# Heat Transfer in a beam problem

Hi !

I have a problem with the fact that I can’t determine T2, T3 and T4 considering the fact that the matrix is non-invertible and the fact that Q1=Q2=Q3=Q4=Q5=0 is incompatible with T1≠T5.
If I missed something please tell me, thank’s in advance for the help

Best,
Karim

Hi Karim!

Are you talking about the training inside the Academy? I do not remember all the exercises by heart so if you could be a bit more precise that would help

Cheers,

Jousef

Hi @jousefm !

Thank you for your feedback and sorry I’m new to the forum, I will try not to forget it next time . I was referring to :

We didn’t had enough information as it is so we have to make a lot of assumption to calculate the unknown temperature values with the global assembly of equation MT = Q.

Therefore, I used the hint “temperatures will change linearly” to asume T = T(x) = ax +b and solve for a, b considering the fact that T2 = T(d), T3 = T(2d) and T4 = T(3d).
I found answers similar to the modeling with it but is there a way to solve this question as it was meant to (solving MT = Q even without information on Q) ?

Best,
Karim

Hi Karim!

T1 and T5 are known. Put them inside the system and you should be able to solve the rest of the nodal values

Best,

Jousef

Well, if we don’t know Q1, Q2, Q3, Q4 and Q5 there is basically 8 variables for 5 equations so, it’s unsolvable.
My question actually was what information do we have on Q1, Q2, Q3, Q4 and Q5 (I know they aren’t equal to 0 because it will lead to T1 = T5 and that’s absurd and assuming Q1 = Q2 = Q3 = Q4 = Q5 ≠ 0 will lead to T2 = (4T1 +T5)/5 =358 K the real value being 354,25 K).

PS: what’s bothering the most is that they say “given all the values” meaning they are useful but assuming Q1 = Q2 = Q3 = Q4 = Q5 we don’t need the actual value of kA/L and the same statement with the method T = T(x) = ax + b

Best,
Karim

If I have the time Karim, I can solve it step-by-step and DM you. Posting it here won’t make much sense as people would be just copying the solution. I actually did not solve it so far but it should not be that hard (at first glance at least ) - getting back to you as soon as I can.

Best,

Jousef