In this work we enable the commercial computational fluid dynamics code Fluent, to successfully trace a complete solution branch, even past turning points. Here the so-called Recursive Projection Method (RPM) is implemented as a computational shell "wrapped" around Fluent, in conjunction with a pseudo-arc-length method for convergence on the unstable branch. The case study is a mixed convection flow in a stagnation point chemical vapor deposition (CVD) reactor. Multiple steady states coexist over a range of inlet Reynolds numbers, due to the competition of the two dominant physical mechanisms: forced and free convection. Continuation on the solution branch reveals a curve consisting of a stable branch, dominated by free convection, followed, past the first turning point, by an unstable branch. Past a second turning point, follows another stable branch dominated by forced convection. Taking the problem a step further, it is augmented with a chemical model describing the deposition of silicon (Si) from silane (SiH4), silylene (SiH2) and hydrogen (H-2). The solution branch does not alter since the gas mixture is dilute and the carrier gas, in this case nitrogen (N-2), and the precursor, in this case SiH4, are of similar molar masses; the concentration differences cannot lead to solutal convection. Results for the mass fraction distribution inside the reactor and the film growth rates are reported in all parts of the solution branch. (C) 2011 Elsevier Ltd. All rights reserved.