Section 17.5: Diffusion into a Falling Liquid Film: Forced Convection Mass Transfer

> restart;

> Az:=W*dx; Ax:=W*dz;

> eq:=(NAz(x,z)-NAz(x,z+dz))*Az + (NAx(x,z)-NAx(x+dx,z))*Ax; This should be zero.

> eq2:=limit(eq/(W*dx*dz),dx=0);

> pde:=-limit(eq2,dz=0); Compare to eq. 17.5-3

> NAz:=(x,z)->vz(x)*cA(x,z);

> NAx:=(x,z)->-DAB*D[1](cA)(x,z);

> pde; Compare to eq. 17.5-6

> pdsolve(pde,cA(x,z)); I keep trying this, but all it tells me is to try separation of variables.

> cA:=(x,z)->cA0*(1-erf(x/sqrt(4*DAB*z/vmax))); Let's try the book's solution

> vz:=x->vmax;

> D[2](NAz)(x,z);

> diff(NAz(x,z),z);

> simplify(pde);

> simplify(diff(NAz(x,z),z)+diff(NAx(x,z),x));

> limit(cA(x,z),z=0,right); BC 1 eq. 17.5-12

> assume(DAB>0,vmax>0,x>0,z>0);

> limit(cA(x,z),z=0,right);

> cA(0,z); BC 2 eq. 17.5-13

> limit(cA(x,z),x=infinity); BC 3 eq. 17.5-4

> restart; This was one way to get rid of the assumptions

> cA:=(x,z)->cA0*(1-erf(x/sqrt(4*DAB*z/vmax)));

> NAx:=(x,z)->-DAB*D[1](cA)(x,z);

> NAx(0,z); Compare to eq. 17.5-16

> WA:=W*int(NAx(0,z),z=0...L); eq. 17.5-17

> combine(%); Compare to eq. 17.5-17

>