Fin area and heat transfer direction

In summary: This simplifies the analysis and makes it easier to calculate the efficiency. However, this neglects a small amount of heat transfer and may result in a small error in the final efficiency calculation. In summary, the sides of the fin are typically ignored in heat transfer calculations because they have a negligible area and it simplifies the analysis, but this may result in a small error in the final efficiency calculation.
  • #1
Axe199
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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 don't understand how is this a one dimensional system to begin with, we have conduction in x direction and convection in y direction so that's 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 don't ignore it in our course
 

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  • #2
Axe199 said:
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 don't understand how is this a one dimensional system to begin with, we have conduction in x direction and convection in y direction so that's 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 don't ignore it in our course
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
benny_91 said:
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!
i think i got the one dimensional thing, but i don't 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
Axe199 said:
i think i got the one dimensional thing, but i don't 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
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.
 
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  • #5
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
Axe199 said:
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
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.
 
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  • #7
Chestermiller said:
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.
ok thanks
 

FAQ: Fin area and heat transfer direction

1. What is a fin and why is it used in heat transfer?

A fin is an extended surface that is attached to a heat transfer surface to increase the surface area for heat transfer. It is used to enhance heat transfer by increasing the surface area available for heat exchange between a hot and cold medium.

2. How does the shape and size of a fin affect the heat transfer direction?

The shape and size of a fin play a significant role in determining the direction of heat transfer. A larger and thicker fin will have a greater surface area for heat exchange, resulting in higher heat transfer rates. Additionally, fins with a larger surface area facing the hot medium will transfer more heat in that direction.

3. What is the relationship between fin thickness and heat transfer direction?

Thicker fins will transfer heat in the direction of the smaller surface area, while thinner fins will transfer heat in the direction of the larger surface area. This is because thicker fins have a lower thermal resistance and are more effective at conducting heat, while thinner fins have a higher thermal resistance and are less efficient at conducting heat.

4. Can fins be used to control the direction of heat transfer?

Yes, fins can be used to control the direction of heat transfer. By adjusting the size, shape, and orientation of fins, heat transfer direction can be manipulated to meet specific heat transfer requirements. For example, fins with a larger surface area facing the cold medium can be used to transfer more heat in that direction, while fins with a larger surface area facing the hot medium can be used to transfer more heat in that direction.

5. How do fins affect the overall heat transfer rate?

Fins increase the overall heat transfer rate by increasing the surface area available for heat exchange. This allows for a larger temperature difference between the hot and cold medium, resulting in a higher heat transfer rate. However, fins also add additional thermal resistance, so their design and placement must be carefully considered to optimize heat transfer efficiency.

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