  The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at
different controllable rates through the Bose-Einstein condensation phase
transition is studied numerically in the premise of a recent experiment in an
anisotropic harmonic trap. Our findings based on the stochastic (projected)
Gross-Pitaevskii equation are shown to be consistent at early times with the
predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by
collapsing the early dynamical evolution of densities, spectral functions and
correlation lengths for different quench rates, based on an appropriate
characterization of the distance to criticality felt by the quenched system.
The subsequent long-time evolution, beyond the identified dynamical critical
region, is also investigated by looking at the behaviour of the density
wavefront evolution and the corresponding phase ordering dynamics.
