What is the characteristic length of a cooling fin?

[CraigH]

Hi
This is just a quick question, it should have a pretty simple answer however I can't find the information anywhere on the internet.

When you are calculating/estimating the heat transfer coefficient for a prismatic fin using the reynolds, prandtl, grashof, and nusselt number, what length do you choose as the characteristic length?

I remember that it is different for forced convection as opposed to natural convection.
I know that when the fin is undergoing forced convection, e.g being blown by a fan, then you use the reynolds number and the prandtl number to calculate the nusselt number, and when it is undergoing natural convection you use the grashof number and the prandtl number to calculate the nusselt number.

However in these equations what do you use for L when:

a) it is undergoing forced convection

i) when the velocity of the air is parallel to the length of the fin
ii) when the velocity of the air is parallel to the width of the fin
ii) when the velocity of the air is parallel to the height of the fin
(I think this one is hard to answer, as the velocity of the air can not be parallel to the height of the fin as the base is in the way)​

b) it is undergoing natural convection

i) when the fin is vertical (as shown in the picture)
ii) when the fin is horizontal
​

My guess is that for a(i) it is the length of the fin, as this is the length that the air flows past. For a(ii) it is the thickness of the fin as this is the length that the air flows past (per fin). For a(iii) I do not think that the equations work, and for b(i) it will be the height, and b(ii) it will be length. This is just my gut feeling though. I may be wrong.

So to summarize my question:
Please can someone tell me how I am supposed to know what value for the characteristic length I am supposed to use in the Re, Gr and Nu Numbers?

Thanks!

P.S

I should also point out that the purpose of doing all this would be to calculate the heat transfer coefficient per fin. So when you are calculating the nusselt number you can do it as if there is only one fin there. From this number you can work out the heat transfer coefficient of that fin. Then from this you can work out the heat flux per fin and thus the total heat flux. I know this is a bit of an assumption, because in reality if the pitch (the space in between the fins (b)) was small then the airflow would be different to if there was a large pitch, or just one fin. However for the purpose of this question assume that this is for working out the heat transfer coefficient of just one fin.

 

[Chestermiller]

For forced convection with the air blowing parallel to the fins, the characteristic length is the distance between the fins. The fins form channels for the air flow between them. Look up in a handbook or a book on fluid mechanics and heat transfer how to calculated the heat transfer coefficient for forced convection flow between fins.

Chet