Transient Conduction Heat Transfer

 I am trying to say that the nodes from 2-40 are all initially 19 Celsius and that the first node = 27 Celsius. Then as time progresses through the simulation the nodes from x> to x==n_x should increase in temperature. The whole simulation should run for 180 seconds. I have seemed to fixed the issues I was having however I am now having different errors, wondered if you could help.

%Aluminium Material Properties%
clear all
close all
clc
rho =   2700  ;   %kg/m^3 Density
k   =   170   ;   % 
cp  =   910   ;   %
alpha = k/(rho*cp); %
L_d     =   0.0047;                 %m  Diameter
L_x     =   0.047;                  %m  Length in x direction
L_r     =   L_d/2;                  %m  Radius
n_r     =   2;                      %   Nodes in r direction
n_x     =   40;                     %   Nodes in x direction
del_x   =   L_x/(n_x-1);             %m  Spacing of Nodes
T_h     =   27;                     %C  Temperature of Hot Side
T_i     =   19;                     %C  Initial Temperature
t_2     =   180;                    %s  Simulation Time
t(1)    =   0;                      %s  Initial Time
Fo      =   0.25;                   %   Fourier Number Stability 0.25 For 3D
del_t   =   (Fo*del_x^2)/alpha;      %   Calculate time step using Fourier Number for Stability
h       =   5;
%Set Inital Matrices Temp
T(1:n_r,1:n_x+2) =  T_i;
Fo                      = alpha*del_t/(del_x.^2)                            ; %        Fourier Number
Bi                      = h*del_x/k                                       ;  %     Biot Number
if Fo > 0.25
    fprintf('Fo Number to big, code unstable \n \n')
elseif Fo*(1-Bi) > 0.25
    fprintf('Bi Number to big, code unstable')
end
k = 1;
while t<t_2                         %   Time Loop
      for r=1:n_r                     %   Space Loop r direction
           for x=1:n_x                 %   Space Loop x direction
                if x==1                %   Boundary Condition First Node = 27 Celius                %   Boundary Condition First Node = 27 Celius
                  T(r,x,k+1) = 27;
              elseif x>1 && x==n_x   %   Middle to End of Material
                  T(r,x,k+1) = alpha*((T(r,x+1,k)-2*T(r,x,k)+T(r,x-1,k))/del_x.^2)+((T(r+1,x,k)-2*T(r,x,k)+T(r-1,x,k))/del_x.^2) ;
              end
          end
      end
         for r = 1:n_x
             T(r,1,k+1)   = T(r,3,k);
             T(r,n_x+2,k+1) = T(r,n_x,k);
         end
t(k)  =   k+del_t;
k       =   k+1;
end
Temp(1:n_r,1:n_x)   =   T(1:n_r,1:n_x,k-1);
The error that is occurring now is -----

??? Attempted to access T(0,2,1); index must be a positive integer or logical.

Error in ==> Transient2D at 39
                T(r,x,k+1) =
                alpha*((T(r,x+1,k)-2*T(r,x,k)+T(r,x-1,k))/del_x.^2)+((T(r+1,x,k)-2*T(r,x,k)+T(r-1,x,k))/del_x.^2)
                ;
Hopefully someone can help.

Answer 1

[Azzi Abdelmalek]

In line 37 you have the expression on the right contains

T(r-1,x,k)

with r beginning at 1, make the index=0

[Luke Cartwright]

If you mean

   T(r,x,k+1) = alpha*((T(r,x+1,k)-2*T(r,x,k)+T(r,x-1,k))/del_x.^2)+((T(r+1,x,k)-2*T(r,x,k)+T(r-1,x,k))/del_x.^2) ; T(r,x,k+1) = alpha*((T(r,x+1,k)-2*T(r,x,k)+T(r,x-1,k))/del_x.^2)+((T(r+1,x,k)-2*T(r,x,k)+ T(r-1,x,k))/del_x.^2) ;

Then that should be that as it has to look at the previous r.

[Azzi Abdelmalek]

This is it. But what index r=0 means for you? There is no such index in your array T. Maybe you should begin tour r at 2.