Efficient Computation of Heat Distribution of Processed Materials under Laser Irradiation

Jianxin Zhu and Wencheng Lin
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Jianxin Zhu: Department of Mathematics, Jinan University, Guangzhou 510632, China
Wencheng Lin: Department of Mathematics, Jinan University, Guangzhou 510632, China

Mathematics, 2021, vol. 9, issue 12, 1-31

Abstract: In this paper, a solution is provided to solve the heat conduction equation in the three-dimensional cylinder region, where the laser intensity of the material irradiation surface is expressed as a Gaussian distribution. Based on the symmetry of heat distribution, firstly, the form of the heat equation in the common rectangular coordinate system is changed to another form in the two-dimensional cylindrical coordinate system. Secondly, the ADI with the backward Euler method and with Crank–Nicolson method are established to discretize the model in the cylindrical coordinate system, after which the simulation results are obtained, where the first kind of boundary value condition is used to verify the accuracy of these two algorithms. Then, the above two methods are used to solve the model with the third kind of boundary value condition. Finally, the comparison is performed with the results obtained by the MATLAB’s PDETOOL, which shows that the solution is more feasible and efficient.

Keywords: heat distribution; three-dimensional heat equation; cylindrical coordinate system; ADI method; laser irradiation; numerical computation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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