How can I add the differential equation attached to my script to run in the loop, where n = 4 for the first value of n.

clear all;

T0H = 1158;
H = 0.3;          % in Degrees Kelvin/Second - Rate of Change
K0 = 1.067e17;      % Pre-Exponential Factor
QH = 4.4516e+05;    % in Joules/Mole using Kelvin
R = 8.314;          % Gas Constant

Ft = [201];

n1 = [201];



Ft(1) = 0;
n1(1) = 4;


for i = 1159: 1 : 1358
    T = i;
    Kt = K0*exp(-(QH/(R*T)));
    Ft(i - 1157) = 1 - exp(-(Kt*(T-T0H)/H)^n1(i-1158));
    n1(i - 1157) = -((log(-log((1-(Ft(i - 1157)))))) - (log(-log((1-(Ft(i - 1158))))))/((QH/R*T) - (QH/R*(T-1))));
    
end
   
figure ('Name','Phase Fraction vs Temperature');  
disp(Ft);
xs = 1158:1:1358;
ys = Ft;
plot(xs,ys);
title('Phase Fraction vs Temperature')
xlabel('Temperature in K');
ylabel('Phase Fraction of \beta ');
grid on;
hold on;

[darova]

What is dependent variable?

[Abhishek Cherukara]

So basically the Ft is dependent on n as shown here;

But n is dependent on the Ft at each temperature T of the loop. Where Q, R and T are constants.

Does that make any sense?

Answer 1

[darova]

If you have formula for you don't need diff equation

T = 1159: 1 : 1358;
fr = 1 - exp(-(K*(T-T0)/H).^n);
c1 = diff( log(-log(1-fr)) );
c2 = diff( Q./R./T );
nn = c1./c2;

[Abhishek Cherukara]

Hi @darova, Unfortunately, I'm still getting an error with this? Is there anything else I could do to adjust this?

[darova]

Please show the error