Solving non linear equations
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Hi all,
The folloiwng code solves non linear equations for T1, T2, T3 and T4 as well as for J1, J2 and J3. I am only interested on the tempreture:
It returns an array solution that includes several answers for each T. How Can I obtain the exact solution (one single soution) for each T?
syms J1 J2 J3 T1 T2 T3 T4
Jm = 5077.12;
Js = 301.32;
Je = 330.136;
A2 = 449200;
A4 = 519000;
Fms = 0.305;
Fm1 = 0.45;
Fme = 0.245;
F1s = 0.610;
F1m = 0.389;
eps = 0.85;
K2 = 15;
L2 = 0.03;
eq1 = (Jm - Js)*(A2*Fms) + (Jm - J1)*(A2*Fm1) + (Jm - Je)*(A2*Fme) == 0;
eq2 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (J1 - Js)*(A4*F1s) + (J1 - Jm)*(A4*F1m) == 0;
eq3 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (T1-T2)*K2*A4/L2 == 0;
eq4 = -(T1 - T2)*K2/L2 + (5.67e-8*T2^4 - J2)*eps/(1-eps) == 0;
eq5 = -(5.67e-8*T2^4 - J2)*eps/(1-eps) + (J2 - J3) == 0;
eq6 = -(J2-J3) + (5.67e-8*T3^4 - J3)*eps/(1-eps) + 185.95 == 0;
eq7 = -(5.67e-8*T3^4 - J3)*eps/(1-eps) + (T3 - T4)*K2/L2 == 0;
eqs = [eq1, eq2, eq3, eq4, eq5, eq6, eq7];
vars = [J1, J2, J3, T1, T2, T3, T4];
sol = solve(eqs, vars);
T1_val = real(double(sol.T1))
T2_val = real(double(sol.T2))
T3_val = real(double(sol.T3))
T4_val = real(double(sol.T4))
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Akzeptierte Antwort
Torsten
am 3 Feb. 2024
Bearbeitet: Torsten
am 3 Feb. 2024
Each of the 16 quadruples (T1(i),T2(i),T3(i),T4(i)) (i = 1,...,16) constitutes a solution for your system of equations.
You must check which of the 16 quadruples are physical. E.g. the first quadruple (with the corresponding values for J1, J2 and J3 printed) would be
syms J1 J2 J3 T1 T2 T3 T4
Jm = 5077.12;
Js = 301.32;
Je = 330.136;
A2 = 449200;
A4 = 519000;
Fms = 0.305;
Fm1 = 0.45;
Fme = 0.245;
F1s = 0.610;
F1m = 0.389;
eps = 0.85;
K2 = 15;
L2 = 0.03;
eq1 = (Jm - Js)*(A2*Fms) + (Jm - J1)*(A2*Fm1) + (Jm - Je)*(A2*Fme) == 0;
eq2 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (J1 - Js)*(A4*F1s) + (J1 - Jm)*(A4*F1m) == 0;
eq3 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (T1-T2)*K2*A4/L2 == 0;
eq4 = -(T1 - T2)*K2/L2 + (5.67e-8*T2^4 - J2)*eps/(1-eps) == 0;
eq5 = -(5.67e-8*T2^4 - J2)*eps/(1-eps) + (J2 - J3) == 0;
eq6 = -(J2-J3) + (5.67e-8*T3^4 - J3)*eps/(1-eps) + 185.95 == 0;
eq7 = -(5.67e-8*T3^4 - J3)*eps/(1-eps) + (T3 - T4)*K2/L2 == 0;
eqs = [eq1, eq2, eq3, eq4, eq5, eq6, eq7];
vars = [J1, J2, J3, T1, T2, T3, T4];
sol = solve(eqs, vars);
J1_val = real(double(sol.J1(1)))
J2_val = real(double(sol.J2(1)))
J3_val = real(double(sol.J3(1)))
T1_val = real(double(sol.T1(1)))
T2_val = real(double(sol.T2(1)))
T3_val = real(double(sol.T3(1)))
T4_val = real(double(sol.T4(1)))
Weitere Antworten (1)
Walter Roberson
am 3 Feb. 2024
syms J1 J2 J3 T1 T2 T3 T4
Jm = 5077.12;
Js = 301.32;
Je = 330.136;
A2 = 449200;
A4 = 519000;
Fms = 0.305;
Fm1 = 0.45;
Fme = 0.245;
F1s = 0.610;
F1m = 0.389;
eps = 0.85;
K2 = 15;
L2 = 0.03;
eq1 = (Jm - Js)*(A2*Fms) + (Jm - J1)*(A2*Fm1) + (Jm - Je)*(A2*Fme) == 0;
eq2 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (J1 - Js)*(A4*F1s) + (J1 - Jm)*(A4*F1m) == 0;
eq3 = -(5.67e-8*T1^4 - J1)*(A4*eps)/(1-eps) + (T1-T2)*K2*A4/L2 == 0;
eq4 = -(T1 - T2)*K2/L2 + (5.67e-8*T2^4 - J2)*eps/(1-eps) == 0;
eq5 = -(5.67e-8*T2^4 - J2)*eps/(1-eps) + (J2 - J3) == 0;
eq6 = -(J2-J3) + (5.67e-8*T3^4 - J3)*eps/(1-eps) + 185.95 == 0;
eq7 = -(5.67e-8*T3^4 - J3)*eps/(1-eps) + (T3 - T4)*K2/L2 == 0;
eqs = [eq1, eq2, eq3, eq4, eq5, eq6, eq7];
vars = [J1, J2, J3, T1, T2, T3, T4];
sol = solve(eqs, vars);
vals = double(subs([T1, T2, T3, T4], sol));
valid_vals = vals(all(vals > 0, 2),:)
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