Details

Assume that the reactions have different activation energies and that all species have equal intrinsic properties; further assume that temperature does not affect these properties and that axial diffusion can be neglected in comparison to axial convection.

The energy and mass balances for this system with these assumptions are:

,

,

,

and

,

with boundary conditions:

,

,

,

,

at and

at .

Here , and are the species concentrations; and are the temperatures of the reactor and the heat exchange fluid, respectively; is the reactant fluid density; is the maximum laminar parabolic velocity in the reactor; is the heat capacity of the reactants; and are the axial and radial coordinates, while stands for the reactor radius; and are the pre-exponential factors, and and are the activation energies of the two consecutive reactions; is the gas constant; is the concentration of reactant entering the reactor; is the diffusion coefficient; is the thermal conductivity; is the temperature of the fluids entering both the reactor and the heat exchanger; is the product of the heat transfer coefficient and the heat exchanger surface area; and the suffixes in the ordinary differential equation refer to properties of the fluids flowing in the heat exchanger and the reactor .