A fin array are made of straight rectangular fins of 2024 aluminum alloy {k = 185 W m-K). as shown below. The fin length is L = 15 mm. the fin width is w = 20 mm. and fin thickness is t = 3 mm. Its base temperature is T_b = 100 degree C, and it is exposed to a fluid for which T_infinity = 20 degree C and h m 50 W/m^-K. The fin pitch is S = 10 mm. If there are total N = 50 fins, you are asked to do the following: Find the fin efficiency, eta f, by using the adiabatic fin tip approximation: eta_f = tanh mL_c/mL_c Calculate the fin resistance of a single fin: R_t, f = 1/eta_f h A_f Calculate the bare base area. A_nf, that is not covered by fins: A_nf = A_b - NA_c with A_b, = H - w where H is the height of the substrate of the fin array. Calculate the total heat transfer from the fin array: q = h(N_eta f A_f + A_nf)(T_b - T_infinity) Drawing a thermal circuit and determine the total heat transfer from the fin array by using the thermal circuit method: q = T_b - T_infinity/T_total with 1/R_total = 1/(R_t, f/N) + 1/(1/hA_nf)
The answer of following question is as follows.
The fin efficiency is 78%
The base area is 7 m2
The resistance is 65
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