help solving for Delx
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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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Accepted Answer
Torsten
on 12 Jul 2024
Edited: Torsten
on 12 Jul 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)
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