MATLAB: I want to know what causes error in the code using fsolve…..very much thanks in advance

fsolve

%My function is following
function F = funhddtryone(X)
T2 = X(1);
T3 = X(2);
T4 = X(3);
T5 = X(4);
T6 = X(5);
% Known values
Acond = 3.5;
UL = 7.04;
a = 300;
Q = 10000;
Ucond = 47.9;
K = 0.0015;
cp = 4.193;
cpw = 4.193;
cpa = 1.009;
Ma = 0.028966;
Mw = 0.018016;
G = 0.040;
L = 0.015;
Hvap = 2332.20*1000;
P = 101.1*1000;
Tamb = 25+273;
T1 = 25+273;
A = 0.1225;
V = 0.0410375;
P0 = 7.384*1000;
A1 = 67.35;
B1 = -7218.15;
C1 = -7.9939;
D1 = 0.00052333;
E1 = L*cp*(T1 - T2) - A*UL*(T5/2 + T6/2 - Tamb) - G*(T5*cpa - T6*cpa + (Mw*P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5)*(Hvap + T5*cpw))/(Ma*(P - P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5))) - (Mw*P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)*(Hvap + T6*cpw))/(Ma*(P - P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6))));
E2 = L*cp*(T2 - T1)-(Ucond*Acond*[(T6 - T2)-(T5 - T1)]/(log((T6 - T2)/(T5 - T1))));
E3 = G*(T5*cpa - T6*cpa + (Mw*P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5)*(Hvap + T5*cpw))/(Ma*(P - P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5))) - (Mw*P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)*(Hvap + T6*cpw))/(Ma*(P - P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)))) - A*UL*(T5/2 + T6/2 - Tamb) + L*cp*(T3 - T4);
E4 = - G*(T5*cpa - T6*cpa + (Mw*P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5)*(Hvap + T5*cpw))/(Ma*(P - P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5))) - (Mw*P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)*(Hvap + T6*cpw))/(Ma*(P - P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)))) - (K*V*a*(T3*cpa - T4*cpa + T5*cpa - T6*cpa + (Mw*P0*exp(A1 + B1/T3 + C1*log(T3) + D1*T3)*(Hvap + T3*cpw))/(Ma*(P - P0*exp(A1 + B1/T3 + C1*log(T3) + D1*T3))) - (Mw*P0*exp(A1 + B1/T4 + C1*log(T4) + D1*T4)*(Hvap + T4*cpw))/(Ma*(P - P0*exp(A1 + B1/T4 + C1*log(T4) + D1*T4))) + (Mw*P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5)*(Hvap + T5*cpw))/(Ma*(P - P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5))) - (Mw*P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)*(Hvap + T6*cpw))/(Ma*(P - P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)))))/log((T3*cpa - T6*cpa + (Mw*P0*exp(A1 + B1/T3 + C1*log(T3) + D1*T3)*(Hvap + T3*cpw))/(Ma*(P - P0*exp(A1 + B1/T3 + C1*log(T3) + D1*T3))) - (Mw*P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6)*(Hvap + T6*cpw))/(Ma*(P - P0*exp(A1 + B1/T6 + C1*log(T6) + D1*T6))))/(T4*cpa - T5*cpa + (Mw*P0*exp(A1 + B1/T4 + C1*log(T4) + D1*T4)*(Hvap + T4*cpw))/(Ma*(P - P0*exp(A1 + B1/T4 + C1*log(T4) + D1*T4))) - (Mw*P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5)*(Hvap + T5*cpw))/(Ma*(P - P0*exp(A1 + B1/T5 + C1*log(T5) + D1*T5)))));
E5 = Q - (L*cp*(T3 - T2));
F = [E1;E2;E3;E4;E5];
end
% fsolve code is following
clc
format short
 X0 = [44.2;62.2;46.4;41.7;47.5];
options = optimset(options,'StepTolerance =1e-10 ');
FSol = abs(vpa(fsolve(@funhddtryone, X0,options)))

Best Answer

x = sym('x', [1 5]);
F = funhddtryone(x);
digits(16);
sol = vpasolve(F);
However, vpasolve() says that there is no solution.
Equations 1, 2, and 4 can be solved for x1, x2, x3 in ways that are not totally unreasonable. After substitution, that leaves two equations in x4 and x5, and solving those for closed form solutions is difficult or not possible.
It would be about that point that you would start graphing to determine whether any solution is feasible.
Related Question