  We study the minimal speed of propagating fronts of convection reaction
diffusion equations of the form $u_t + \mu \phi(u) u_x = u_{xx} +f(u)$ for
positive reaction terms with $f'(0 >0$. The function $\phi(u)$ is continuous
and vanishes at $u=0$. A variational principle for the minimal speed of the
waves is constructed from which upper and lower bounds are obtained. This
permits the a priori assesment of the effect of the convective term on the
minimal speed of the traveling fronts. If the convective term is not strong
enough, it produces no effect on the minimal speed of the fronts. We show that
if $f''(u)/\sqrt{f'(0)} + \mu \phi'(u) < 0$, then the minimal speed is given by
the linear value $2 \sqrt{f'(0)}$, and the convective term has no effect on the
minimal speed. The results are illustrated by applying them to the exactly
solvable case $u_t + \mu u u_x = u_{xx} + u (1 -u)$. Results are also given for
the density dependent diffusion case $u_t + \mu \phi(u) u_x = (D(u)u_x)_x
+f(u)$.
