  We model gas phase metallicity radial profiles of galaxies in the local
Universe by building on the `bathtub' chemical evolution formalism - where a
galaxy's gas content is determined by the interplay between inflow, star
formation and outflows. In particular, we take into account inside-out disc
growth and add physically-motivated prescriptions for radial gradients in star
formation efficiency (SFE). We fit analytical models against the metallicity
radial profiles of low-redshift star-forming galaxies in the mass range
$\log(M_\star/M_\odot)$ = [9.0-11.0] derived by Belfiore et al. 2017, using
data from the MaNGA survey. The models provide excellent fits to the data and
are capable of reproducing the change in shape of the radial metallicity
profiles, including the flattening observed in the centres of massive galaxies.
We derive the posterior probability distribution functions for the model
parameters and find significant degeneracies between them. The parameters
describing the disc assembly timescale are not strongly constrained from the
metallicity profiles, while useful constrains are obtained for the SFE (and its
radial dependence) and the outflow loading factor. The inferred value for the
SFE is in good agreement with observational determinations. The inferred
outflow loading factor is found to decrease with stellar mass, going from
nearly unity at $\log(M_\star/M_\odot) = 9.0$ to close to zero at
$\log(M_\star/M_\odot) =11.0$, in general agreement with previous empirical
determinations. These values are the lowest we can obtain for a
physically-motivated choice of initial mass function and metallicity
calibration. We explore alternative choices which produce larger loading
factors at all masses, up to order unity at the high-mass end.
