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The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.

This study aims to enhance merging of additive manufacturing (AM) techniques with powder injection molding (PIM). In this way, the prototypes could be 3D-printed and mass production implemented using PIM. Thus, the surface properties and mechanical performance of parts produced using powder/polymer binder feedstocks [material extrusion (MEX) and PIM] were investigated and compared with powder manufacturing based on direct metal laser sintering (DMLS).

PIM parts were manufactured from 17-4PH stainless steel PIM-quality powder and powder intended for powder bed fusion compounded with a recently developed environmentally benign binder. Rheological data obtained at the relevant temperatures were used to set up the process parameters of injection molding. The tensile and yield strengths as well as the strain at break were determined for PIM sintered parts and compared to those produced using MEX and DMLS. Surface properties were evaluated through a 3D scanner and analyzed with advanced statistical tools.

Advanced statistical analyses of the surface properties showed the proximity between the surfaces created via PIM and MEX. The tensile and yield strengths, as well as the strain at break, suggested that DMLS provides sintered samples with the highest strength and ductility; however, PIM parts made from environmentally benign feedstock may successfully compete with this manufacturing route.

This study addresses the issues connected to the merging of two environmentally efficient processing routes. The literature survey included has shown that there is so far no study comparing AM and PIM techniques systematically on the fixed part shape and dimensions using advanced statistical tools to derive the proximity of the investigated processing routes.