Mid-plane temperature (top), H/r (middle), and surface density Σ_G (bottom) for discs at different time evolutions. The values for T, H/r, and Σ_G have been calculated from Eqs. (A.6) to (A.11) with a metallicity of 0.5%. As time evolves, the surface density reduces and with it the inner region that is dominated by viscous heating, so that the disc is dominated by stellar irradiation at the late stages of the evolution, after a few Myr. In this late stage, the aspect ratio is nearly constant in the inner parts of the disc and T and Σ_G follow simple power laws.