The aim of the present work is to develop a flow model which can be used to determine the paths of the polyurethane foam in the mold filling process of a refrigerator cabinet so that improvements in the distribution and the size of the venting holes can be achieved without the expensive prototyping and experiments. For this purpose, the multi-component, two-phase chemically reacting flow is described by Navier Stokes and 12 scalar transport equations. The air and the multi-component foam zones are separated by an interface, which moves only with advection since the mass diffusion of species are set zero in the air zone. The inverse density, viscosity and other diffusion coefficients are calculated by a mass fraction weighted average of the corresponding temperature-dependent values of all species. Simulations are performed in a real refrigerator geometry, are able to reveal the problematical zones where air bubbles and voids trapped in the solidified foam are expected to occur. Furthermore, the approach proves itself as a reliable design tool to use in deciding the locations of air vents and sizing the channel dimensions.