# help solving for Delx

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Ghanim on 6 Jul 2024
Edited: Torsten on 12 Jul 2024 at 19:43
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);

Torsten on 12 Jul 2024 at 15:07
Edited: Torsten on 12 Jul 2024 at 19:43
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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