> restart;

> T:=r->T1*(r/r1)^n; equation 17.2-16

> DAB:=T->DAB1*(T/T1)^(3/2); equation 17.2-17

> DAB(T(r)); Use equations 17.2-16 and 17.2-17 to achieve equation 17.2-22. Equation 17.2-22 illustrates the variation of diffusivity with position.

> c:=T->p/(R*T);

> cDAB(r):=c(T(r))*DAB(T(r)); cDAB is replaced in equation 17.2-19. cDAB now depends on r.

> NAr:=r->NAr1*r1^2/r^2;

> eqn162_2:=NAr(r)=xA(r)*NAr(r)-cDAB(r)*diff(xA(r),r); Use Fick's first law in terms of NA, the molar flux of a species A. This is equation 16.2-2 modified to for the specifics of this problem. This equation is also a variation of equation 17.0-1.

> assume(r>0, r1>0, r2>r1);

> assume(n, real);

The assumptions above are necessary so that Maple can read the variable correctly in order to achieve an answer in its most simplified form. Don't believe it? Try taking out the assumptions above!!! :)

> soln:=dsolve({eqn162_2,xA(r1)=xA1},xA(r)):

>

> assign(soln);xA:=unapply(xA(r),r):

> eqn:=xA2=xA(r2): lengthy output

> NAr1:=solve(eqn, NAr1); Very similar to part A. Solve for NAr1 with xA at r2.

> xA1:=1-xB1;xA2:=1-xB2; Define the relationships between xA1 and xB1 and xA2 and xB2.

> simplify(NAr1);

> W_A:=4*Pi*r1^2*NAr1: To obtain the molar flow of A across a spherical surface, multiply the area of a sphere by NAr1.

> simplify (W_A); Now show the output with simplification.

> BSLform:=4*Pi*(p*DAB1/R/T1)*(1+n/2)*ln(xB2/xB1)/((r1^(-1-n/2)-r2^(-1-n/2))*r1^(n/2)); This equation should look like equation 17.2-24.

> final_ans:=simplify(W_A-BSLform);