I Fin area and heat transfer direction

1. Jul 28, 2016

Axe199

So, i was studying some fin design in a heat transfer course , and then came the part where the efficiency is to be calculated, then i noticed that when he calculated the surface area and the sides of a rectangular fin weren't included, so i searched and i found out that it was neglected because it's a one dimensional system, i understand how will that add an extra dimension, but i dont understand how is this a one dimensional system to begin with, we have conduction in x direction and convection in y direction so thats 2 directions
edit: i just watched a video where he said he neglected the sides because they have negligible area...makes sense but i am not sure that this is 100% right because he also ignored the tip and we dont ignore it in our course

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2. Jul 28, 2016

benny_91

Well, I believe you have two questions here: 1-Why do we assume that heat transfer in fins is one dimensional? and 2-Why is the side surface area of the fin neglected?
So first of all I have never heard of a 3-D convection or a 2-D convection or simply one dimensional convection though we do hear about these in conduction. Convection mainly depends upon the exposed surface area and in which direction is heat being convected is of no interest to us. When it comes to conduction in fins it is very much one dimensional. Note that conduction occurs only when there is a temperature gradient within the medium (in this case the fin). There is temperature gradient only in the direction along the length of the fin hence heat transfer occurs only in that direction within the fin. So heat transfer within the fin material is 1-D.
For the second question I think whether you want to neglect something or not depends entirely upon the level of accuracy required. If neglecting a dimension does not create a large error but eases the calculation process then there is no harm in that!

3. Jul 28, 2016

Axe199

i think i got the one dimensional thing, but i dont get it why the sides are ignored, i mean every single textbook is doing the same thing , and when i asked my professor he simply said " because it's one dimensional " and then he called me stupid :D but anyway, aren't the sides exposed area? then why aren't we considering it? my professor's answer doesn't indicate that it's a matter of accuracy, but it's simply mathematically incorrect

4. Jul 28, 2016

Staff: Mentor

The surface area of the sides and the far end is much smaller than the surface area of the faces where most of the heat transfer is occurring. And, if you neglect the heat transfer on these other faces, the analysis is much simpler. After the simpler analysis is complete, you can go back and calculate how much heat transfer has been omitted by neglecting the other faces. You can then decide for yourself whether it is worth the great amount of additional effort necessary to include this small effect.

5. Jul 29, 2016

Axe199

maybe, but if this was the case he would've mention it, and why ignore the sides but not the tip?
the sides are also considered in the proof but ignored in every single question specially when using efficiency

6. Jul 29, 2016

Staff: Mentor

I thought I answered these questions in my response. Whenever you are doing modeling, you look at the simplest situation first. You then have an answer in a very short time. You then can refine the model and add complexity if you judge that this is necessary for the degree of accuracy you feel you need.

7. Jul 29, 2016

ok thanks