A simple model is presented for simultaneous nucleation and coagulation in combination with convective and diffusive particle transport in gas-phase aerosol reactors over the entire particle-size spectrum. This model is applied to a spatially inhomogeneous aerosol reactor. The flow and reaction characteristics correspond to a confined coflow diffusion flame of SiCl4 and NH3 in a wall-heated flow. The reactor geometry and the initial and boundary conditions suggest the application of the boundary layer approximations. The reaction process is described by the flame-sheet model. The particle-size spectrum is approximated by a unimodal lognormal function. The characteristics of the SiN4 aerosol (concentration, polydispersity, and average particle size) calculated at every point in the reactor vary significantly in space. At the position of the reaction zone in the outlet cross section, for example, the average particle radius is small (r(g) approximate to 1 nm) and the standard deviation is large (sigma > 2). At other radial positions the particles are much larger (r(g) approximate to 15 nm) and the size distribution is almost self-preserving (sigma approximate to 1.36).