  The luminosity distance - redshift relation for a wide class of generalized
Randall-Sundrum type II brane-world models with Weyl fluid is compared to the
presently available supernova data. We find that there is a class of spacially
flat models with different amounts of matter $\Omega_{\rho}$ and Weyl fluid
$\Omega_{d}$, which have a very similar fitting quality. The best-fit models
are equally likely and can be regarded as extensions of the $\Lambda $CDM
model, which is also included. We examine three models with different
evolutionary history of the Weyl fluid, characterized by a parameter $\alpha
=0,~2$ and$~3$. The first model describes a brane which had radiated energy
into the bulk some time ago, but in recent times this energy exchange has
ceased and only a dark radiation ($\alpha =0$) is left. In the other two models
the Weyl-fluid describes a radiating brane throughout the cosmological
evolution, up to our days. We find that the trought of the fitting surface
extends over a wider $\Omega_{d}$-range with increasing $\alpha $, but the
linear correlation of $\Omega_{d}$ and $\Omega_{\rho}$ holds all over the
examined $\Omega_{d}$ range.
