The equations describing the transport of suprathermal charged particles, electromagnetic radiation and neutrinos across accretion flows onto compact objects are solved analytically, the effects of shocks in the flow being included. These solutions are used in discussing three illustrative astrophysical examples: acceleration of cosmic rays, generation of spectral continua in quasars and the effect of neutrinos during the collapse of supernova precursors. The main results are: (a) Accretion flows with shocks accelerate cosmic rays very efficiently up to the highest energies. (b) The emergent spectra of electromagnetic radiation from such flows reproduce the observed spectra of quasars from infrared to the hard X-ray region. (c) The neutrinos in the collapsing cores of red giants develop a very hard non-thermal tail in their distribution facilitating the rebound of the gravitational collapse leading to the supernovae.