A model for the drag and heat transfer of spheres in the laminar regime at high temperature differences

Modern powder metallurgical processes such as additive manufacturing or metal injection molding require metal powders with specific properties, which are commonly produced by gas atomization processes. Modeling of cooling and solidification of molten metal droplets requires the knowledge of the droplet and particle motion and heat transfer. While there are correlations for drag and heat transfer of spheres at isothermal conditions or temperature differences between droplet and gas smaller than 200 K, knowledge for temperature differences as high as 1000 K is limited. In this work, we first critically review common correlations for the drag coefficient and Nusselt number of spheres and develop a computational model to solve the non-isothermal flow for such conditions. After validation, new correlations are benchmarked against computational experiments. While we could confirm a good agreement for the Nusselt number correlations, we develop a novel temperature-dependent correction for the drag coefficient in the laminar regime. This correlation is based on data for 1 < Re < 130 for two different ideal gases.