(22e) The Effect of Transport on Reactions in Homogeneous Tubular Flow

In our previous work, analytical solutions were developed and numerical solutions were carried out for the upper bounding conversion, corresponding to perfect radial mixing, and for the lower bounding conversion corresponding to negligible radial mixing in both fully developed laminar and fully developed turbulent flow under isothermal conditions. We also developed exact asymptotic solutions for slightly energetic reactions and carried out numerical solutions to test these expressions. For all of these conditions the behavior was one-dimensional and the models were in the form of ordinary differential equations. We have since carried out exact numerical solutions for representative conditions in fully developed laminar and turbulent flow that take into account the radial transport of both species and energy by molecular and turbulent fluctuations for strongly energetic reactions and with heat exchange with the surroundings. The model thereby consists of coupled partial differential equations. The results reveal that, on the one hand, finite radial rates of transport of species and energy by molecular diffusion, and in turbulent flow by eddy diffusion as well, do affect the mixed-mean conversion significantly for most practical conditions. On the other hand, the energetic reactions are found to affect the coefficient for heat exchange with the wall, in some cases by an order-of-magnitude. Because of the many dimensionless variables and parameters and the lack of a theoretical structure, the development of generalized algebraic correlative or predictive equations such as those that have been devised for pure convection is very difficult. As an alternative, sensitivity coefficients have been evaluated for the first-order effects of the enthalpy change, the energy of activation, and the frequency factor of the reaction, for that of the Reynolds, Prandtl, and Schmidt numbers, and for that of the imposed heat flux density or fixed temperature of the wall upon the mixed-mean conversion and the Nusselt number. The numerical results are limited to a single first-order irreversible reaction but the methodology can and will be extended to other reacting systems. The results differ from all previous ones in that an essentially exact model is utilized for turbulent flow and transport.