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Propagation and reflection of thermal waves in a finite medium due to axisymmetric surface sources. (English) Zbl 0834.35057

Summary: For situations involving extremely short times following the start of transients, or very high heat fluxes, the classical diffusion theory of heat conduction breaks down since the wave nature of thermal energy transport dominates. In this work, the hyperbolic temperature response in a finite, isotropic medium with one surface insulated and the other surface irradiated with an axially symmetric heat flux is considered. The spatial profile of the heat flux is chosen to be either Gaussian, doughnut-shaped, or some combination of the two. The temporal profile is either continuous or a rectangular pulse. The choice of these profiles is based upon the premise that they approximate the outputs from some common laser sources. Calculations for a Gaussian source reveal the existence of a severe thermal wavefront which propagates through the medium, dissipating energy in its wake upon reflection at the boundaries. Also discussed is the relative importance of the parabolic and hyperbolic heat conduction models for a metal exposed to three ranges of rectangular pulse duration.

MSC:

35K05 Heat equation
80A20 Heat and mass transfer, heat flow (MSC2010)
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