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I think i should have posted here instead of where I posted before. I don't know how I missed the homework help section... anyway

Well, I'm required to solve this heat transfer problem.

Develop a MATLAB code that computes the two-dimensional

temperature distribution in the rectangular plate. Load coefficients

into a matrix array of the form [A][T] = [C] where [A] is an M by

N matrix containing the leading coefficients of the temperature

nodes derived from the energy balance procedure of Task 1.

Solve the system of equations using MATLABâ€™s routine [T]= [A ]^-1*[C]

T1 is 25c and q'' is 100w/m^{2}

Ok, so I can get it to do it in 1 dimension and my numbers are correct based upon past work done in Excel (checked by Prof). I am not sure how to combine two dimensions into one matrix.

Currently my code is as follows:

T1 comes out toCode (Text):%{

Zach Cross

7-17-2010

Computes 2D temperature distribution in a rectangular plate

%}

clear all; close all; format short g

%boundaries

T1 = 25;

TE = T1;

TS = T1;

TW = T1;

%degrees C

q = 100;

%w/m^2

L = 0.2;

W = 0.1;

% meter

k = 0.1;

%W/(m*K)

%size of matrix

i = 5;

j = 5;

dx = L/i;

dy = W/j;

%set some helpful constants

dx_ = dx/dy;

dy_ = dy/dx;

d1 = (3*k*dx_ + 3*k*dy_);

d2 = (3*k*dx_ + 2*k*dy_);

d3 = (2*k*dx_ + 3*k*dy_);

d4 = (2*k*dx_ + 2*k*dy_);

%west interior node going from north to south (not accounting for 25c west boundary condition)

A1 = [1, -1, 0, 0, 0, 0, 0;

-2*k*dx_/d1, 1, -k*dx_/d1, 0, 0, 0, 0;

0, -k*dx_/d3, 1, -k*dx_/d3, 0, 0, 0;

0, 0, -k*dx_/d3, 1, -k*dx_/d3, 0, 0;

0, 0, 0, -k*dx_/d3, 1, -k*dx_/d3, 0;

0, 0, 0, 0, -k*dx_/d1, 1, -2*k*dx_/d1;

0, 0, 0, 0, 0, 0, 1];

C1 = [q*dy/(2*k);

0;

0;

0;

0;

0;

TS];

T1 = inv(A1)*C1

T1 =

25.901

15.901

7.8263

5.6215

7.6328

15.369

25

which is precisely what it should be [if this were a 1D problem].

I realize that it's stuck at the current size and I can work on making it capable of whatever size later; right now I want a 5x5 mesh plus the boundaries so, really 7x7.

I have derived equations from an energy balance for all the different types of nodes (corner, interior, boundary, etc) but I'm unsure how to get them to work together in this scheme. I can do it iteratively but it's not what he wants.

Could someone help me out a little here? Do I need to have a 7x7 solution matrix? (ugh, please not!)

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# Homework Help: 2d temperature in a plate using Matrix Inversion and MATLAB

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