How to Calculate Heat Transfer Rate in Rectangular Fin Design?

[kdb12]

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

η_o = 1 - (NAc/At) (1-η_f)
A_t = NA_c+A_b

The Attempt at a Solution

n_f = tanh(mL_c)/mL_c

(I know this equation is right, but I'm lost from this point forward. Any help would be excellent.)

 

[Chestermiller]

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

 

[caldweab]

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.