Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters
Journal article, 2019

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 look-up 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.

Powder bed fusion

Moving heat flux

Electron beam melting

Three-dimensional

Analytical solution

Author

Robert Forslund

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Stig Larsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Anders Snis

Applied Mathematical Modelling

0307-904X (ISSN)

Vol. 66 227-240

Matematik för elektronstrålesmältning: 3D-skrivning i metall

Swedish Foundation for Strategic Research (SSF), 2016-01-01 -- 2020-12-31.

Subject Categories

Other Engineering and Technologies

Mathematical Analysis

Roots

Basic sciences

DOI

10.1016/j.apm.2018.09.018

More information

Latest update

1/31/2019