code is returning NaN when taking inverse of matrx

clear all;close all;clc

N = 11; %number of nodes per row
Ntot = N^2; %total number of nodes
L = 25; %cm
W = 25; %cm
dx = L/(N-1); %cm

As=25*25;

x = 0:dx:L; %cm
tinf = 298; %C
h = 20; %W/m2K
k = 16.2; %W/mK
tin = 1500; %K

A = zeros(Ntot,Ntot);
b = zeros(Ntot,1);

A(1,1) = 2*h*dx + 2*k;  % top left node
A(1,2) = -k;
A(1,N+1) = -k;
b(1,1) = 2*h*dx*tinf;

A(N,N) = 2*h*dx + 2*k;   %top right node 
A(N,N-1) = -k;
A(N,N+N) = -k;
b(N,1) = 2*h*dx*tinf; 

for i= Ntot-(N-1)
    A(i,i) = 2*h*dx+2*k ;   %bottom left node
    A(i,i+1) = -k;
    A(i,i-N) = -k; 
    b(i,1) = tinf*2*h*dx;
end


for i= Ntot
    A(i,i) = 2*h*dx+2*k ;   %bottom right node
    A(i,i-1) = -k;
    A(i,i-N) = -k; 
    b(i,1) = tinf*2*h*dx;
end

for i= 2:10
    A(i,i) = 2*k +h*dx ;
    A(i,i-1) = -k;
    A(i,i+1) = -k;
    b(i,1)= dx*(As*tin+tinf*h);
end

for i= 112:120
    A(i,i) = 2*k +h*dx ;
    A(i,i-1) = -k;
    A(i,i+1) = -k;
    b(i,1)= dx*(h*tin+tinf*h);
end
for i=12:11:100
    A(i,i) = h*dx+2*k;
    A(i,i-11)=-k;
    A(i,i+11) = -k;
    b(i,1) = dx*(h*tinf + tin*As);
end
for i=22:11:110
     A(i,i) = h*dx+2*k;
    A(i,i-11)=-k;
    A(i,i+11) = -k;
    b(i,1) = dx*(h*tinf + tin*As);
end
for i=13:21
       b(i,1)=tin;
end
for i=24:32
       b(i,1)=tin;
end
    for i=35:43
       b(i,1)=tin;
    end
    for i=46:54
       b(i,1)=tin;
    end
    for i=57:65
       b(i,1)=tin;
    end
    for i=68:76
       b(i,1)=tin;
    end
    for i=79:87
       b(i,1)=tin;
    end
   
 for i=90:98
       b(i,1)=tin;
 end
  for i=101:109
       b(i,1)=tin;
  end

  T = A\b
  Tf = transpose(reshape(T,11,11));
  contourf(Tf)
    

[KSSV]

Where you are getting NaN? Check aby where are you dividing with zeros.

[David Goodmanson]

Hi Alyssa,

A and b have no infs or nans, but matirx A has a huge condition number

cond(A)
ans = 8.9403e+64

so solving A\b is not going to happen.

[Walter Roberson]

rank(A) is 40, on a 121 x 121 matrix, so the condition number will not be of importance in this particular case.

Have a look at spy(A) and it will become obvious that there are number of all-zero columns and all-zero rows. For example observe that nothing in your code sets anything in row 13 of A.

[Vladimir Sovkov]

Search and read Matlab "Help" for the "pinv" call function and, if it suits you, change "T = A\b" to "T = pinv(A)*b".