  We present the results of numerical integrations yielding the structure of
and meridional flow in axisymmetric thin viscous accretion disk models. The
solutions are obtained by simplifying and approximating first the equations,
using systematic asymptotic expansions in the small parameter $\epsilon$,
measuring the relative disk thickness. The vertical structure is solved
including radiative transfer in the diffusion approximation. Carrying out the
expansion to second order in $\epsilon$ we obtain, for low enough values of the
viscosity parameter $\alpha$, solutions containing {\em backflows}. These
solutions are similar to the results first found by Urpin (1984), who used
approximations that are only valid for large radii and the asymptotic
analytical solutions of Klu\'zniak & Kita (1997), valid only for polytropic
disks. Our results may be important for several outstanding issues in accretion
disk theory.
