A first-order chemical reaction occurs in a tubular (cylindrical) plug-flow reactor. You are interested in modeling the steady-state concentration of reactant A as a function of r and z in this reactor. You may assume that flow is laminar and as a result the velocity profile is: vz=vmax(1(Rr)2) where Vmaxmax is the velocity at the center line and R is the internal radius of the tube. a) Write the simplified continuity equation describing this system in terms of the flux of A in the r - and z - direction. Clearly state all assumptions. b) Simplify Fick's rate equation to determine an equation for the flux of A in the r-and z-direction. Clearly state all assumptions. c) Write the continuity equation in terms of the concentration of A,CA D) Define the following non - dimensional variables: =vmaxkz,C=cA0cA,=kR2D,U=Rr where cA0 is the concentration at the inlet. Substitute these variables in the differential equation you obtained in part c and show that it becomes: (1U2)C=(U22C+U1UC)C e) State appropriate boundary and initial conditions for this problem in terms of the non dimensional variables defined