Problem #5: Plug flow through a porous catalyst plug Species A is carried into and through a tube in a gas stream with linear velocity v (the flow profile can be considered uniform, or plug, as shown in the diagram). The concentration of species A in the input gas stream is Cai. Near the middle of the tube, the gas flows through a porous catalytic material of width l. In the presence of the catalyst, species A reacts to form B ( AB) by a homogeneous, first order reaction with the reaction rate given by RA= - kyCA. At steady state, what is the concentration of species A in the output gas stream? A B 2R Aout Ain L a) For this calculation, you may ignore the diffusion of species A along the axis of the tube. Under what condition is this approximation appropriate? (Define a Peclet number, state its value, and briefly explain your analysis.) b) Neglecting diffusion and assuming that the velocity of A is constant (and equal to v, in the catalyst plug), write the differential equations describing the variation of CA in the tube. Also, clearly identify the boundary conditions needed to solve this problem. c) Integrate the differential equations, apply the boundary conditions, and obtain an expression for the concentration of A at the exit of the tube