Analytical solution for a transient, three-dimensional temperature distribution due to a moving laser beam

Araya, Guillermo; Gutierrez, Gustavo

doi:10.1016/j.ijheatmasstransfer.2006.03.026

Cited by 63 publications

(29 citation statements)

References 11 publications

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“…In order to validate the present method on the transient heat conduction analysis, degenerate the double-layer plate into a single layer whose parameters are the same as Araya and Gutierrez [72,73], dimensions of the single layer are Comparison of the present method with Araya and Gutierrez [72,73] in the y coordinate on the top surface ðz ¼ 0Þ. Fig.…”

Section: Numerical Examples and Discussionmentioning

confidence: 99%

Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

Jiang

Dai

2015

International Journal of Heat and Mass Transfer

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Section: Numerical Examples and Discussionmentioning

confidence: 99%

Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

Jiang

Dai

2015

International Journal of Heat and Mass Transfer

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“…Some authors try to deal analytically with the ablation process [8,9]. Hereby the calculation time can be kept very low but it lacks the possibility of advanced modelling, e.g.…”

Section: Laser-matter Interactionmentioning

confidence: 99%

Numerical calculation of temperature and surface topology during a laser ablation process for ceramic coatings

et al. 2015

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In this paper a numerical procedure is presented to calculate a laser ablation process for ceramic thick film coatings. The code is required to cover temperature dependent material data, projected beam intensities and inhomogeneous coating-substrate combinations to calculate the hole shape geometry, the temperature distribution under the surface and the ablation rate per pulse. Therefore, the ablation speed was calculated by an Arrhenius equation while the temperature distribution was simulated by means of the heat conduction equation, which is solvable by a finite differences scheme. Hence, an adaptive mesh is used and the expansion of the code to three spatial dimensions enables the simulation of more complex ablation geometries. The simulation time was held low by introducing actualization frequencies, where critical and time consuming steps were only run if necessary. A validation of the numerical simulation was done by comparing the calculated temperature depth distribution and hole geometry with micrographs of experimental ablations.

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“…The analytical temperature distribution due to a moving heat source has been derived for a vast variety of problems in both semi-infinite [7,8,9,10] and finite [7,11,12,13] three-dimensional domains, and with different heat source models. In this paper the problem under consideration is the heat equation in the lower half-space with a Gaussian distributed heat flux that travels over the surface.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters

Forslund

Snis²,

Larsson

2019

Applied Mathematical Modelling

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We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated lookup tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed.

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Analytical solution for a transient, three-dimensional temperature distribution due to a moving laser beam

Cited by 63 publications

References 11 publications

Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

Numerical calculation of temperature and surface topology during a laser ablation process for ceramic coatings

Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters

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