Section 18.3 Diffusion with Heterogeneous Chemical Reaction
Deriving eq. 18.3-9 for the flux of A through a film of thickness delta when the reaction
2A->B takes place at z=delta. It is assumed that all of the A is converted instantly at the catalytic surface.
>  restart;
>  deq:=NAz=-c*DAB*D(xA)(z)+xA(z)*(NAz+NBz); Eq. 18.0-1
>  NBz:=-(1/2)*NAz; From the stoichiometry of the reaction
>  s:=dsolve({deq,xA(0)=xA0},xA(z)); Using the BC eq. 18.3-6 at z=0.
>  assign(s);
>  xA:=unapply(xA(z),z);
>  eq:=xA(delta)=0; The BC eq. 18.3-7 at z=delta.
>  solve(eq,NAz);

> 
This is identical to 18.3-9 except for the division by -2 of the top and bottom of the ln function.
Now we will try Example 18.3-1: see ex1831.mws and ex1831b.mws