4-18. Diffusion and Convection in a Porous Catalyst It is proposed to increase the rate of reaction in a porous catalyst by using flow through the porous material to augment delivery of the reactant. As shown in Fig. P4-18, assume that the reaction occurs in a slab of thickness L and that there is a uniform velocity U across the slab. The irreversible reaction follows second-order kinetics, such that RV=kC2 for the reactant. The reactant concentrations at the upstream (x=L) and downstream (x=0) sides are C0 and 0 , respectively, the flow being in the x direction. (a) Show that the dimensionless reactant concentration is governed by Da1d2d2+DaPedd2=0,(0)=0,(1)=1. How must the Damkhler number (Da) and Pclet number (Pe) be defined? (b) Suppose that the reaction is fast relative to diffusion, but not fast relative to convection. That is, assume that Da1 but Da/Pe1. For =Da10 and =Da/Pe=O(1), this becomes a singular perturbation problem. There is just one boundary layer. Where is it and how should the coordinate by rescaled there? (c) Find the first term in the expansion for in each region. Apply asymptotic matching and construct a composite solution