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

Journal article
Authors Robert Forslund
A. Snis
Stig Larsson
Published in Applied Mathematical Modelling
Volume 66
Pages 227-240
ISSN 0307-904X
Publication year 2019
Published at Department of Mathematical Sciences
Pages 227-240
Language en
Keywords Analytical solution, Three-dimensional, Moving heat flux, Powder bed fusion, Electron beam melting
Subject categories Mathematics


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.

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