，and then multi-dimensional high-order nonlocal equations of non-Fourier heat conduction were derived. The two-dimensional numerical examples were computed to analyze the non-Fourier heat conduction in the different microstructures of multiphase materials. Numerical result s demonst rated the validity and effectiveness of the multi-dimensional high-order nonlocal model obtained by the high-order mathematical homogenization theory.