  In this article we study the long-time behaviour of a system of nonlinear
Partial Differential Equations (PDEs) modelling the motion of incompressible,
isothermal and conducting modified bipolar fluids in presence of magnetic
field. We mainly prove the existence of a global attractor denoted by $\A$ for
the nonlinear semigroup associated to the aforementioned systems of nonlinear
PDEs. We also show that this nonlinear semigroup is uniformly differentiable on
$\A$. This fact enables us to go further and prove that the attractor $\A$ is
of finite-dimensional and we give an explicit bounds for its Hausdorff and
fractal dimensions.
