  Many models of Gamma Ray Bursts invoke a central engine consisting of a black
hole of a few solar masses accreting matter from a disk at a rate of a fraction
to a few solar masses per second. Popham et al. and Narayan et al. have shown
that, for Mdot >~ 0.1 Msun/s, accretion proceeds via neutrino cooling and
neutrinos can carry away a significant amount of energy from the inner regions
of the disks. We improve on these calculations by including a simple
prescription for neutrino transfer and neutrino opacities in such regions. We
find that the flows become optically thick to neutrinos inside a radius
R~6-40R_s for Mdot in the range of 0.1 -10 Msun/s, where R_s is the black hole
Schwarzchild radius. Most of the neutrino emission comes from outside this
region and, the neutrino luminosity stays roughly constant at a value L_{\nu} ~
10^{53} erg/s. We show that, for Mdot > 1 Msun/s, neutrinos are sufficiently
trapped that energy advection becomes the dominant cooling mechanism in the
flow. These results imply that neutrino annihilation in hyperaccreting black
holes is an inefficient mechanism for liberating large amounts of energy.
Extraction of rotational energy by magnetic processes remains the most viable
mechanism.
