I am writing a code to solve a set of nonlinear equations using fsolve, but i keep getting this message "no solution found" and also " fsolve stopped because the last step was ineffective. the vector of function value is not near zero "

This is the function file below.

function E=trial2(s)
u = 10; % wind speed
Ta=286;% ambient temp in kelvin
hwind = 2.3 + u; %(convective heat transfer coeff)
G=1000; % solar radiation

Tg=15; % glass temp
Rpvg=0.0014286; % resistance of glass-pv
Rbpv=1.93*10^(-3);% resistance of base pv
Tsky=0.0552*Ta^1.5; % radiation sky temp
alpha_g=1; % absoprptivity of glass
epsilon_g=0.84;% emissivity of glass
sigma=5.67*(10^8);% boltzman's constant
hrad=epsilon_g*sigma*(Tg^2+Tsky)*(Tg+Tsky); % radiation heat transfer coefficient

Tpv=s(1);
Tb=s(2);

E(1)=(Tpv/Rpvg)-(Tg*(hwind+(1/Rpvg)))-(Tg*hrad)+(hrad*Tsky)-(Ta*hwind)+(G*alpha_g);% glass energy balance equation
E(2)=G*alpha_g+((1/Rpvg)*(Tg-Tpv))+((1/Rbpv)*(Tb-Tpv));% pv thermal balance eqn

end

and the execution script below

sg = [50;50]; % iterating with random temperature
s = fsolve(@trial2,sg) % using fsolve to get Tpv and Tb

Answer 1

[Walter Roberson]

If you have the Symbolic Toolkit, then you can use

s = [sym('S1'), sym('S2')];
E = trial2(s);
s1 = solve(E(1), s(1));
s2 = solve(subs(E(2),s(1),s1),s(2));
double(s1), double(s2)

The outputs are approximately -23786403074636.8 and -55921190932736.1

Considering the 50 and 50 you used as starting values, I suspect you are not expecting values that large and negative, but these are the solutions given those equations.

Answer 2

[george mobol]

Thank you for your answers using the symbols kit. I am trying to solve a similar equation using it but keep getting errors. This is the function file below:

function Eq = trial3(s)
Tg=s(1);
Tpv=s(2);
Tb=s(3);
Teva=s(4);

Eq(1)=8+(3.81*10^(-10)*((276.84^4)-(Tg)^4))+0.1424*(293-Tg)+4.8*(Tpv-Tg);
Eq(2)=-4740.76*(Tpv)+4736*(Tb)-10.733+Tg*(4.8);
Eq(3)=4736*(Tpv+Tb)+1.71;
Eq(4)=4736*(Tpv)-5787.25*(Tb)+1051.25*(Teva);
end

And the execution file as shown.

s = [sym('S1'), sym('S2'), sym('S3'), sym('S4')];
Eq = trial3(s);
s1 = solve(Eq(1), s(1),s(2));
s2 = solve(Eq(2), s(2),s(3));
s3 = solve(Eq(3), s(2),s(3));
s4 = solve(Eq(4), s(2),s(3), s(4));

double(s1), double(s2),double(s3),double(s4)

Thank you

[Walter Roberson]

you cannot solve() one equation for two variables. Also, after you solve the first equation for the first variable you nee to substitute that value into the second equation and solve the result for the second variable, then take the third equation and substitute the first variable's value and then substitute the second variable's value, and then solve the result for the third variable, and so on. Or you could just ask to solve the four equations simultaneously,

solve(Eq)

Note: the solution involves a 4th order polynomial, so there will be 4 sets of solutions.