Example 18.2-3 Part a: Diffusion through a Spherical Film
See also the web pages on this example by Matt Hayenga: http://www.owlnet.rice.edu/~ceng402/ed1projects/bonus98/mhayenga.html for part b.
>  restart;
>  A:=r->4*Pi*r^2; Transfer area in a sphere
>  WAr:=r->A(r)*NAr(r); Mass transport rate at position r
>  eq:=WAr(r)-WAr(r+dr); Mass Balance
>  deq1:=limit(eq/(dr*A(r)),dr=0);
>  s:=dsolve({deq1,NAr(r1)=NAr1},NAr(r));
>  assign(s); NAr:=unapply(NAr(r),r);
>  deq:=NAr(r)=-c*DAB*D(xA)(r)+xA(r)*NAr(r); eq. 18.0-1 with NBr=0
>  s:=dsolve({deq,xA(r1)=xA1},xA(r));
>  assign(s);
>  xA:=unapply(xA(r),r);
>  eq:=xA(r2)=xA2;
>  NAr1:=solve(eq,NAr1);
>  xA1:=1-xB1; xA2:=1-xB2;
>  WAr(r1);

>  WAmaybe:=4*Pi*c*DAB*ln(xB2/xB1)/((1/r1)-(1/r2));
>  WAr(r1)-WAmaybe; Comparing to eq. 18.2-27
>  dif:=simplify(%,assume=positive); We agree with the eq. given for WA.