%%%%  Heat Diffusion in a Thin Insulated Wire,   From Zhilin Li  %%%%%% 
 
clear all;  close all; 

L = 1.0;                %  Lenth of the Wire 
T = 150.;               %  Final Time 
n = 10;  dx = L/n;      %  Number of Space Steps 

cond = .001; spheat = 1.0; rho = 1.;             % material properties

a = cond/(spheat*rho);                           % Simplify
dt = dx*dx/(a*2.1);  maxk=fix(T/dt);             % Find the No. of steps
b = dt/(dx*dx); d = a*b; 

%  Initial Temperature 
for i = 1:n+1 
    x(i) =(i-1)*dx; 
    u(i,1) =sin(pi*x(i)); 
end 
 
figure(1); plot(x,u'); axis([0 1 0 100]);
pause(3)

%  Boundary Temperature 
for k=1:maxk+1 
    u(1,k) = 0.; 
    u(n+1,k) = 0.; 
    time(k) = (k-1)*dt; 
end 
 
%  Time Loop 

for k=1:maxk 
%  Space Loop   
   for i=2:n; 
       u(i,k+1) =1.*dt/(spheat*rho)+(1-2*d)*u(i,k) + d*(u(i-1,k)+u(i+1,k)); 
   end 
   figure(1); plot(x,u'); pause(2) 
end 
 
figure(2);  mesh(x,time,u')