Apin fin of uniform, cross-sectional area is fabricated of an aluminum alloy (k = 160 w/m-k). the fin diameter is d = 4 mm, and the fin is exposed to convective conditions characterized by h = 220 w/m2-k. it is reported that the fin efficiency is ηf = 0.65. determine the fin length l and the fin effectiveness εf. account for tip convection.

This question involves the concepts of the efficiency and the effectiveness of the circular fin.

(a) Fin length is found to be "35.2 mm".

(b) Fin effectiveness is found to be "23.52".

(a)

For circular fin:

where,

m = effective mass = ?

h = convective coefficient = 220 W/m².K

K = Thermal Conductivity = 160 W/m.K

D = diameter = 4 mm = 0.004 m

Therefore,

Now, we will use the formula for efficiency of the circular fin to find out the corrected length of the fin ():

using the iterative method to solve this equation, we get the following

Lc = 0.0362 m = 36.2 mm

Now, the actual length of the fin (L) can be found using the following formula:

L = 35.2 mm

(b)

Now, the formula for the fin effectiveness of the circular fin is given as follows:

Effectiveness = 23.52

Learn more about fin effectiveness here:

link

The attached picture shows the different configurations of fins and their formulae.

Given that

D= 4 mm

K = 160 W/m-K

h=h = 220 W/m²-K

ηf = 0.65

We know that

For circular fin

m = 37.08

By solving above equation we get

L= 36.18 mm

The effectiveness for circular fin given as

ε = 23.52