Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters
Preprint, 2018

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.

moving heat flux

powder bed fusion

three-dimensional

electron beam melting

analytical solution

Författare

Robert Forslund

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Stig Larsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Anders Snis

Matematik för elektronstrålesmältning: 3D-skrivning i metall

Stiftelsen för Strategisk forskning (SSF), 2016-01-01 -- 2020-12-31.

Ämneskategorier

Beräkningsmatematik

Mer information

Senast uppdaterat

2019-01-31