  We use simulations to probe the flow properties of dense two-dimensional
magnetorheological fluids. Prior results from both experiments and simulations
report that the shear stress $\sigma$ scales with strain rate $\dot \gamma$ as
$\sigma \sim \dot \gamma^{1-\Delta}$, with values of the exponent ranging
between $2/3 <\Delta \le 1$. However it remains unclear what properties of the
system select the value of $\Delta$, and in particular under what conditions
the system displays a yield stress ($\Delta = 1$). To address these questions,
we perform simulations of a minimalistic model system in which particles
interact via long ranged magnetic dipole forces, finite ranged elastic
repulsion, and viscous damping. We find a surprising dependence of the apparent
exponent $\Delta$ on the form of the viscous force law. For experimentally
relevant values of the volume fraction $\phi$ and the dimensionless Mason
number (which quantifies the competition between viscous and magnetic
stresses), models using a Stokes-like drag force show $\Delta \approx 0.75$ and
no apparent yield stress. When dissipation occurs at the contact, however, a
clear yield stress plateau is evident in the steady state flow curves. In
either case, increasing $\phi$ towards the jamming transition suffices to
induce a yield stress. We relate these qualitatively distinct flow curves to
clustering mechanisms at the particle scale. For Stokes-like drag, the system
builds up anisotropic, chain-like clusters as the Mason number tends to zero
(vanishing strain rate and/or high field strength). For contact damping, by
contrast, there is a second clustering mechanism due to inelastic collisions.
