By taking into account photon absorption, we investigate the vertical structure of accretion flows with comparable radiation and gas pressures. We consider two separate energy equations for matter and radiation in the diffusion limit. In order to solve the set of radiation hydrodynamic equations in steady state and axisymmetric configuration, we employ self-similar technique in the radial direction. We need the reflection symmetry about the mid-plane to find gas density at the equator. For a typical solution, we assume that the gas pressure has 10–50 per cent portion of the total pressure. In this paper, since the radiation energy is involved directly, we are able to estimate how much energy of viscous heating is transported in the radial direction and advected towards the central object. Our results show that although the mass accretion rate does not approach the Eddington limit, the energy advection is rather high. Moreover, in a disc with greater accretion rate and less portion of gas pressure at the total pressure, more energy is advected to its centre. In addition, as we expect the accretion flow becomes thicker with greater values of gas pressure. Based on Solberg–Høiland conditions, we notice that the flow is convectively stable in all parts of such a disc.

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