We solved the set of two-dimensional magnetohydrodynamic (MHD) equations for optically thin black hole accretion flows incorporating the toroidal component of the magnetic field. Following global and local MHD simulations of black hole accretion disks, the magnetic field inside the disk is decomposed into a large-scale field and a fluctuating field. The effects of the fluctuating magnetic field in transferring the angular momentum and dissipating the energy are described through the usual α description. We solved the MHD equations by assuming a steady-state and radially self-similar approximation in the r − θ plane of the spherical coordinate system. We found that as the amount of magnetic field at the equatorial plane increases, the heating by the viscosity decreases. In addition, the maximum amount of the heating by the viscous dissipation is produced at the midplane of the disk, while that of the heating by the magnetic field dissipation is produced at the surface of the disk. Our main conclusion is that in terms of the no-outflow solution, thermal equilibrium still exists for the strong magnetic field at the equatorial plane of the disk.

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