Question

A heat recovery device involves transferring energy from the hot flue gases passing through an annular region to pressurized water flowing through the inner tube of the annulus. The inner tube has inner and outer diameters of 24 and 30 mm and is connected by 8 struts to an insulated outer tube of 55-mm diameter. Each strut is 3 mm thick and is integrally fabricated with the inner tube from carbon steel ( k = 50 W/m·K).

Consider conditions for which water at 300 K flows through the inner tube at 0.161 kg/s while flue gases at 800 K flow through the annulus, maintaining a convection coefficient of 100 W/m²·K on both the struts and the outer surface of the inner tube. What is the rate of heat transfer per unit length of tube from gas to the water? q = W/m?    Use the Dittus-Boelter equation to obtain the water-side convection coefficient

1=3 mm N + D. D.2 DAL h Water Gas

Answer 1

Solny givene DE 24. 2,- 30 mm Po55m 55 mm N-8 As = 0.003m, L= .055-103 -0.0125m 2 50 W/m.k, tem-300k, we = 0.161 8/3 Then gook ho = 100 W/m2K q = Up AC ( Thim - Tem) - ④ 2 ㅗ It Ret helle ㅗ hhath Up Ac Info Pt = Die ) Di, L 20AL In( 34 ) 20x50x?m R = 7.1810-4 Reol Api, oble Roo cold water (at Tom 300k) Ald, = 8558106 m2 Real .48.161 - 9989. qu 9950 7 (1024) X 8558100 feoc>2300 flow is tear bulone Dittes - Boelder equation w cesing Nue= he Digi 0.8 0.023 Re my04

for cold fluid water (Aut. Tomi 3006) ke=0.613 W/miss Pr=5.83 0.613 -) x 0 23x 23x (9990 )®3x (5083)0.4 he •024 The = 1893.2 W/m2K surface Area of the HE in A = IT Di, IXL - TX-R4X Im o.0754 m2 Arc = 1883.28.0754 h 4 = 142 W/R fin efficiences - n = 1-4 (1-24) ③ Ar = NX2(4.0) fin Surface Area E882 x .012581 AF - Af=0.2 m2 A = Aft (70i, 2-8 ods) -0.2+( 71X.03- 88.003) TA = 0.24 m 2

lanhlme) Mf ML (2x100 (2hn tele 12 m- 50X1003 m = 36.51 nf tanh (36.51X00125) 36-518.0125 ng - 0.936 No 1- (220)(1-0.93 0.936) -1-1-33% 14.936) no=0.95 hohn An= 0.988 100x 87 rohn An = 25.65 W/ room aga oo ③ put into ag ③ L - 2 + 7./8169 + esios UCAC 192 ㅗ KIN -0.04674 U AC Up Ac = 21.4 W/k q = 21.4 x(800-300) = 10697.8 W Hence heat rate pen uned length 19 = 10.697 kW