Finned surface question - heat transfer

[Yr11Kid]

Hey everyone, I've got a finned surface question

I've got a finned wall is constructed of aluminium alloy with k = 150 W/mK. The wall thickness is 2.0 mm and the fins, with a thickness of 2.0 mm, are straight with rectangular profile. The inside of the wall is maintained at a constant temperature of 80°C and the finned section of the wall are exposed to a convection environment at 20°C with the convective heat transfer coefficient being at 8 W/m2K. The assembly will be cast from the aluminium material. You can assume that the finned wall is a 5 cm  5 cm square section. The fin pitch is 6 mm.

Given the efficiency to be 98% how would i determine the length of the fin, first of all I've got the formula for fin efficiency which in its simplest form is

nf = tanh (mL)/mL m = sqrt(2h/kt)

I have no idea how to solve the mathematics of this to find the length, its possible I'm completely off track :(

Also if i wanted to find the heat transfer rate from the ENTIRE wall how would i go about that??

 

[edgepflow]

Keep in mind fins add to the heat transfer area but have an efficiency. The total heat transfer rate is:

q = [N * eff * hfin * Af * (Tbase - Tamb)] + [hbase * Ab * (Tbase - Tamb)]

where,

q = heat transfer rate
N = number of fins
eff = fin efficiency
hfin = convection heat transfer coefficient for fin
Af = surface area of individual fin
Tbase = base temperature
Tamb = surrounding temperature
hfin = convection heat transfer coefficient for base (often assumed hfin = hbase)
Ab = surface area of base

Notice each group of terms is the heat transfer for the fin and base.