Question

(c) Steam flows a pipe of external diameter 30 mm, where the pipe outer surface temperature is 130oC. Circular annular fins (k = 180 W·m-1·K-1) of outer diameter 60 mm and thickness 1 mm are fitted tightly to the pipe. Heat is transferred by convection (h=10 W·m-2·K-1) to the surrounding air at 20oC.

1. (i) Determine the efficiency of a single fin.

2. (ii) Determine the heat transfer rate for a single fin.

(8 marks) (6 marks)

(iii) Determine the effectiveness of a 1 m length of finned pipe, assuming a 4 mm gap between

successive fins.

Answer 1

(C)

(i)

The efficiency of a single fin:

$\eta = 97\%$

(ii)

The heat transfer rate for a single fin:

$\dot{Q}_{fin}=4.725W$

(iii)

The effectiveness of a 1 m length of finned pipe:

$\epsilon =9.92$

The detailed solution is given below:

Giveni> 30mm Tp = 130°c Too = 20°C lo w m?.K h = =Amm 18ow/m.k ivey =7 d = 30mm 1o0 (Thi knes) D = 60mm d = 30mm = 0.015m = 0.03 m D = 60mm = 0-06 m 3 Y2 = 0.03m L= -= 0.03-0.015 = 0.015m 0.03 + X 0.001 2.03 0.015 V kxt

low/m?.k 180w/m.k Xx 0.00m (0:015 +x 0.001X 0.1155 and Det = 2.03,We get # Noww for g - 0.1155 → Fin efkiacy, , - 0.97 = 170 sing gogl] -> Fin 0.97 = 97-10 L usig goaglh] ctre of ting Afrz Qñ(-5)+270t = Q7[[003²-(0,015)*] + RX(003)x(0.0) 0.004429 m? The heat tr ans for sate, fin max (0.97) x low m? K x (0.004421n* ) x [(1204273)-(20+273)

4.725 W [Le lm] 1 gah,g = m (00 No fin TA(0.03)x| 0.0942m? Ang fon hx Ano, fin X (To-To) 0.0942m² }x ( Bo+273)-(20+273) īdL 103.62 W with fon Qfn = 4.725 W (from section (i)) # Unfimud þor tion - A(0.03) x (0.004)= Ampfên = Tdxg = Qun fin = hx Aum,fin X (T- To) 0.000377m² -> = (» )«(aco0s+2)x [itars) (20t20) - 0.414-7w

4mm Imm< Amm 7. Imm lomm From figure we (on see that in lonm Number of in = Vum ber of Pm ter fin Surtace = 2 In Im ling th, total fin = 3 x 2 x looomm lomm = 200 Tumber of fine /ruimber of inter for Surfacl unifin (4. Fa5+ 0.4147) X 200 = l027.94u #3 Effechve nets, E = dsm, n lo२৭.१4- 9.92 1o 3.62