  The general form of the anisotropy parameter of the expansion for Bianchi
type-III metric is obtained in the presence of a single diagonal imperfect
fluid with a dynamically anisotropic equation of state parameter and a
dynamical energy density in general relativity. A special law is assumed for
the anisotropy of the fluid which reduces the anisotropy parameter of the
expansion to a simple form. The exact solutions of the Einstein field
equations, under the assumption on the anisotropy of the fluid, are obtained
for exponential and power-law volumetric expansions. The isotropy of the fluid,
space and expansion are examined. It is observed that the universe can approach
to isotropy monotonically even in the presence of an anisotropic fluid. The
anisotropy of the fluid also isotropizes at later times for accelerating models
and evolves into the well-known cosmological constant in the model for
exponential volumetric expansion.
