  Starbursts are galaxies undergoing massive episodes of star formation. The
combined effect of stellar winds from hot stars and supernova explosions
creates a high-temperature cavity in the nuclear region of these objects. The
very hot gas expands adiabatically and escapes from the galaxy creating a
superwind which sweeps matter from the galactic disk. The superwind region in
the halo is filled with a multi-phase gas with hot, warm, cool, and
relativistic components. The shocks associated with the superwind of starbursts
and the turbulent gas region of the bubble inflated by them might accelerate
cosmic rays up to high energies. In this work we calculate the cosmic ray
production associated with the superwind using parameters that correspond to
the nearby southern starburst galaxy NGC 253, which has been suggested as a
potential accelerator of ultra-high energy cosmic rays. We evaluate the
efficiency of both diffusive shock acceleration (DSA) and stochastic diffusive
acceleration (SDA) in the superwind of NGC 253. We estimate the distribution of
both hadrons and leptons and calculate the corresponding spectral energy
distributions of photons. We find that the strong mass load of the superwind,
recently determined through ALMA observations, strongly attenuates the
efficiency of DSA in NGC 253, whereas SDA is constrained by the age of the
starburst. We conclude that NGC 253 and similar starbursts can only accelerate
iron nuclei beyond $\sim10^{18}$ eV under very special conditions. If the
central region of the galaxy harbors a starved supermassive black hole of
$\sim10^6$ $M_{\odot}$, as suggested by some recent observations, a
contribution in the range $10^{18}-10^{19}$ eV can be present for accretion
rates $\dot{m}\sim10^{-3}$ in Eddington units. Only if very strong magnetic
field amplification occurs close to the superwind shock energies of the order
of 100 EeV might be achieved.
