1D Heat Equation Explicit Scheme

Hi, I am trying to write a program to find the minimum depth required to avoid pipes at a depth of xm from freezing, after a temperature of -15oC for 60 days.

I am getting the error message "Index in position 1 is invalid. Array indices must be positive integers or logical values."

Here is my code.

clear all
p=2050;     % density(kg/m^3)
k=0.52;     % conductivity(W/m-K)
c=1840;     % specific heat capacity(J/kg-K)
T_ini=20;    % initial temperature(K)
T_inf=-15;    % external temperature(K)
alpha=k/(p*c);      % Let thermal diffusivity be alpha

M=100;      % number of time steps
t=60;
DELTA_t=t/(M);  % time step duration(s)
for j=1:M
    time(j)=(j-1)*DELTA_t;
end

N=10;                           
L=0.05;
DELTA_x=L/(N);                   
x=0:DELTA_x:L;                   


%Initial wall temperatures T(i,1)
for i=1:N+1
    T(i,1)=T_ini;
    T(i,N)=0;
end
% Step trough time
for j=1:(M-1)
    for i=1:(N)
        if (alpha*DELTA_t)/(DELTA_x^2)<=0.5
            T(i,j+1)=T(i,j)+((alpha*DELTA_t)/((DELTA_x)^2))*(T(i+1,j)-2*T(i,j)+T(i-1,j));
        end
    end
end

Answer 1

[Alan Stevens]

Look at

for i=1:(N)
        if (alpha*DELTA_t)/(DELTA_x^2)<=0.5
            T(i,j+1)=T(i,j)+((alpha*DELTA_t)/((DELTA_x)^2))*(T(i+1,j)-2*T(i,j)+T(i-1,j));
        end

You have a term T(i-1,j). When i is 1 this would be T(0,j), but Matlab indices must start at 1, not 0.