1991/07/01 by Masayoshi Yamada Masayoshi Yamada · 6 citations
Chemistry · Engineering · Mathematics · #Beam (structure) #Chemistry #Composite material #Gaussian #Heat equation #Laplace transform #Laser #Laser Material Processing Techniques #Laser and Thermal Forming Techniques #Laser flash analysis #Materials science #Mathematical analysis #Mathematics #Nonlinear system #Optics #Physics #Thermal conductivity #Thermal diffusivity #Thermodynamics #Thermography and Photoacoustic Techniques
paper · doi:10.1143/jjap.30.1418
published in Japanese Journal of Applied Physics 30(7R), 1418 (Institute of Physics)
openalex publication_date 1991/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Laplace-transformed Green's function solutions to linear heat equations are derived for multilayered structures. An analytic expression for linear temperature distribution produced by a scanning CW elliptical Gaussian laser beam is given in a double integral form and its numerical results are presented. In conjunction with the linear temperature formula, a nonlinear algorithm has been developed in order to incorporate temperature-dependent thermal diffusivity, conductivity, and surface reflectivity. The temperature distributions for the Si/SiO 2 /Si structure are calculated, including effects of melting of Si. From comparison between the calculation and a measurement on the melting width, it is found that the excess energy absorbed above the melting temperature is spatially redistributed on melting.