Extended Surfaces (Fins) Adiabatic Tip

In summary, extended surfaces, or fins, are protrusions attached to a surface to increase its surface area and enhance heat transfer. They work by increasing the surface area available for heat transfer and disrupting the boundary layer of the fluid. Adiabatic tips are used on fins to maintain a constant temperature at the tip and improve overall performance. The performance of fins is affected by material, shape, size, fluid properties, and temperature difference. Common applications of fins include heat exchangers, electronic cooling systems, and industrial processes, as well as in natural systems to regulate body temperature.
  • #1
ksukhin
34
1

Homework Statement


Please see images - full problem statement given.
Summary: I have to calculate TL for an adiabatic tip extended surface

I found all the equations for points 1-6 but cannot figure out 7.

Homework Equations



1st BC: θ(0) = Tb - T∝
2nd BC: x=L

The Attempt at a Solution


If it is an adiabatic tip, the formula from Fourier's Law is dθ/dx = 0 (@x=L)
It is case specific which in mine is an adiabatic tip (no heat release from the tip)

I don't get why I am being asked to calculate for TL then...can someone please clarify.
Doc - Mar 30, 2015, 1-13 PM - p1.jpg
Doc - Mar 30, 2015, 1-13 PM - p2.jpg
 
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  • #2


It seems like you are on the right track with using Fourier's Law for this problem. The TL in this case refers to the tip length, which is the length of the extended surface beyond the base temperature. This is important to calculate because it affects the overall heat transfer from the surface.

Since the tip is adiabatic, there is no heat transfer occurring at the tip. However, the temperature gradient (dθ/dx) at the tip is still important in determining the overall heat transfer. This is why you are being asked to calculate for TL.

To calculate TL, you can use the boundary conditions given in the problem (θ(0) = Tb - T∝ and x=L) and solve the Fourier's Law equation for TL. This will give you the length of the extended surface beyond the base temperature.
 

Related to Extended Surfaces (Fins) Adiabatic Tip

1. What are extended surfaces (fins)?

Extended surfaces, also known as fins, are protrusions or projections attached to a surface to increase its surface area. They are commonly used in heat transfer applications to enhance the heat transfer rate between the surface and the surrounding fluid.

2. How do extended surfaces (fins) work?

Fins work by increasing the surface area available for heat transfer. This increased surface area allows for more efficient transfer of heat between the surface and the surrounding fluid. Fins also disrupt the boundary layer of the fluid, reducing the thickness of the stagnant layer and promoting better heat transfer.

3. What is the purpose of adiabatic tips on extended surfaces (fins)?

Adiabatic tips are used on fins to prevent heat loss or gain at the tip. This can occur due to heat transfer between the tip and the surrounding fluid, which can affect the overall heat transfer rate and efficiency of the fins. Adiabatic tips help to maintain a constant temperature at the fin tip, improving the overall performance of the fins.

4. What factors affect the performance of extended surfaces (fins)?

The performance of extended surfaces is affected by several factors, including the material of the fins, the shape and size of the fins, the fluid properties, and the heat transfer coefficient between the fins and the fluid. Additionally, the temperature difference between the surface and the fluid, as well as the presence of adiabatic tips, can also impact the performance of the fins.

5. What are some common applications of extended surfaces (fins)?

Extended surfaces are commonly used in various heat transfer applications, such as in heat exchangers, electronic cooling systems, and air conditioning units. They can also be found in industrial processes and engines to improve the efficiency of heat transfer. Additionally, fins are used in natural systems, such as the fins on a whale or the wings of a bird, to regulate body temperature.

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