Question

The diffusion of component A in dilute concentration in a tube of radius r filled with a liquid is expressed by the equation N_A = -D_AB (dC_A / dz). Here, z represents the distance in the direction of the tube axis. The inner walls of the tube exhibit a catalytic effect and degrade component A by the rate of kC_AA_w. Where k is the reaction rate constant and A_w is the tube wall area. By neglecting the radial concentration gradient and making the appropriate assumptions, derive the differential equation for this system, including diffusion and reaction terms, for unsteady state. What are the necessary boundary conditions for the solution?

Answer 1