  We investigate blow-up phenomena for positive solutions of nonlinear
reaction-diffusion equations including a nonlinear convection term $\partial_t
u = \Delta u - g(u) \cdot \nabla u + f(u)$ in a bounded domain of
$\mathbb{R}^N$ under the dissipative dynamical boundary conditions $\sigma
\partial_t u + \partial_\nu u =0$. Some conditions on $g$ and $f$ are discussed
to state if the positive solutions blow up in finite time or not. Moreover, for
certain classes of nonlinearities, an upper-bound for the blow-up time can be
derived and the blow-up rate can be determinated.
