NONCLASSICAL HEAT CONDUCTION ANALYSIS IN PERIODIC STRUCTURES WITH MULTIPLE SPATIAL AND TEMPORAL SCALES ANALYSIS METHOD

A spatial and temporal multiple scale method is studied to simulate the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials . The model is derived from the higher-order homogenization theory with multiple spatial and temporal scales. Amplified spatial and reduced temporal scales are respectively introduced 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 is eliminated and the fourth-order differential equations are derived. To avoid the necessity of C¹- continuity in finite element implementation, the C⁰-continuous mixed finite element approximation of the resulting nonlocal equations of non-Fourier heat conduction is put forward. Numerical examples are computed to demonstrate the efficiency and validity of the theories and model developed.