  Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black
holes (BHs) have been theorized as the central engine of relativistic jets
launched in massive star core collapse events or compact star mergers. In this
work, we calculate the electron neutrino/anti-neutrino spectra of NDAFs by
fully taking into account the general relativistic effects, and investigate the
effects of viewing angle, BH spin, and mass accretion rate on the results. We
show that even though a typical NDAF has a neutrino luminosity lower than that
of a typical supernova (SN), it can reach $10^{50}-10^{51}~{\rm erg~s^{-1}}$
peaking at $\sim 10$ MeV, making them potentially detectable with the upcoming
sensitive MeV neutrino detectors if they are close enough to Earth. Based on
the observed GRB event rate in the local universe and requiring that at least 3
neutrinos are detected to claim a detection, we estimate a detection rate up to
$\sim$ (0.10-0.25) per century for GRB-related NDAFs by the Hyper-Kamiokande
(Hyper-K) detector if one neglects neutrino oscillation. If one assumes that
all Type Ib/c SNe have an engine-driven NDAF, the Hyper-K detection rate would
be $\sim$ (1-3) per century. By considering neutrino oscillations, the
detection rate may decrease by a factor of 2-3. Detecting one such event would
establish the observational evidence of NDAFs in the universe.
