Change the yo (3rd boundary condition: y[0]) to meet the target(4th boundary condition): funy'[1] + pey*bd*funy[1]
=0, and get the answer yo (0<yo<1)
Initial yo=0.3
but,the program cannot run, please give me some help, many thans------------------------------------Clear[fx, fy, cxo, cy1, h, pey, noofc, hox, ans];
(*Input data for the calculation of the outlet concentrations*)
{
{Flowrate of Cu Raff (m3/h), fx = 5}
} ;
{
{Flowrate of barren solvent (m3/hr), fy = 1}
} ;
{
{Subscript[U, 3] Subscript[O, 8] concentration in Cu Raff (mg/L),
cxo = 267}
} ;
{
{Subscript[U, 3] Subscript[O, 8]
concentration in barren solvent (mg/L), cy1 = 130}
} ;
{
{Effective column height (m), h = 9}
} ;
{
{Peclet number of organic phase , pey = .7}
} ;
{
{no of compartments, noofc = 13}
} ;
{
{Height of transfer unit (m), hox = 1.65855537601783531}
} ;
(* Equilibrium constants represented by Langmuir model, \
cx^*=(a*cy)/(b*cy+1) *)
a = 0.00982089325801922;
b = -0.0002962283775423278;
(* Press once you complete the input section *)
nox = h/hox;
uxuy = fx/fy; dc = h/noofc; bd =
h/dc; SuperStar = (a/cxo - b)^-1; SuperStar[cx1] = (a*cy1)/(
b*cy1 + 1);
b1 = cxo - SuperStar[cx1]; b2 = SuperStar - cy1; a1 =
a*(SuperStar - cy1); a2 = a*cy1; a3 = b*(SuperStar - cy1);
a4 = (b*cy1) + 1;
yo = .3; parta[yo_] :=
Module[{useless},
ini = NDSolve[{-x' - (nox/
b1)*(b1*x + SuperStar[cx1] - (a1*y + a2)/(
a3*y + a4)) == 0,
y'' +
pey*bd*y' + ((nox*pey*bd*uxuy)/
b2)*(b1*x + SuperStar[cx1] - (a1*y + a2)/(
a3*y + a4)) == 0, y'[0] == 0, x[0] == 1,
y[0] == yo}, {x, y}, {z, 0, 1}]; funx[z_] = ini[[1, 1, 2]];
funy[z_] = ini[[1, 2, 2]]; funy'[1] + pey*bd*funy[1]];
try = FindRoot[parta == 0, {ans, 0, 1}, MaxIterations -> 350,
AccuracyGoal -> 6];
Plot[{funx, funy}, {z, 0, 1}, Frame -> True,
FrameLabel -> {"Dimensionless length (Z) ",
"Dimensionless conc (X,Y)"}, PlotStyle -> AbsoluteThickness[2],
PlotRange -> All, ImageSize -> 350]
Print["y0 = " , ans, " mg/L "]
Print["Concentration in Raff = " ,
funx[1]*(cxo - SuperStar[cx1]) + SuperStar[cx1], " mg/L "]
Print["Concentration in Loaded Solvent = " ,
funy[0]*(SuperStar - cy1) + cy1, " mg/L "]The 1st and 2nd boundary conditions are:y'[0] == 0, x[0] == 1
