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

TL;DR

This paper derives an analytical solution for heat conduction caused by a moving Gaussian heat flux with piecewise constant parameters, relevant for optimizing powder bed fusion processes.

Contribution

It introduces a new analytical solution expressed as integrals over time and a quadrature scheme for efficient numerical computation.

Findings

Solution applicable to powder bed fusion heat control

Efficient quadrature scheme with look-up tables

Potential for process optimization

Abstract

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.