Hyperbolic temperature profiles for laser surface interactions

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Abstract
This study theoretically analyzes the transient temperature distributions in laser irradiated materials by considering a hyperbolic heat conduction model. Exact and limiting mathematical solutions for the temperature distributions are developed and important parameters are identified. Traditional Fourier transient heat conduction models are parabolic in nature, which imply an infinite speed of propagation of the thermal signal in the material. Hyperbolic non-Fourier models have been introduced to account for the finite speed of the thermal wave. The effects of finite speed are significant in short-pulse applications where the time period of the laser input is comparable to the thermal characteristic time of the material, and the resultant temperature variations are significantly different from that of traditional infinite-speed Fourier predictions. Two different types of materials, biological materials and inorganic solids, are considered for laser-surface interactions in the study. The parameter of greatest significance is found to be the ratio of thermal characteristic length to the laser beam width. Values of this parameter in the range between 0.1 and 3, corresponding to different applications, are examined and local temperature maximas, or hot spots, are found to occur at initial time periods for values greater than ∼0.2.