Example 17.2-2 Part a: Diffusion through a Spherical Film

> 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. 17.0-1 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;

> WAmaybe:=4*Pi*c*DAB*ln(xB2/xB1)/((1/r1)-(1/r2));

> WAr(r1)-WAmaybe;

> dif:=simplify(%);

> assume(xB1>0,xB2>0);

> simplify(dif);

>