  X-ray flares can be accounted for a hint to the late time activity of
Gamma-ray bursts (GRBs) central engines. Such a long term activity has been
described through some models, one of which is the viscous evolution of the
outer disc fragments that proposed by Perna et al. (2006), and developed
quantitatively by Dall Osso et al. (2017). Here, we reconstruct Dall Osso et
al. (2017) framework through taking both small and large scale effects of
magnetic field into account. To consider the magnetic barrier as a possible
mechanism that might govern the accretion process of each magnetized clump, we
make a simple pattern in boundary condition through which this mechanism might
happen. Regarding various model parameters, we probe for their influence and
proceed some key analogies between our model predictions and previous
phenomenological estimates, for two different choices of boundary conditions
(with and without a magnetic barrier). Our model is remarkably capable of
matching flare bolometric and X-ray light-curves, as well as reproducing their
statistical properties, such as the ratios between rise and decay time, width
parameter and peak time, and the power-law correlation between peak luminosity
and peak time. Combining our results with the conclusions of previous studies,
we are led to interpret magnetic barrier as a less probable mechanism that
might control the evolution of these clumps, especially the later created (or
viscously evolved) ones.

High Energy Astrophysical Phenomena