Q3. As shown in the figure, assume that a reaction occurs in a slab of porous material of thickness L and that there is a uniform velocity of U across the slab. We assume that the reactant species has concentration C and undergoes a reaction with reaction rate Ry =-kC2 within the slab. The reactant concentrations upstream (x = L) is Co and downstream at (x = 0) is 0. Thus the flow is in the x direction. = Porous Catalyst C=0 Ry=-kC C= Co U X= 0 X= L Figure 3: Question 3 02 (a) Show that the dimensionless reactant concentration is governed by 1 dle Pe de + = 0, 0(0) = 0, 0(1) 1 Da dn2 Da dn How must the Damkohler number Da and the Peclet number, Pe be defined? (b) Suppose the reaction is fast relative to diffusion but not fast relative to convection. Thus = Da >> 1 but Da/Pe ~ 1. For e = Da-1 + 0 and a = Da/Pe O(1) this becomes a singular perturbation theory problem. There is just one boundary layer. Where is it, and how should the coordinate be rescaled there? (c) Find the first term in the expansion for @ for each region. Apply asymptotic mapping and construct a composite solution. (30 points)