Theoretical Analysis And Calculation Of Non-Fourier Heat Conduction Arisen As Laser Irradiation

As a light soruce with extremly high power density, laser had been wildly used in various areas of engineering, especially in the surface treatment of metal, bio-medical and so on. Intensive studies of thermal and stress distribution inside the material, when materials are suddently heated by laser beam, becomes more and more important. Comparing with the numerical solutions, analytic solutions of the model problems can show out relations between variables more directly and precisely. But, it is a very challenging to find analytic solutions. Most literatures of recent reasearches can only provide analytic solutions in some filed of transforms or to problems of one dimentional, and very few of authors reported their works about finding analytic solutions for high dimensional heat conduction and in the original physical space-time coordinate space. In this paper, we built the rotational symmetry non-Fourier model involving thermal wave hehaviour, and derived their analytical solutions by using integral transforms with respect to space and time. The key to achieve these analytic solutions is to find analytic representation of inverse Laplace transforms. Based on these works, we discussed the thermal distribution, thermal damages (for skin), and thermal stress with the term of inertia. The main conclusions of this paper are listed in the following.(1) The heat conduction of laser irradiating on the surface of a semi-infinite material was discussed. Mathematical models of non-Fourier heat conduction in case of suddently heating by laser and pulse laser were built. By using Laplace-Hankel transforms and their inverse transforms, analytic solutions of single integral form in the original space-time coodinates system were derived. The key is that of successfully finding analytic representations of inverse Laplace transforms. The exact thermal wave front can be found directly by using these analytic solutions and thermal propagation behaviours inside the materails can be shown clearly too. Moreover, these conclusions are also verified by comparing with numerical solutions obtained from an implicit differential method.(2) To the problem of heat conduction as laser irradiating in a locally circular area on the surface of a semi-infinite material, the analytic solution in the original space-time coordinate system was also derived. Some intensive studies about behaviours of thermal propagation were shown in cloud charts, contour plots and streamline plots.(3) Two types of non-Fourier heat conductions as laser irradiating on the surface of skin were discussed, in which blood perfusion was considered. By using idea of elevate function and integral transforms, the analytic representations of inverse Laplace transforms were provided. Based on these conclusions, the single integral form analytic solutions were derived. Also, thermal damages were discussed and they were compared with that of classical Fourier heat conductions.(4) To the nonhomogeneous functional gradient materials with exponential parameters, non-Fourier heat conductions of laser irradiation was studied, and analytic solutions in original space-time coordinate system were successfully derived with respect to various parameters. The evolvement of thermal distribution was shown in series of cloud charts and effects of parameters were discussed.(5) The stress in an elastic material suddently heated by a laser beam on its surface were studied. Changes of inertia was considered. The analytic solutions of stresses in the homogenous and functional gradient elastic material were obtained by means of stress and displacement, respectively. Intensive discussions and conclusions about the behaviors of stress were also shown.