To plot 1D temperature distribution plot versus lenght of the channel of the fin

Hello,

I am using this piece of code to get the temperature distribution across Fin of varying channel length. Kindly help me with changes in code where i can vary the lenght of the fin and see the corresponding changes in temperature.

help me in including the dx parameter inside the loop.

clc
clear all
L=1000;
N=100;
dx=L/(N-1);
T=zeros(N,1);
Tb=300;
k=1;
for j=1;1;k
    T(1,1)=Tb;
    for i=2:1:N-1
        T(i,1)=(T(i+1,1)+T(i-1,1))/2;
    end 
    T(N,1)=T(N-1,1);
end
plot(T);

Answer 1

[Walter Roberson]

L=0.1;
n=10;
T0=0;
T1s=40;
T2s=20;
dx=L/n;
alpha=0.0001;
t_final=60;
dt=0.1;
x = dx/2:dx:L-dx/2;     %important change
T=ones(n,1)*T0;
dTdt=zeros(n,1);
t=0:dt:t_final;
for j=1:length(t)
    for i=2:n-1
        dTdt(i)=alpha*(-(T(i)-T(i-1))/dx^2+(T(i+1)-T(i))/dx^2);
    end
    dTdt(1)=alpha*(-(T(1)-T1s)/dx^2+(T(2)-T(1))/dx^2);
    dTdt(n)=alpha*(-(T(n)-T(n-1))/dx^2+(T2s-T(n))/dx^2);
    T=T+dTdt*dt;
    plot(x,T,'LineWidth',3)
    hold on
    axis([0 L 0 50])
    xlabel('Distance(m)')
    ylabel('Temperature(\circC)')
    %pause(0.1)

end
hold off

[Ashwini nanjunda]

If I vary the length, T1s and T2s the graph is appearing differently. I need to vary the length and also temperature but still need same characteristics. How do i go with it??

[Walter Roberson]

I do not see much change.

L=0.1;
n=10;
T0=0;
T1s=50;
T2s=10;
dx=L/n;
alpha=0.0001;
t_final=60;
dt=0.1;
x = dx/2:dx:L-dx/2;     %important change
T=ones(n,1)*T0;
dTdt=zeros(n,1);
t=0:dt:t_final;
for j=1:length(t)
    for i=2:n-1
        dTdt(i)=alpha*(-(T(i)-T(i-1))/dx^2+(T(i+1)-T(i))/dx^2);
    end
    dTdt(1)=alpha*(-(T(1)-T1s)/dx^2+(T(2)-T(1))/dx^2);
    dTdt(n)=alpha*(-(T(n)-T(n-1))/dx^2+(T2s-T(n))/dx^2);
    T=T+dTdt*dt;
    plot(x,T,'LineWidth',3)
    hold on
    axis([0 L 0 50])
    xlabel('Distance(m)')
    ylabel('Temperature(\circC)')
    %pause(0.1)

end
hold off

[Ashwini nanjunda]

Sorry for the confusion. Try this with this piece of code.

I have taken L=6.3*10^-5; and T1s = 0; and T2s= 608. Now characteristics are coming in Straight lines. I tried changing n value and stepsize. Have a look into the code by changing these parameters and help me with this.

Answer 2

[Walter Roberson]

Lvals = [500, 750, 900, 950, 1000, 1050, 1100, 1500];
numL = numel(Lvals);

N = 100;
dx = L/(N-1);

T = zeros(N,numL);
Tb = 300;

for Lidx = 1 : numL
    L = Lvals(Lidx);
    for j=1:1:k
        T(1,Lidx) = Tb;
        for i=2:1:N-1
            T(i,Lidx) = (T(i+1,Lidx)+T(i-1,Lidx))/2;
        end
        T(N,Lidx) = T(N-1,Lidx);
    end
end

surf(Lvals, 1:N, T);
xlabel('L');
ylabel('N');
zlabel('T');

However, the only point in the code in which you use L is to calculate dx and you never use dx, so the value of L does not affect the output in any way.

[Ashwini nanjunda]

Thank you for the help sir. searching for a conceptual part to vary the lengh of a fin and observe the temperature distribution..This gave an insight to approach the problem.

[Walter Roberson]

I recommend that you study this pattern for iterating over values that are not consecutive integers (that start with 0 or 1) -- that is:

create a vector holding the values, count how many there were, pre-allocate the output based on the count of values, then loop an index from 1 to the number of values; inside the loop, pull out the "current" value from the list of values into a variable, and do computations based on the variable; store the result of the iteration into the pre-allocated variable indexed by the current loop index.

When you use this pattern, the values to be looped over do not need to be integers, do not need to be consecutive, do not need to be unique.

Do this even if you have something like

for L = 1:.1:5
  out((L-.9)*10, :) = something
end

the calculation of the row index based upon current value is likely to go wrong, not producing exact integers for the indices.

Answer 3

[Ashwini nanjunda]

Hello sir. This piece of code can be used to plot Temperature Vs Length.Help me with this

Finding it difficult to debug error and correct it.

clc
L=0.1;
n=10;
T0=0;
T1s=40;
T2s=20;
dx=L/n;
alpha=0.0001;
t_final=60;
dt=0.1;
x=dx/2;dx;L-dx/2;
T=ones(n,1)*T0;
dTdt=zeros(n,1);
t=0:dt:t_final;
for j=1:length(t)
    for i=2:n-1
        dTdt(i)=alpha*(-(T(i)-T(i-1))/dx^2+(T(i+1)-T(i))/dx^2);
    end
    dTdt(1)=alpha*(-(T(1)-T1s)/dx^2+(T(2)-T(1))/dx^2);
    dTdt(n)=alpha*(-(T(n)-T(n-1))/dx^2+(T2s-T(n))/dx^2);
    T=T+dTdt*dt;
    figure(1)
    plot(x,T,'LineWidth',3)
    axis([0 L 0 50])
    xlabel('Distance(m)')
    ylabel('Temperature(\circC)')
    pause(0.1)

end