Temperature distrubution in a cooling fin (result interpretation)

In summary, the conversation involves analyzing the lengthwise temperature distribution in a cooling fin with specific dimensions and parameters. The calculation for the dimensionless temperature distribution results in a curve with a minimum at 2/3 of the fin length and then an increase towards the tip, which is questioned by one of the parties. They suggest a mistake may have been made in the calculation and the other party confirms that the calculation should achieve its minimum at x=L.
  • #1
eveS
3
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I am analyzing the lengthwise temperature distribution in a cooling fin (length: 30mm, width: 10mm, the tip is assumed to be adiabatic, Biot number is smaller than 0.1).

When I try to calculate the dimensionless temperature distribution (see calculation below), I obtain a curve which has a minimum at about 2/3 of the fin length and increases again after that (see attachment).

I don't understand why the temperature should increase again towards the tip of the fin. Using Ansys to model the fin I obtained the other curve in the graph, which shows decreasing temperatures towards the tip of the fin (and makes more sense to me).
I don't know whether I am making a mistake in my calculations, or whether there is a simple explanation.
Any advice would be appreciated!

calculation:

distribution "theta" (x) = cosh(m*(1-x/L)) / cosh(m) ,

where m= sqrt [ ( P*L*h) / (A*k) ]

L=length
P=perimeter
A=area
h=heat transfer coefficient
k=thermal conductivity
 

Attachments

  • Fin_Temp.jpg
    Fin_Temp.jpg
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  • #2
distribution "theta" (x) = cosh(m*(1-x/L)) / cosh(m)

Pretty sure you've made a mistake in evaluating the above. For "m" a constant that expression definitely achieves its minimum when x = L.
 
  • #3
Thanks for the suggestion uart, I'm not sure why it wasn't working, but it does now:)
 

What factors affect the temperature distribution in a cooling fin?

The temperature distribution in a cooling fin is affected by several factors such as the material of the fin, the geometry of the fin, the air flow rate, and the initial temperature of the fin. These factors can impact the rate of heat transfer and the overall temperature distribution in the fin.

How does the temperature distribution change over time in a cooling fin?

The temperature distribution in a cooling fin changes over time as the fin dissipates heat. Initially, the temperature is highest at the base of the fin and decreases towards the tip. As time passes, the temperature at the base decreases while the temperature at the tip approaches the ambient temperature. This results in a more even temperature distribution along the length of the fin.

What is the significance of a uniform temperature distribution in a cooling fin?

A uniform temperature distribution in a cooling fin is important for efficient heat transfer. If there are hot spots on the fin, they can lead to localized overheating and potentially damage the fin or the equipment it is cooling. A uniform temperature distribution ensures that the fin is functioning properly and can effectively dissipate heat.

How does the temperature distribution in a cooling fin vary with different materials?

The material of the cooling fin can have a significant impact on the temperature distribution. Materials with high thermal conductivity, such as copper or aluminum, will have a more uniform temperature distribution compared to materials with lower thermal conductivity. This is because heat can transfer more easily through these materials, resulting in less variation in temperature along the fin.

What are some ways to improve the temperature distribution in a cooling fin?

There are several ways to improve the temperature distribution in a cooling fin. One way is to increase the air flow rate, which can help dissipate heat more quickly and evenly. Another way is to adjust the geometry of the fin, such as increasing the surface area or changing the shape, to optimize heat transfer. Using materials with higher thermal conductivity can also improve the temperature distribution. Additionally, regularly cleaning and maintaining the fin can help ensure it is functioning properly and maintaining a uniform temperature distribution.

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