# Rectangular Fin Heat Transfer

## 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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Chestermiller
Mentor
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, lets 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.

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