NUMERICAL MODELLING OF MICROSCALE EFFECTS IN CONDUCTION FOR DIFFERENT THERMAL BOUNDARY CONDITIONS

Non-Fourier microscale effects are significant during the rapid heating of metallic substrates. Recently, a two phase lag model for conduction has been proposed, which accounts for the finite propagation speed of a thermal wave and the equilibration time between the electrons and lattice. Available closed-form solutions for the dual phase lag model are found to be very different for apparently similar boundary conditions. In this study, the origin of the discrepancy in the available analytical results has been identified as the sensitivity of the predicted solution to the way of implementing the surface boundary condition. A numerical solution procedure based on the finite element method and fourth-order Runge?Kutta time marching procedure has been employed for the spatial and temporal discretisations, respectively. The predicted results for different boundary conditions clearly capture thermal wavelike and pure diffusion-type phenomena in the appropriate range of time lag values. Application of the two phase lag model to laser pulse heating illustrates that the effects of microscale phenomena on the spatial and temporal variations of temperature could become important for high frequency pulsing.