# help solving for Delx

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Ghanim il 6 Lug 2024
Modificato: Torsten il 12 Lug 2024
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);
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### Risposta accettata

Torsten il 12 Lug 2024
Modificato: Torsten il 12 Lug 2024
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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