  We solved the set of two-dimensional magnetohydrodynamic (MHD) equations for
optically thin black hole accretion flows incorporating toroidal component of
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 $ \alpha $ description. We solved the MHD equations
by assuming steady state and radially self-similar approximation in $ r-\theta
$ plane of 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 mid-plane 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 filed at the equatorial plane
of the disk.
