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Finned surface question - heat transfer

  1. Sep 12, 2011 #1
    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??
  2. jcsd
  3. Sep 12, 2011 #2
    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)]


    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.
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