# Question:System of PDE's error in solve and plot the graphs

## Question:System of PDE's error in solve and plot the graphs

Maple 13

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))]);

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