Direct numerical simulations of the transition process from periodic to chaotic dynamics are presented for two variable Oregonator-diffusion model coupled with convection. Numerical solutions to the corresponding reaction-diffusion-convection system of equations show that natural convection can change in a qualitative way, the evolution of concentration distribution, as compared with convectionless conditions. The numerical experiments reveal distinct bifurcations as the Grashof number is increased. A transition to chaos similar to Ruelle-Takens-Newhouse scenario is observed. Numerical results are in agreement with the experiments.