In polymer micro-engineering, the process of micro injection molding is more and more widespread. Nowadays, the improvement in this field leads to an increase trend towards a micro-size parts, and it is involved in many technologies: communication, health, aerospace and automotive sectors. The process steps of micro-injection are similar to those in marco-injection. But the size of flowing geometries leads to new physical phenomena which need new investigations, in order to understand the process material interaction in such configuration. In this work, an unsymmetrical stepped part was the subject of a numerical investigation through a two-phase model including the governing equations of mass, momentum and energy conservation coupled with the crystallization kinetics by means of the Kolmogroff-Avrami-Evans equations with the Hoffman Lauritzen model. A‘’convergent’’ flow injection of a Poly(oxymethylene) POM from the thicker plaque with a thickness of about 850 µm through an intermediate plaque to achieve a thin plaque of 200 µm thickness for four micro molding conditions, is proposed. A parametric analysis is performed, including all the steps of the process. The velocity and temperature fields are analyzed and simultaneously reveal a parabolic distribution of velocity field, while a rise in temperature at the thin plaque toward the wall has been obtained. This is attributed mainly to the energy dissipation by the viscous effect during the filling phase, but also to the involved characteristic times for the thermal behavior of the material. Depending on the molding conditions and the location of the micro-part, different evolution of crystallization rate is obtained leading to distinguish at least three morphological layers, which constitute an original analysis and results, and allows a clear understanding of the process polymer interaction relationship. The numerical results are explained and confirmed by an experimental investigation in a previous work.