  There is a wide consensus that the ubiquitous presence of magnetic
reconnection events and the associated impulsive heating (nanoflares) is a
strong candidate for solving the solar coronal heating problem. Whether
nanoflares accelerate particles to high energies like full-sized flares is
unknown. We investigate this question by studying the type III radio bursts
that the nanoflares may produce on closed loops. The characteristic
frequency-drifts that type III bursts exhibit can be detected using a novel
application of the time-lag technique developed by Viall & Klimchuk (2012) even
when there are multiple overlapping bursts. We present a simple numerical model
that simulates the expected radio emission from nanoflares in an active region
(AR), which we use to test and calibrate the technique. We find that in the
case of closed loops the frequency spectrum of type III bursts is expected to
be extremely steep such that significant emission is produced at a given
frequency only for a rather narrow range of loop lengths. We also find that the
signature of bursts in the time-lag signal diminishes as: (1)the variety of
participating loops within that range increases; (2)the occurrence rate of
bursts increases; (3) the duration of bursts increases; and (4) the brightness
of the bursts decreases relative to noise. In addition, our model suggests a
possible origin of type I bursts as a natural consequence of type III emission
in a closed-loop geometry.
