Question

2. Straight metal fins (k = 100 W/m°C) with rectangular profile protrude from a l m high wall. The wall is maintained at 200 °C and exposed to a convection environment at 25°C with h = 20 W/m² °C. The fins have a length (L) of 8 cm and a thickness (1) of 3 mm. The space between two adjacent fins is 2 mm. Calculate the following for per unit depth of wall: (a) the fin efficiency, (8 points) (b) the heat transfer from one (1) fin, (7 points) (c) the heat transfer from one open space between two adjacent fins (5 points) (d) the heat transfer from this finned wall, (5 points) (e) the fin effectiveness, (5 points) and (1) the device (wall) effectiveness. (5 points)

Answer 1

Solution y Chironi K= 100 Wymic W cim (426da Thea 200°c To = 25°C 9 h= 2011/mol x adut L = 8cm = 0.08m ta = D.003 m - 2 min = 0.002m Space between two Adjammt fins 3 mm (a) for straight rectangular fine nfia = tan hombe) Mhe 2h Kt LE=L+t/ 2x 20 100 X 0.003 ms 11.547 ml le=L+t Les 0.08 + 0.003 0.0815 Efficiency of fin, (M-fin) – tanh (mle) , tanh ( 11.547x0.0815) mhe 11.541 X 0.0815 [Mafin = 0.782 = 78,2 %

(b) heat trans for fromce one fin! Itin =h finh h 1 finh Aqin (Ten-To) Afin - 2nehe = 2x lmx 0.0815 m Afin = 0.16392 Ti - 200 + 273 = 473 k T2 = 25 +273 = 298k Pfin 20.782 x 20x 0.163 (200-25) Pofin = 446.131 day (1) Heat transfer from one open space between two adjacent find DEVA, (5,4-724) 8 = 5.67x1018 W xt 0.002 ms) 4- 2984)x+ m²K4 = 4.782 W Ao a w+ = 1X0-002 m? (oly Heat transfer from finned wall. Aawt D = h A AT = 0.003 m = 20 W m2 ( 200-25)2 *1 473 almx 0.003m 0.003 1 m²"C = 10.5 W e fin effectiveness (6) Q fin a withart fin 446.131 10.5 E = 42.49 Any

(1) Derice wall e effectiveness (6) Shail a without wall 10.5 4.782 2.2 € Avs

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