dear maple user help me to correct this error .

I want to solve the coupled pdes plot the graphs but unable to get it. please help me. Here are the maple codes

restart:

L:=0.4:

d1:=0.3: d2:=0.3:

h:=z->piecewise( z<=d1, 1,

z<=d1+L, 1-(delta/(2))*(1 + cos((2*(Pi)/L)*(z - d1 - L/2))),

z<=d1+L+d2, 1 ):

a:=x4*S*Gr/(4*x1*x5)*sin(alpha):

b:=1/Da+(x3*M/(x1*(1+m^2))):

c:=(1/x1)*DP:

x1:=1/((1-phi1)^2.5*(1-phi2)^2.5):

x5:=khnf/kf:

x3:=shnf/sf:

x4:=(1-phi2)*((1-phi1)+phi1*(RBs1)/(RBf))+phi2*RBs2/RBf:

shnf:=sbf*((ss2+2*sbf-2*phi2*(sbf-ss2))/(ss2+2*sbf+phi2*(sbf-ss2))):

sbf:=sf*((ss1+2*sf-2*phi1*(sf-ss1))/(ss1+2*sf+phi1*(sf-ss1))):

ss2:=2.7*10^(-8):

ss1:=59.6*10^(6):

sf:=6.67*10^(-1):

khnf:=kbf*((ks2+2*kbf-2*phi2*(kbf-ks2))/(ks2+2*kbf+phi2*(kbf-ks2))):

kbf:=kf*((ks1+2*kf-2*phi1*(kf-ks1))/(ks1+2*kf+phi1*(kf-ks1))):

ks1:=401:

ks2:=76.5:

kf:=0.4972:

RBs1:=8933*16.7*10^(6):

RBs2:=6320*18*10^(6):

RBf:=1063*1.8*10^(6):

DP:=(1/192)*(18432*F-77*b^2*h(z)^8+308*b*h(z)^8*a+768*h(z)^6*a+12*b*h(z)^8)/(h(z)^4*(b*h(z)^2-6)):

conds:= w(h(z),0)=0, theta(h(z),0)=0, D[1](w)(r,0)=0, D[1](theta)(r,0)=0:

pdes:= diff(w(r, z), r, r)+(1/r)*(diff(w(r, z), r))-(1/Da+(x3/x1)*M)*w(r, z)-(1/x1)*(DP+theta*x4*sin(alpha))=0,

diff(theta(r, z), r,r)+(1/r)*(diff(theta(r, z), r))+(S/x5)=0:

pars:= { F=1.5,Da=0.1,phi1=0.01,phi2=0.02,alpha=Pi/4,S=0.1,Gr=2,m=0.5}:

PrVals:=[2, 5, 7,9]:

colors:=[red, green, blue, black]:

for j from 1 to numelems(PrVals) do

pars1:=`union`( pars, {M=PrVals[j]}):

pdSol:= pdsolve( eval([pdes], pars1),

eval([conds], pars1),

numeric

);

plt[j]:=pdSol:-plot( w(r,z), z=1, r=0..1, numpoints=200, color=colors[j]);

od:

plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);

Error, final value in for loop must be numeric or character

Error, unable to execute seq

PrVals:=[2, 5, 7,9]:

colors:=[red, green, blue, black]:

for j from 1 to numelems(PrVals) do

pars1:=`union`( pars, {M=PrVals[j]}):

pdSol:= pdsolve( eval([pdes], pars1),

eval([conds], pars1),

numeric

);

plt[j]:=pdSol:-plot( theta(r,z), z=1, r=0..1, numpoints=200, color=colors[j]);

od:

plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);

Error, final value in for loop must be numeric or character

Error, unable to execute seq

PrVals:=[2, 5, 7,9]:

colors:=[red, green, blue, black]:

for j from 1 to numelems(PrVals) do

pars1:=`union`( pars, {M=PrVals[j]}):

pdSol:= pdsolve( eval([pdes], pars1),

eval([conds], pars1),

numeric

);

plt[j]:=pdSol:-plot( DP, z=0..1, numpoints=200, color=colors[j]);

od:

plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);