Assuming that temperature does not affect the fluid properties and that axial diffusion can be neglected in comparison to axial convection, the energy and mass balances for this system are:

,

,

,

with boundary conditions:

,

,

,

,

.

Here is the fluid density, is the maximum laminar parabolic velocity, is the fluid heat capacity, is the thermal conductivity, and are the rate and heat of reaction, respectively, and and are the axial and radial coordinates, while stands for the reactor radius, is the pre-exponential factor, is the activation energy, is the gas constant, is the concentration of reactant , is the diffusion coefficient, is the concentration of reactant entering the reactor, and is the temperature of the wall of the reactor and the fluid entering the reactor.