% Heat transfer with three materials, heat2.m
clear                       % variables
format short e              % E format
% format long               % double precision

temp1=70                    % inside temperature
temp3=20                    %outside temperature

kxx = [0.3 0.03]            % thermal conductivity
len = [0.75 6]/12            % length
k12 = kxx(1) / len(1);      % therm cond, length
k23 = kxx(2) / len(2);
beta = k12*1e7              % zienk factor

stiff = [ k12   -k12      0    % stiffness matrix
         -k12  k12+k23  -k23
           0    -k23     k23 ]
df =  [ temp1*beta; 0; temp3*beta ];  % combined
zienk = stiff;
zienk(1,1)=zienk(1,1)+beta;
zienk(3,3)=zienk(3,3)+beta
format short
temp = inv(zienk) * df;    % displacements
heat = stiff * temp;       % force vector

% print the results
fprintf('\n    Heat2, two materials ')
fprintf('\n  Your name, MENG 421, ')
disp(date)

fprintf('\n   Node Temperature   Heat')
fprintf('\n              F      Btu/Hr\n')
for i = 1:length(df)
  fprintf('    %2.0f   %7.1f   %7.2f \n',i,temp(i),heat(i))
end

%    Heat2, two materials 
%   Your name, MENG 421, 11-Mar-2004

%    Node Temperature   Heat
%               F      Btu/Hr
%      1      70.0      2.96 
%      2      69.4     -0.00 
%      3      20.0     -2.96