Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters
For researchers and engineers in additive manufacturing, this offers a computationally efficient tool for heat transfer analysis in powder bed fusion, though it is an incremental improvement over existing numerical methods.
The paper provides an analytical solution for heat conduction from a moving Gaussian heat flux with piecewise constant parameters, enabling efficient computation via a quadrature scheme with look-up tables. This solution is aimed at controlling and optimizing powder bed fusion processes.
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.