Thermal Behavior of a Multi-layered Thin Slab Carrying Periodic Signals Under the Effect of the Dual-Phase-Lag Heat Conduction Model

The thermal behavior of a two–layered thin slab carrying periodic signals under the effect of the dual-phase-lag heat conduction model is investigated. Two types of periodic signals are considered, a periodic heating source and a periodic imposed temperature at the boundary. The deviations among the predictions of the classical diffusion model, the wave mode, and the dual-phase-lag model are investigated. Analytical closed-form solutions are obtained for the temperature distribution within the slab. The effect of the angular frequency, thickness of the plate, dimensionless thermal relaxation time, dimensionless phase-lag in temperature gradient, thermal conductivity, and thermal diffusivity on the temperature distribution of the slab was studied. It is found that the deviations among the three models increase as the frequency of the signals increases and as the thickness of the plate decreases. It is found that the use of the dual-phase-lag heat conduction model is necessary when the metal film thickness is of order 10^–6 m and the angular frequency of the signals is of order 10¹²rad · s^–1.