any other option to solve this system??
is there exist any other way of solving that kind of system?

dear jakubi,
thanks for your advice.
in fact the program started to run.
but i complicated the system a little bit ( in fact  the only think i have done is to change k from a numeric value to a function of rf(z,t)) and the message that iget is :
Error, (in pdsolve/numeric/par_hyp) input system is too far from a 'standard' form (see ?pdsolve,numeric for more detail)
 the system is:

> A1 := 120;
A2 := 78;
A3 := 2000;
E1 := 40000;
E2 := 30000;
E3 := 25000;
R := 8.314151;
rf0 := 650;
eta := rf(z, t)/rf0;
k := 5*eta+(1-eta)*8;
h := 13*T(z, t)*(1/100);
Cpf := (4.184*(1/100))*T(z, t);
Cpc := (9.12*(1/100))*T(z, t); Tfinal := 1323; eb := .8;
e0 := .3;
deff := 0.3e-2*(1/100);
km := 0.1e-1*(1/100);
em := .9; s := 5.3068*10^(-23);
k1 := A1*exp(-E1/(R*T(z, t)));
k2 := A2*exp(-E2/(R*T(z, t)));
k3 := A3*exp(-E3/(R*T(z, t)));
pde := {diff((rc(z, t)*Cpc+rf(z, t)*Cpf)*T(z, t), t)+(diff(z^2*e(z, t)*Y(z, t)*T(z, t), t))/z^2 = (diff(z^2*k*(diff(T(z, t), z)), z))/z^2-41100*Y(z, t)*rc(z, t), diff(e(z, t)*Y(z, t), t) = (diff(z^2*deff*(diff(Y(z, t), z)), z))/z^2,
diff(e(z, t), t) = k3*(eb-e(z, t)),
diff(rc(z, t), t) = k2*rf(z, t)-Y(z, t)*rc(z, t),
diff(rf(z, t), t) = -(k1+k2)*rf(z, t), diff(rtg(z, t), t) = k1*rf(z, t)};
ibc := {T(z, 0) = 298, Y(z, 0) = 0, e(z, 0) = e0, rc(z, 0) = 0, rf(z, 0) = 650, rtg(z, 0) = 0, (D[1](T))(0, t) = 0, (D[1](T))(0.1e-1, t) = Tfinal-T(0.1e-1, t)+em*s*(Tfinal^4-T(0.1e-1, t)^4), (D[1](Y))(0, t) = 0, (D[1](Y))(0.1e-1, t) = (km*T(0.1e-1, t)*(1/(deff*T(0.1e-1, t))))*(1-Y(0.1e-1, t))};
sol := pdsolve(pde, ibc, numeric);

can you help me,please?

do you mean that i have to substitute epsilon(t),with epsilon(z,t)?

this equation is coupled with the first pde.and so are the rest of odes.
should i put them along with the pdes?


i 've tried to incroporate the odes in the pde but it nothing changed.can anyone help me please!!