Question

Steam in a heating system flows through a tube whose height (H), outer diameter (D), and outer surface temperature (T) are 1m, 3m and 120°C respectively. Circular aluminium fins (k = 180 W/m.°C) of outer diameter D, = 6cm and constant thickness t=2mm are attached to the tube as shown in the figure. The space between the fins is 3 mm. Heat is transferred to the surrounding air at 25°C with a heat transfer coefficient of h = 60 W/m².°C. Determine: a) Number of fins r2 = 3 cm - H ri= 1.5 cm b) Percentage increase in heat transfer by fins c) Overall effectiveness. Is it justified? d) Overall efficiency

Answer 1

given that, To =25% h = 60 W/m? & k = 180 W/m.ec Ty = 120° s - 3mm ri = 115 cm , D, = 3cm 8 = 3cm , D2 = 6 cm H = im t = 2 mm 2 L=8-8, = (3-1.5) cm = 1.5cm -0.015 m 32+tit 0.03m +_ x0.002m) = 2.066 o.Dism are = L + Lut) = 0.015+ļ x 0.002) * - v 1800.002 = 0.2065 now, a = 0.2065 and rett 2.066 from this we get efficiency, = 0.95 (for one fin) - Fin

Area of Fin, A fin = 20 (82-72) +20 Ezt - an [10.03) - 0.055] + 27 0.03)(0.001) = 4.618 yio ma -) RFR = nFino Finmar = 2 an* [hx Afin "(T6-To] +0.95% Cox (4.618x1Đ ) x (120-25) - 25W - Unfinned portion: Aunfin= ADIS = 75 0.03 0.003) 22.827 x 104 me Quentin = hy Aunfin* (Tb-To) = 604 2-829x109) x (120-25) = 1-61139 bal Total heat transfer from the fined tube: Ototal fin = No. of Fins y Ofin + Austin) = 200+ (as +1.61139) =5322.278 W

No fin presence, Ano fin = ND, l- = nyo.0341 = 0.0742 m² Qno fin = hx Ano finx (76 To) = (60) x 0.0942) (120-25) =536.94 W a) 3 mm 11 30m, 3 mm 3mm u 524- mm from figure, we can see that in 10 mm length number of fin = number of interfin surface =2 as In Im length total fin = 3 x 1000 m 10nm 5 200 b) increase in heat transfer, Pincrease = Ototal fin - One Rin - 5322 · 278 – 536.94 =4785. 338 W the percentage increase - 4985.338x 100 = 891.92 . 536.94

c) The overall effectiveness : Go = total, fin . itored, no fin 5322.298 - - 536.94 1 € -9.911 transfer is increased - we can see that heat 9.91 times. d) we know that 6= Afin Mein Ano fin to = Afin +200), (Ano fin fin overall efficienu 9.914 6.0942 m) (4.665x10° +2.827 x 1543x200) 2 -0.9524 = 95.240% )