temperature distribution

inverse heat

free convection

transient heat

stefan problem

radiation heat

conduction problems

heat source

transfer characteristics

Applied Mathematical Modelling

• An analytical solution of the moving heat flux problem in the context of powder bed fusion . • A quadrature scheme based on an offline step that decreases the computation time of the solution. • The solution enables efficient process control. 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.

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