Solving symbolic equation using solve

Hi,

I am trying to minimize the value of phi here. I want the values of E for which phi becomes zero but the code is not providing any solution, also there is some problem in the execution of solve function.

Can someone please help with the proper function to be used here for minimization.

b = [(5/60) (10/60) ];
syms E xfun Ifun phi phidiff
xfun = sym(zeros(10,2));
Ifun = sym(zeros(10,2));
phi = sym(zeros(10,2));
phidiff = sym(zeros(10,1));
E_Vyas = zeros(10,1);

for prog = 1:1:2
    for conv = 1:1:10
        xfun(conv,prog) = -(E)./(8.314.*T(conv,prog));                         %here T is temperature file(10 by 2 matrix) 
        Ifun(conv,prog) = (T(conv,prog).*exp(xfun(conv,prog)))-(Eiget(-xfun(conv,prog))./8.314);
    end
end

for conv = 1:1:10
     phi(conv) = (Ifun(conv,1).*b(2))./(Ifun(conv,2).*b(1)) + (Ifun(conv,2).*b(1))./(Ifun(conv,1).*b(2));
     phidiff = diff(phi,E);
     E_Vyas(conv) = (real(solve(phidiff,E)))/1000;
     conv;
     show = E_Vyas(conv);
end
E_Vyas = smooth(E_Vyas,0.1,'loess');

function [Eix] = Eiget(xfun)                                               %function for approximation for I(E,T)
     A = log((0.56146./xfun)+0.65).*(1+xfun);
     B = (xfun.^4).*(exp(7.7*xfun)).*((2+xfun).^3.7);
     Eix= (((A.^-7.7)+B).^-0.13)-((exp(-xfun))./xfun);
end

Answer 1

[Walter Roberson]

b = [(5/60) (10/60) ];
syms E xfun Ifun phi phidiff
xfun = sym(zeros(10,2));
Ifun = sym(zeros(10,2));
phi = sym(zeros(10,1));
phidiff = sym(zeros(10,1));
E_Vyas = zeros(10,1);

for prog = 1:1:2
    for conv = 1:1:10
        xfun(conv,prog) = -(E)./(8.314.*T(conv,prog));                         %here T is temperature file(10 by 2 matrix) 
        Ifun(conv,prog) = (T(conv,prog).*exp(xfun(conv,prog)))-(Eiget(-xfun(conv,prog))./8.314);
    end
end

guess = sym('1.0');
for conv = 1:1:10
     phi(conv) = (Ifun(conv,1).*b(2))./(Ifun(conv,2).*b(1)) + (Ifun(conv,2).*b(1))./(Ifun(conv,1).*b(2));
     phidiff(conv) = diff(phi(conv),E);
     tic
     sol = vpasolve(phidiff(conv),E,guess);
     toc
     if isempty(sol)
         E_Vyas(conv) = nan;
     else
         E_Vyas(conv) = real(sol)/1000;
         guess = sol;
     end
end
E_Vyas_smooth = smooth(E_Vyas,0.1,'loess');

function [Eix] = Eiget(xfun)                                               %function for approximation for I(E,T)
     A = log((0.56146./xfun)+0.65).*(1+xfun);
     B = (xfun.^4).*(exp(7.7*xfun)).*((2+xfun).^3.7);
     Eix= (((A.^-7.7)+B).^-0.13)-((exp(-xfun))./xfun);
end

[Vithusha T]

Thanks. It's working.