help solving for Delx

Hi all,

I am trying to solve a system of equation for the variable delx. The solution is [T1 T2 T3 T4 T5]. delx appears in the equations and I have T1 as a given. Fsolve seems not the best option. How can I obtain the value of delx?

I intend to vary the values of w,t and delx as a paramtric syudy to find the smallest size (can you please give me tips on that? the code is as follow:

qf = 38.6;
T(1) = 25;
e=0.95;
s=5.67e-8;
K=300;
t=0.12;
w=3;
fun = @(T) [
    qf - K*w*t/delx*(T(1)-T(2)) - 2*e*w*delx*s*T(1)^4;
    K*w*t/delx*(T(1)-T(2)) - K*w*t/delx*(T(2)-T(3)) - 2*e*w*delx*s*T(2)^4;
    K*w*t/delx*(T(2)-T(3)) - K*w*t/delx*(T(3)-T(4)) - 2*e*w*delx*s*T(3)^4;
    K*w*t/delx*(T(3)-T(4)) - K*w*t/delx*(T(4)-T(5)) - 2*e*w*delx*s*T(4)^4;
    K*w*t/delx*(T(4)-T(5)) - s*e*w*t*T(5)^4 - e*s*w*delx*T(5)^4;
];


% Initial guess for the solution
T0 = [25; 75; 70; 65; 60];

T = fsolve(fun, T0);

Answer 1

[Torsten]

qf = 38.6;
T1 = 25;
e=0.95;
s=5.67e-8;
K=300;
t=0.12;
w=3;
fun = @(T,delx) [T(1)-T1;
    qf - K*w*t/delx*(T(1)-T(2)) - 2*e*w*delx*s*T(1)^4;
    K*w*t/delx*(T(1)-T(2)) - K*w*t/delx*(T(2)-T(3)) - 2*e*w*delx*s*T(2)^4;
    K*w*t/delx*(T(2)-T(3)) - K*w*t/delx*(T(3)-T(4)) - 2*e*w*delx*s*T(3)^4;
    K*w*t/delx*(T(3)-T(4)) - K*w*t/delx*(T(4)-T(5)) - 2*e*w*delx*s*T(4)^4;
    K*w*t/delx*(T(4)-T(5)) - s*e*w*t*T(5)^4 - e*s*w*delx*T(5)^4;
];
% Initial guess for the solution
x0 = [25; 75; 70; 65; 60; 20];
x = fsolve(@(x)fun(x(1:5),x(6)), x0)

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

x = 6x1

25.0000 13.6759 9.9746 8.4303 7.9868 269.8531

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[Alex Sha]

There is one more solution:

delx: 261.664699051376
t2: 11.5149307545147
t3: 1.63207753763982
t4: -8.24932193641395
t5: -17.1818716720288