Heat Transfer: Matlab 2D Conduction

[Singed5059]

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Homework Statement

Having trouble with code as seen by the gaps left where it asks me to add things like the coefficient matrices. Any Numerical Conduction MATLAB wizzes out there?
A long square bar with cross-sectional dimensions of 30 mm x 30 mm has a specied temperature on each side, The temperatures are:

Tbottom = 100 C
Ttop = 150 C
Tleft = 250 C
Tright = 300 C

Assuming isothermal surfaces, write a software program to solve the heat equation to determine the two-dimensional
steady-state spatial temperature distribution within the bar.
Your analysis should use a finite difference discretization of the heat equation in the bar to establish a system of equations:

Homework Equations

AT = C

Must use Gauss-Seidel Method to solve the system of equations

The Attempt at a Solution

clear all
close all

%Specify grid size
Nx = 10;
Ny = 10;

%Specify boundary conditions
Tbottom = 100
Ttop = 150
Tleft = 250
Tright = 300

% initialize coefficient matrix and constant vector with zeros
A = zeros(Nx*Ny);
C = zeros(Nx*Ny,1);

% initial 'guess' for temperature distribution
T(1:Nx*Ny,1) = 100;

% Build coefficient matrix and constant vector

% inner nodes
for n = 2:(Ny-1)
for m = 2:(Nx-1)
i = (n-1)*Nx + m;
DEFINE COEFFICIENT MATRIX ELEMENTS HERE
end
end

% Edge nodes

% bottom
for m = 2:(Nx-1)
6%n = 1
i = m;

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

end
%top:
for m = 2:(Nx-1)
% n = Ny
i = (Ny-1)*Nx + m;

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

end
%left:
for n=2:(Ny-1)
%m = 1
i = (n-1)*Nx + 1;

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

end
%right:
for n=2:(Ny-1)
%m = Nx
i = (n-1)*Nx + Nx;

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

end
% Corners
%bottom left (i=1):
i=1

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

%bottom right:
i = Nx

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

C(Nx) = -(Tbottom + Tright);
%top left:
i = (Ny-1)*Nx + 1;

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

%top right:
i = Nx*Ny;

DEFINE COEFFICIENT MATRIX AND CONSTANT VECTOR ELEMENTS HERE

%Solve using Gauss-Seidel
residual = 100;
iterations = 0;
while (residual > 0.0001) % The residual criterion is 0.0001 in this example
7% You can test different values
iterations = iterations+1
%Transfer the previously computed temperatures to an array Told
Told = T;
%Update estimate of the temperature distribution

INSERT GAUSS-SEIDEL ITERATION HERE

%compute residual
deltaT = abs(T - Told);
residual = max(deltaT);
end
iterations % report the number of iterations that were executed
%Now transform T into 2-D network so it can be plotted.
delta_x = 0.03/(Nx+1)
delta_y = 0.03/(Ny+1)
for n=1:Ny
for m=1:Nx
i = (n-1)*Nx + m;
T2d(m,n) = T(i);
x(m) = m*delta_x;
y(n) = n*delta_y;
end
end
T2d
surf(x,y,T2d)
figure
contour(x,y,T2d

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Valkarie]

clear allclose all%Specify grid sizeNx = 10;Ny = 10;%Specify boundary conditionsTbottom = 100Ttop = 150Tleft = 250Tright = 300% initialize coefficient matrix and constant vector with zerosA = zeros(Nx*Ny);C = zeros(Nx*Ny,1);% initial 'guess' for temperature distributionT(1:Nx*Ny,1) = 100;% Build coefficient matrix and constant vector% inner nodesfor n = 2:(Ny-1)for m = 2:(Nx-1)i = (n-1)*Nx + m;A(i,i) = -4; % main diagonal elementA(i,i+1) = 1; % right-side elementA(i,i-1) = 1; % left-side elementA(i,i+Nx) = 1; % top elementA(i,i-Nx) = 1; % bottom elementC(i) = 0; % right-hand side of equationendend% Edge nodes% bottomfor m = 2:(Nx-1)%n = 1i = m;A(i,i) = -3; % main diagonal elementA(i,i+1) = 1; % right-side elementA(i,i-1) = 1; % left-side elementA(i,i+Nx) = 1; % top elementC(i) = -Tbottom; % right-hand side of equationend%top:for m = 2:(Nx-1)% n = Nyi = (Ny-1)*Nx + m;A(i,i) = -3; % main diagonal elementA(i,i+1) = 1; % right-side elementA(i,i-1) = 1; % left-side elementA(i,i-Nx) = 1; % bottom elementC(i) = -Ttop; % right-hand side of equationend