How to Calculate Heat Transfer Rate in Rectangular Fin Design?

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SUMMARY

The discussion focuses on calculating the heat transfer rate from a rectangular fin made of 2024 aluminium and copper under specific conditions. For the aluminium fin, parameters include a thickness of 3mm, length of 20mm, base temperature of 100 °C, and a fluid temperature of 20 °C with a convective heat transfer coefficient (h) of 60 W/m²-K and thermal conductivity (k) of 185 W/m-K. For the copper fin, the convective heat transfer coefficient increases to 400 W/m²-K. The key equations involve determining the parameters m and M, which are essential for calculating the heat transfer rate.

PREREQUISITES
  • Understanding of heat transfer principles, specifically convective and conductive heat transfer.
  • Familiarity with the properties of materials, particularly 2024 aluminium and copper.
  • Knowledge of thermal conductivity (k) and convective heat transfer coefficient (h).
  • Ability to apply mathematical equations related to heat transfer in fins.
NEXT STEPS
  • Calculate the heat transfer rate using the derived parameters m and M for both aluminium and copper fins.
  • Explore the impact of varying the thickness and length of the fin on heat transfer efficiency.
  • Investigate the use of different materials for fins and their thermal properties.
  • Learn about the application of the steady state differential heat balance equation in heat transfer analysis.
USEFUL FOR

Mechanical engineers, thermal analysts, and students studying heat transfer who are involved in designing and optimizing fin structures for enhanced thermal performance.

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Homework Statement


A straight, rectangular fin made from 2024 aluminium has a thickness of t = 3mm and length L = 20mm. Base temperature is 100 °C and it is exposed to a fluid at 20 °C.
h = 60 W/m^2-K
k = 185 W/m-K

(a) Determine the heat transfer rate from the fin to the fluid per unit length
(b) Repeat (a) if the fin is made of copper (h = 400 W/m^2-K)

Homework Equations



ηo = 1 - (NAc/At) (1-ηf)
At = NAc+Ab

The Attempt at a Solution



nf = tanh(mLc)/mLc

(I know this equation is right, but I'm lost from this point forward. Any help would be excellent.)
 
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Do you know how to write the steady state differential heat balance equation for a cooling fin, including the conductive heat transfer along the fin and the convective heat transfer from the fin to the surrounding air? If so, let's see it.

Chet
 
There's formulas for this...it's really plug and chug, you're given everything you need.

You need to calculate your m and M

for a rectangular fin m=(2h/kt)^1/2; plug in your h, k and thickness

For a rectangular fin M= (2hw^2tk)^1/2 *(tb-tinfinity) again substitute your h,k, width and thickness.

Now that you have M and m you can just apply the formula, you have everything you need.
 
Last edited:

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