Formulation of the Axial Dispersion Model

The simplest description of axial dispersion of mass for constant diffusivities is given by Fick s law (5.1) 

The axial dispersion of heat (axial heat conduction) is described by Fourier s law (5.2) 

We introduce the axial dispersion of mass and heat for a single reaction in a tubular reactor that operates at a steady state with the generalized rate of reaction r per unit volume. 

By At we denote the cross sectional area of the reactor tube. Then the steady-state mass balance with axial dispersion gives us the equation 

After dividing this equation by Al, rearranging to obtain difference quotients for n and Ni, and then taking limAi- o, we get 

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