Abstract: This study studies the effect of activation energies and strong viscous dissipation term on two-step Arrhenius combustion reactions to give further insight into the theory of combustion under physical reasonable assumptions. We extend the non-uniformity of vessels discussed in Olanrewaju. It is shown, as in one step reaction that in a non-uniform vessel, maximum temperature occurs toward the end of the tube. On the other hand, in a uniform tube maximum temperature occurs at the centre. Also maximum temperature for diverging or converging channel is greater than that of a uniform vessel. The graph shows effect of viscous dissipation term on the temperature of the system.