  We report on a scheme for incorporating vertical radiative energy transport
into a fully relativistic, Kerr-metric model of optically thick, advective,
transonic alpha disks. Our code couples the radial and vertical equations of
the accretion disk. The flux was computed in the diffusion approximation, and
convection is included in the mixing-length approximation. We present the
detailed structure of this "two-dimensional" slim-disk model for alpha=0.01. We
then calculated the emergent spectra integrated over the disk surface. The
values of surface density, radial velocity, and the photospheric height for
these models differ by 20%-30% from those obtained in the polytropic,
height-averaged slim disk model considered previously. However, the emission
profiles and the resulting spectra are quite similar for both types of models.
The effective optical depth of the slim disk becomes lower than unity for high
values of the alpha parameter and for high accretion rates.
