Section 17.3 in BS&L: Diffusion with Heterogeneous Chemical Reaction

deriving eq. 17.3-9 for the flux of A through a film of thickness delta when the reaction

2A->A2 takes place at z=delta. It is assumed that all of the A is converted instantly at the catalytic surface.

> restart;

> deq:=NAz=-c*DAA2*D(xA)(z)+xA(z)*(NAz+NA2z); Eq. 17.0-1 for NBz=NA2z: ie B=A2

> NA2z:=-(1/2)*NAz; From the stoichiometry of the reaction

> s:=dsolve({deq,xA(0)=xA0},xA(z)); Using the BC at z=0.

> assign(s);

> xA:=unapply(xA(z),z);

> eq:=xA(delta)=0; The BC at z=delta.

> NAz:=solve(eq,NAz);

This is identical to 17.3-9 except for the division by -2 of the top and bottom of the ln function.

Now we will try Example 17.3-1

We need first to free up NAz:

> NAz:='NAz';

> eq2:=xA(delta)=NAz/(c*kpp); The BC from eq 17.3-11

> NAz:=solve(eq2,NAz); A little more complicated this time.

> simplify(%); Not much simplification.

> ?LambertW

> ?taylor;

> kpp:=DAA2/(delta*x); Let's try a Taylor's series in DAA2/(k"delta)

> taylor(1/NAz,x);

Error, (in series/fracpower) unable to compute series

> ser:=series(1/NAz,x,2); Following their suggestion: this worked in Maple Vr4

Error, (in series/fracpower) unable to compute series

> ?series Looking for a way to get rid of the (O(x^2)) term

> pl:=convert(ser,polynom);

> dif:=(1/pl)-2*c*DAA2*ln(1/(1-xA0/2))/(delta*(1+x));

> simplify(%);

> assume(xA0<1);

> simplify(dif); This confirms equation 17.3-14. Not in Vr5!

>