An integral relation is obtained between local temperature and local temperature gradient for the dual-lag model of heat transport, which substitutes classical Fourier law at short time scales. Both the heat flux lag and the temperature gradient lag are considered, however, it is shown that only difference between the two affects temperature profile. Being applied at exposed surface of material, the integral equation predicts surface temperature variation for any form of imposed heat flux. The solution is tested considering solid heating by a picosecond laser impulse. Results are compared with the classical solution of the parabolic heat transfer equation and available experimental data.

Issue Section:
Radiative Heat Transfer
Keywords:
integral equations, heat transfer, temperature distribution, heating, laser beam effects, Analytical, Heat Transfer, Laser, Thin Films
Topics:
Heat transfer, Heating, Integral equations, Temperature, Heat flux, Lasers, Heat
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