  A model for irradiated dust disks around Herbig Ae stars is proposed. The
model is based on the flaring disk model of Chiang & Goldreich (1997), but with
the central regions of the disk removed. The inner rim of the disk is puffed up
and is much hotter than the rest of the disk, because it is directly exposed to
the stellar flux. If located at the dust evaporation radius, its reemitted flux
produces a conspicuous bump in the SED which peaks at 2-3 micron. We propose
that this emission is the explanation for the near-infrared bump observed in
the SEDs of Herbig Ae stars. We study for which stellar parameters this bump
would be observable, and find that it is the case for Herbig Ae stellar
parameters but not for T-Tauri stars, confirming what is found from the
observations. We also study the effects of the shadow cast by the inner rim
over the rest of the flaring disk. The shadowed region can be quite large, and
under some circumstances the entire disk may lie in the shadow. This shadowed
region will be much cooler than an unshadowed flaring disk, since its only
heating sources are radial radiative diffusion and possible indirect sources of
irradiation. Under certain special circumstances the shadowing effect can
suppress, or even completely eliminate, the 10 micron emission feature from the
spectrum, which might explain the anomalous SEDs of some isolated Herbig Ae
stars in the sample of Meeus et al. (2001). At much larger radii the disk
emerges from the shadow, and continues as a flaring disk towards the outer
edge. The complete model, including structure of the inner edge, shadowed
region and the flared outer part, is described in detail in this paper, and we
show examples of the general behavior of the model for varying parameters.
