Asymptotic solution for nonlinear chemical vapor deposition problems

The problem of chemical vapor deposition involving reaction kinetics of any order $n$ at a heated substrate is considered. The deposition process is then described by a convective diffusion equation, coupled to nonlinear boundary conditions, describing the chemical reaction taking place at the heated substrate, where the nonlinearity is given in terms of the order $n$ of the reaction kinetics. We derive boundary layer equations and use a combination of perturbation and similarity methods to find the deposition rate along the susceptor.