I am writing a code using the 4th order runge kutta method, for heat transfer through an adiabatic fin, i am having some problems getting the code to work, any advice?

%%4th order runge kutta-uniform cross section fins
%circular pin fin- pure aluminium
%assumptions
%1D steady state heat transfer
%dimensions 
L=0.05; 
D=0.005;
%parameters
h=50;
k=237;
Tb=60;
Ta=15;
P=pi*D;
Ac=pi*D^2/4;
m=sqrt(h*P/k*Ac);

%Boundary conditions
%BC1 Theta(0)=Tb-Ta
%BC2 dtheta/dx at x=L =0

%inputs
H=0.0004;       %step size
Lmax=0.05;      %total length
N=Lmax/H;       %Number of steps

%Initial conditions
L(1)=0;
T(1)=60;
z(1)=0;
m=1;
z(100)=0;
x(1)=0;

while m>0.00001;
    for i=1:N
        
        %equations for k values
        k1=z(i);
        k2=z(i)+(H*L1/2);
        k3=z(i)+(H*L2/2);
        k4=z(i)+(H*L3);
        %equation for T(i+1)
        T(i+1)=T(i)+(H/6)*(k1+(2*k2)+(2*k3)+k4);
        
        %equations for L values
        L1=((h*P/k*Ac).*(T(i)));
        L2=((h*P/k*Ac).*(T(i)+(H*k1/2)));
        L3=((h*P/k*Ac).*(T(i)+(H*k2/2)));
        L4=((h*P/k*Ac).*(T(i)+(H*k3)));
        
        %equation for z(i+1)
        z(i+1)=z(i)+(H/6)*(L1+(2*L2)+(2*L3)+L4);
        
        %equation for x(i+1)
        x(i+1)=x(i)+H;
        
    end
    z(1)=z(1)-z(i+1);
    m=abs(z(i+1)-z100);
end

[Torsten]

The code does not work since z100 is undefined.

Could you explain what method you use to solve the BVP ?

[Michael Pine]

The Boundary Value problem? these conditions are defined by literature

[Michael Pine]

sol = bvp4c(odefun,bcfun,solinit)

[Torsten]

You solve the boundary value problem

d^2T/dx^2 = 0
T(x=0) = 60
dT/dx(x=0.05) = 0

don't you ?

If this is the case, the solution should be clear:

T(x) = a*x + b

where the constants a and b follow from the boundary conditions (in your case T=60 for all x).