Analytical solution for a transient,three-dimensional temperature distribution due to a moving laser beam |
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Affiliation: | 1. Department of Mechanical Engineering, Tsinghua University, 100084 Beijing, China;2. State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, 100084 Beijing, China |
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Abstract: | This paper presents an analytical solution of the transient temperature distribution in a finite solid when heated by a moving heat source. The analytical solution is obtained by solving the transient three-dimensional heat conduction equation in a finite domain by the method of separation of variables (SOV). Meanwhile previous studies focus on analytical solutions for semi-infinite domains, here an analytical solution is provided for a finite domain. The non-homogeneous equation is solved by using the Laplace transform for a unit impulse and then convoluted with the actual heat source. Two different distributions are used: a Gaussian distribution and a spatially uniform plane heat source. |
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