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Help Solving Multiple Equations

 
Old 02-20-2010 at 11:02 PM   #1
ahmedsu
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Help Solving Multiple Equations

Currently I am working on a heat transfer assignment. I have 10 equations with 10 unknowns (T1 - T10), it is a very tedious method by hand so I thought I would give it a shot in MATLAB, however I am having some trouble. This is the code I formulated:

h = 200;
k = 300;
T0 = 125;
Tinf = 25;
x = 0.025;
A = 0.0004908738521;
P = 0.078639816;
T1;
T2;
T3;
T4;
T5;
T6;
T7;
T8;
T9;
T10;

(h*P*x*(Tinf - T1)) + ((k*A)*((T2-T1)/x)) + ((k*A)*(T0 - T1)) = 0;
(h*P*x*(Tinf - T2)) + ((k*A)*((T3-T2)/x)) + ((k*A)*(T1 - T2)) = 0;
(h*P*x*(Tinf - T3)) + ((k*A)*((T4-T3)/x)) + ((k*A)*(T2 - T3)) = 0;
(h*P*x*(Tinf - T4)) + ((k*A)*((T5-T4)/x)) + ((k*A)*(T3 - T4)) = 0;
(h*P*x*(Tinf - T5)) + ((k*A)*((T6-T5)/x)) + ((k*A)*(T4 - T5)) = 0;
(h*P*x*(Tinf - T6)) + ((k*A)*((T7-T6)/x)) + ((k*A)*(T5 - T6)) = 0;
(h*P*x*(Tinf - T7)) + ((k*A)*((T8-T7)/x)) + ((k*A)*(T6 - T7)) = 0;
(h*P*x*(Tinf - T8)) + ((k*A)*((T9-T8)/x)) + ((k*A)*(T7 - T8)) = 0;
(h*P*x*(Tinf - T9)) + ((k*A)*((T10-T9)/x)) + ((k*A)*(T8 - T9)) = 0;
(h*P*x*(Tinf - T10)) + ((k*A)*((T10-T9)/x)) = 0;

T1
T2
T3
T4
T5
T6
T7
T8
T9
T10

The above 10 are my equations (h*P*x*...) however it is given me an
error when I say "=0", the error reads "Parse Error: "=" usage might be
invalid MATLAB Syntax".

I was wondering if anyone could assist me on how to be able to solve for
my 10 unknowns, and help me correct my code and write it so that I will be able to solve for my unknowns.

Thanks.
Old 02-20-2010 at 11:36 PM   #2
stevennn
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I'm not sure if you can do it like that. If you rearrange the equations and make a matrix of the coefficients, you should be able to solve it using Ax=B.
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Old 02-20-2010 at 11:37 PM   #3
adrian
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Not sure if this will help, but if you formulate your problem in the following manner

[coefficient matrix with 10 columns(T1-T10) and n rows, where n is the number of equations] * [column vector with 10 rows(t1-T10)] = [column vector with 10 rows, each 0)]

let's say you name the above matrices in the following manner:
A*x=b
then you can do
x = A\b
to find x, which is the vector T1-T10

hope it helps somewhat.
Adrian

Last edited by adrian : 02-20-2010 at 11:40 PM.
Old 02-21-2010 at 12:17 AM   #4
adrian
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A matrix should look like this(did the algebra for ya):
Note: I put nonzero elements of the matrix in brackets for readability
MatA=
(-h*P*x-k*A/x-k*A) (k*A/x) 0 0 0 0 0 0 0 0
(k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0 0 0 0 0 0 0
0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0 0 0 0 0 0
0 0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0 0 0 0 0
0 0 0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0 0 0 0
0 0 0 0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0 0 0
0 0 0 0 0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0 0
0 0 0 0 0 0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x) 0
0 0 0 0 0 0 0 (k*A) (-h*P*x-k*A/x-k*A) (k*A/x)
0 0 0 0 0 0 0 0 (-k* A/x) (-h*P*x+k*A/x)

please check my algebra

Now, there seems to be a constant term for each equation, so we must put it(sign-reversed) in the result column vector
so your result column vector should be:
resultb =

(-h*P*x*Tinf-k*A*T0)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)
(-h*P*x*Tinf)

Last edited by adrian : 02-21-2010 at 12:35 AM. Reason: Complete
Old 02-21-2010 at 12:25 AM   #5
ahmedsu
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A = [-27.50893565 5.890486225 0 0 0 0 0 0 0 0;
5.890486225 -27.50893565 5.890486225 0 0 0 0 0 0 0;
0 5.890486225 -27.50893565 5.890486225 0 0 0 0 0 0;
0 0 5.890486225 -27.50893565 5.890486225 0 0 0 0 0;
0 0 0 5.890486225 -27.50893565 5.890486225 0 0 0 0;
0 0 0 0 5.890486225 -27.50893565 5.890486225 0 0 0;
0 0 0 0 0 5.890486225 -27.50893565 5.890486225 0 0;
0 0 0 0 0 0 5.890486225 -27.50893565 5.890486225 0;
0 0 0 0 0 0 0 5.890486225 -27.50893565 5.890486225;
0 0 0 0 0 0 0 0 5.890486225 -21.61844943];

B = [-1129.509858;
-393.19908;
-393.19908;
-393.19908;
-393.19908;
-393.19908;
-393.19908;
-393.19908;
-393.19908;
-393.19908];

v = A\B

v =

47.4967
30.0610
26.1386
25.2561
25.0576
25.0130
25.0029
25.0007
25.0001
25.0000
Old 02-21-2010 at 12:37 AM   #6
adrian
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good stuff
Old 02-21-2010 at 12:21 PM   #7
lmasud
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you could just use maple, this link explains how to do it
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Would be Electrical Engineering II
Old 02-21-2010 at 12:25 PM   #8
adrian
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Hey, we're all grow'd up here. Pfffff....maple....



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