Question

Steam in a heating system flows through a 1-m long tube whose outer diameter is DI = 4 cm and whose walls are maintained at a temperature of T, = 120 °C. Circular fins (k = 46 W/m. °C) of outer diameter D2 = 8 cm and constant thickness t= 3 mm are attached to the tube, as shown in the figure. The space between the fins is 7 mm. Heat is transferred to the surrounding air at T = 20 °C, with a combined heat transfer coefficient of h = 59 W/m?. °C. Determine:

The Fin efficiency a.

b. The total amount of heat transfer from the fin and the overall fin effectiveness

c. The increase of heat transfer because of the addition of the fin.

Answer 1

Given? Length of tube da im outer diameter of tube DI=4 cm 0.04 m tube To 120° ci Temperature of walls of For circular fins k a 46 w/ mici outer diameter D2 = 8 cm thickness of fin t = 3 mm ;' Space between fins ?hona 7mm - 0.007m Surrounding temperature Too - 20°C... heat transfer coefficient of hasa W/m².c. Find! a. Efficiency of fin 2 b. Total amount of heat transfer from the fin and overall fin effective mess c. The increase of heat transfer because of the addition of fin. solution, Analysis: In case of mo. fins, heat trans fer from the - tube per. meter of its length is area; Am sin = MD,L: (0.04) (lm) = 0.12566 m2 without fin heat transfor - ano fin = h Ano fin (To-To)=

- Q no fin = h Ano fin (Tb-Tos) (59 Wme, e] (0.12566 m2) (120-20) = 741.394 W . The efficiency of these circular fins is from the efficiency corre, . (D40) 10.08-0.04 ) - 0.02 m I 2 0:02 wim? 027 0.0 me the one > () - (0.024 0.002)with (46w/mic) (0,003 m) , 1 q 0.445 Heat transfer from a single fin is Afin = 291 (-72): + 2 firet : 211 Colou...03) +277 (0.04 310.003) Afin = 0.0083 m² Popimo min å fin mai fin hafa (Touro) -0.83 (sqrolimzo) (0.0083 m2) (120-20) = 48.933 W n man

83 Fin efficiency, nfin - 2.075 It r2c = r2+t/2 7 Le = L+t/2 . A₂ = Lạt 2 2.2 2.4 2.6 2.8 3 0 0.2 0.4 10.6 0.8 1 1.2 1.4 1.6 1.8 Ś = L3/2(h/kA,)1/2 FIGURE 10–43 Efficiency of annular fins of constant thickness t. FIGURE 10-430 4415

heat transfer from a single unfinned portion of tube is Aun fin = 1l Dixe : TT (008)m (0.007m) .: 20:00176 mei. Quereinsh Ainin (Tb-Tos) = (59.wm2.0) (0.00176m?)( 120-20) LO: 3798 w on fin

Space between thickness of For length fines = 0.007 m fin o 0.003 in i'm of tube Length of tube. thickness = total spaces and fins fins . no. of a no- of spaces cn (0.007) t n (0.003) - (1 m). 2) n c 0.007 70'003) m . Im o na od fins y no. of. n = 100 tube is » nor of fins a not of spaces an= Loo Total heat transfer from the finned @total, fin = n (@fint on tin) = 100 (48.933 +10.3798) 5931,282 W → Total amount of heat trans for from fin /Qkotal, fin=5931:282 w] , Increase in heat transfer from the tube per meter of its length as a result of addition of fins is Q increase = = 5931282- 741.394 Q total, fin- a no fin- Qiname = 5189.888W. Increase of heat transfer because of addition of fin increase = 5189.888 WA rease increase

Effective ness of fins a total, fin . Qwithout fin 7 5931,282 741:394 T41.391 Effectiveness of fin &=81 Fin efficiency - 083