This code performs heat transfer.

Tf=100; % Final Temp
Tint=1000; % Initial Temp
Tinf=20; % Water Temp
h=3000; % W/m^2*K
rho=5550; %kg/m^3
dx=0.005; %m
L=.25/2;%m
num=(L/dx);
T=zeros(num,1);
T(:,1)=Tint;
Cp=600; 
k=27.5; 
Alpha=(k/(rho*Cp));
Bi=((h*dx)/k);
dt=(dx^2)/(2*Alpha*(1+Bi));
Fo=((Alpha*dt)/(dx^2));
i=1;
while T(num,i)>Tf 
    for j=1:num    
        if j==1
            T(j,i+1)=(2*Fo(j)*Bi(j))*Tinf+(2*Fo(j))*T(j+1,i)+(1-(2*Fo(j)*Bi(j))-(2*Fo(j)))*T(j,i);
        elseif j==num
            T(j,i+1)=2*Fo(j)*T((j-1),i)+(1-(2*Fo(j)))*T(j,i);
        else
            T(j,i+1)=(Fo(j))*(T((j-1),i)+T((j+1),i))+(1-(2*Fo(j)))*T(j,i);
        end
        if (20<=(T(j,i)))&&((T(j,i))<600)
            Cp(j)=425+(.773)*(T(j,i))-.00169*((T(j,i))^2)+.00000222*((T(j,i))^3); 
        elseif (600<=(T(j,i)))&&(T(j,i))<(735)
            Cp(j)=666+(13002/(738-(T(j,i))));
        elseif (735<=(T(j,i)))&&(T(j,i))<(900)
            Cp(j)=545+(17820/((T(j,i))-731));
        elseif (900<=(T(j,i)))&&(T(j,i))<=(1000)
            Cp(j)=600;
        end
        if(20<=(T(j,i)))&&((T(j,i))<800)
            k(j)=54-.0333*(T(j,i));
        elseif (800<=(T(j,i)))&&(T(j,i))<=(1000)
            k(j)=27.3;
        end
        Alpha=(k(j)/(rho*Cp(j)));
        Bi(j)=((h*dx)/k(j));
        Fo(j)=((Alpha*dt)/(dx^2)); 
    end
    i=i+1;
end

Index exceeds the number of array elements. Index must not exceed 1.

[Torsten]

Sorry, but your code is full of errors. Maybe it makes more sense if you explain what you are trying to do.

[M Miller]

This is part of the code to find how long it takes a slab of steele to cool from 1200° C to 200° C by using water jets at 40° C

[Torsten]

Seems you try to solve the transient heat conduction equation in 1d.

MATLAB's "pdepe" is the correct tool to do this.

Answer 1

[Cris LaPierre]

Your code is written expecting Fo and Bi to be a vectors, but they are scalars, so only ever has 1 element. You get this error any time you try to index using a value greater than 1.

The easiest solution based on the information we have is to not index these 2 variables.

Tf=200; % Final Temp
Tint=1200; % Initial Temp
Tinf=40; % Water Temp
h=4000; % W/m^2*K
rho=7850; %kg/m^3
dx=0.005; %m
L=.5/2;%m
num=(L/dx)+1;

T=zeros(num,1);
T(:,1)=Tint;

Cp=650; % initial Cp
k=27.3; % Initial k

% used to solve for dt
Alpha=(k/(rho*Cp));
Bi=((h*dx)/k);
dt=(dx^2)/(2*Alpha*(1+Bi));
Fo=((Alpha*dt)/(dx^2));

i=1;
while T(num,i)>Tf
    
    for j=1:num
        
        
        if j==1
            T(j,i+1)=(2*Fo*Bi)*Tinf+(2*Fo)*T(j+1,i)+(1-(2*Fo*Bi)-(2*Fo))*T(j,i);
        elseif j==num
            T(j,i+1)=2*Fo*T((j-1),i)+(1-(2*Fo))*T(j,i);
        else
            T(j,i+1)=(Fo)*(T((j-1),i)+T((j+1),i))+(1-(2*Fo))*T(j,i);
        end
        % Cp and k need to be defined each time it finds a temperature since they are both temperature dependent       
        if (20<=(T(j,i)))&&((T(j,i))<600)
            Cp(j)=425+(.773)*(T(j,i))-.00169*((T(j,i))^2)+.00000222*((T(j,i))^3); 
        elseif (600<=(T(j,i)))&&(T(j,i))<(735)
            Cp(j)=666+(13002/(738-(T(j,i))));
        elseif (735<=(T(j,i)))&&(T(j,i))<(900)
            Cp(j)=545+(17820/((T(j,i))-731));
        elseif (900<=(T(j,i)))&&(T(j,i))<=(1200)
            Cp(j)=650;
        end
        if(20<=(T(j,i)))&&((T(j,i))<800)
            k(j)=54-.0333*(T(j,i));
        elseif (800<=(T(j,i)))&&(T(j,i))<=(1200)
            k(j)=27.3;
        end
        
        %These values are recalculated each time as well based on the Cp and k
        Alpha=(k(j)/(rho*Cp(j)));
        Bi=((h*dx)/k(j));
        Fo=((Alpha*dt)/(dx^2)); 
        
    end
    i=i+1;
end
ttot=(i-1)*dt

ttot = 826.5942