Question

ONLY NEED THE SOLUTION TO PARTS E AND F!!!!!!! PLEASE

Analyzing a Fin Consider an infinitely long fin with a square cross section with 5mm. The base of the fin is held at a fixed temperature of To = 100°C and air is passing by the fin at T = 20°C with a convective heat transfer coefficient of h - 55 W/m-K. The fin is made from aluminum with a thermal conductivity of k- 180 W/mK. T. = 20°C n = 55 W/m²K To=100°C 1 t = 5mm L = infinity X a) Use the Biot number to justify the use of the one-dimensional fin equation for this problem. b) What is the total heat transfer rate from the fin to the air? c) What would be the heat transfer rate from the flat base if the fin was not attached? What is the effectiveness of the fin at removing heat?

Answer 1

Solution Data given To= 100°c To = 20°c h = 55 W/m²K C = 180W/mK side of the squire (a)= 5mm =s perimeter (P) = 2x(4+a)=4a P = 4x5x10 3 = 20x10 3 m -3 Now, 57106 Cross sectional area (A)= a2=585x10 A = 25*10 m² Now, 155X20x103 m = KA 180x2500-3 =15.635 180 m= 15.635 Now, For infinite long fin, (2 fin) = JhPKA (To-Too) For insululed rip fin 12 fin), = JhPICA (To-To) tanhml

there for for a fin to be considered infinite long tin tanhmi = 120.99 [(I find a =( Q fin); / me =tanno.gg [ For 99% = 0.997 " mL = 2.65 2.65 2.65 m. - 15. 635 = 0.169 mi L = 0.169 m = 169 mm Angwer of (e) Now, e efficiency of fin (o long) :- Fin efficiency ( 2 fin) For infinite tong fin n I fin IhPic AmX (T o) Msin = max. possible - h PRL (T TO) heat transfer (whole fin at Tb) - x 100% 15.635% 0.169 = fin - ML In = 37.85% are of (F.):