SimScale CAE Forum

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 :slight_smile:

Best,
Karim

Hi Karim!

Are you talking about the training inside the Academy? :slight_smile: I do not remember all the exercises by heart so if you could be a bit more precise that would help :+1:

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 :wink: . 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 :slight_smile:

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 :smiley: ) - getting back to you as soon as I can.

Best,

Jousef