A model for advection-dominated accretion flows (ADAFs) in a global magnetic field is proposed. In contrast to the well-known ADAF models in which the viscosity of a fluid determines both angular momentum transfer and energy dissipation in the flow, the magnetic field and the electric resistivity, respectively, control them in this model. A manageable set of analytic solutions for the flow and the magnetic field is obtained to vertically nonintegrated basic equations. This set describes mathematically a fully advective accretion flow, and in physically plausible situations for most active galactic nuclei, it is also confirmed that the radiation cooling estimated on this solution is really negligible compared with the internal energy of the flow.
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