A self-consistent solution for a thin accretion disk with turbulent convection is presented. The disk viscosity and the convective flux are derived from a physical model for turbulence, and expressed in terms of the local physical conditions of the disk which, in turn, are controlled by the former two. In the gas pressure region, two distinct solutions are obtained. In one, the convective flux is much larger than the radiative flux and the blackbody region extends over the entire gas pressure region and could also extend down to the inner boundary of the disk. In this solution the temperature profile is close to adiabatic. In the other solution, the convective flux is about a third of the total flux, and there exist the gas pressure blackbody and electron scattering regions as well as the radiation pressure region. In the radiation pressure region, the temperature profile is very close to adiabatic, and the disk is geometrically thin and optically thick even for super Eddington accretion rates. The fraction of the convective flux, out of the total flux, increases with the accretion rate, and for accretion rates comparable to the Eddington limit is close to 1. This variation stabilizes the, radiation pressure region, so that the disk regions are secularily stable.

38 pages including 1 PostScript figure