Abstract
The present study examines self-similarity evolution of advection dominated accretion flow (ADAF) in the presence of a toroidal magnetic field. In this research, it was assumed that the angular momentum transport is due to viscous turbulence and $\alpha$-prescription was used for kinematics coefficient of viscosity. In order to solve the integrated equations which govern the dynamical behavior of the accretion flow, self-similar solution was used. The solutions show that the behavior of physical quantities in a dynamical ADAF are different from steady accretion flow and a disk with polytropic approach. The solution indicates a transonic point in the accretion flow for all selected amounts of advection parameter. Also, by adding strength of the magnetic field and the degree of advection, the radial-thickness of the disk decreased and the disk compressed. The model implies that the flow has differential rotation and is sub-Keplerian at small radii and is super-Keplerian in large radii.
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