help solving for Delx

Question

Ghanim 2024-7-6，8:39

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2136848-help-solving-for-delx

编辑： Torsten 2024-7-12，19:43

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);

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Answer 1

Torsten 2024-7-12，15:07

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2136848-help-solving-for-delx#answer_1484918

编辑：Torsten 2024-7-12，19:43

在 MATLAB Online 中打开

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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