  In this paper, we study the possibility of obtaining a stable flat dark
energy-dominated universe in a good agreement with observations in the
framework of Swiss-cheese Brane-world cosmology. Two different Brane-world
cosmologies with black strings have been introduced for any cosmological
constant $\Lambda$ using two empirical forms of the scale factor. In both
models, we have performed a fine-tuning between the brane tension and the
cosmological constant so that the EoS parameter $\omega(t)\rightarrow -1$ for
the current epoch where the redshift $z\simeq 0$. We then used these fine-tuned
values to calculate and plot all parameters and energy conditions. The
deceleration-acceleration cosmic transition is allowed in both models, and the
jerk parameter $j\rightarrow 1$ at late-times. Both solutions predict a future
dark energy-dominated universe in which $\omega=-1$ with no crossing to the
phantom divide line. While the pressure in the first solution is always
negative, the second solution predicts a better behavior of cosmic pressure
where the pressure is negative only in the late-time accelerating era but
positive in the early-time decelerating era. Since black strings have been
proved to be unstable by some authors, this instability can actually reflect
doubts on the stability of cosmological models with black strings (Swiss-cheese
type brane-worlds cosmological models). For this reason, we have carefully
investigated the stability through energy conditions and sound speed. Because
of the presence of quadratic energy terms in Swiss-cheese type brane-world
cosmology, we have tested the new nonlinear energy conditions in addition to
the classical energy conditions. We have also found that constructing
non-singular and cyclic solutions through certain ansatze in Swiss-cheese
Brane-worlds are not possible.
