Question: BVP with constraining integrals

Hi,

i wrote the following code

restart:
zet:=0.5:
rhop:=3880;
rhobf:=998.2;
cp:=773;
cbf:=4182;

eq1 := diff(u(eta), eta, eta)+0.133762025280e-2/(0.993000000000e-3+0.388362300000e-1*phi(eta)+.530162700000*phi(eta)^2)+(1/(eta-1)+(0.388362300000e-1+1.06032540000*phi(eta))*(diff(phi(eta), eta))/(0.993000000000e-3+0.388362300000e-1*phi(eta)+.530162700000*phi(eta)^2))*(diff(u(eta), eta));
eq2 := diff(T(eta), eta, eta)+(.63267672*((2.66666666666*(-1.1752324*10^6*phi(eta)+4.1744724*10^6))*u(eta)/p2+7.04876575828*(diff(phi(eta), eta))-(1.58058605349*(.597+4.45959*phi(eta)))*(diff(T(eta), eta))/(1-eta)))/(.597+4.45959*phi(eta));
eq3 := diff(phi(eta), eta)-5.00000000000*phi(eta)*(diff(T(eta), eta));
p:=proc(pp2) if not type([pp2],list(numeric)) then return 'procname(_passed)' end if:

res := dsolve({eq1=0,subs(p2=pp2,eq2)=0,eq3=0,u(0)=0,u(1-zet)=0,phi(0)=0.008,T(0)=0,D(T)(0)=1}, numeric);
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)]));
res(parameters=[pp2]);
evalf(2/(1-zet^2)*Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*( F1(eta)*rhop*cp+(1-F1(eta))*rhobf*cbf )/(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))-pp2
end proc;

fsolve(p(pp2)=0,pp2=(20000)..(8000000));

 

it has an error and i cannot find that. would you please help me?

 

thanks

Amir

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