Question

Q2. Shell-and-tube heat exchangers with hundreds of tubes housed in a shell are commonly used in practice for heat transfer between two fluids (shown in Figure 1). Such a heat exchanger used in an active solar hot-water system transfers heat from a water-antifreeze solution flowing through the shell and the solar collector to fresh water flowing through the tubes at an average temperature of 60°C at a rate of 15 L/S. The heat exchanger contains 80 brass tubes 1 cm in inner diameter and 1.5 m in length. Disregarding inlet, exit, and header losses. (a) Determine the pressure drop across a single tube and the pumping power required by the tube- side fluid of the heat exchanger. (25 marks) After operating a long time, 1-mm-thick scale builds up on the inner surfaces with an equivalent roughness of 0.4 mm. For the same pumping power input, (b) Determine the percent reduction in the flow rate of water through the tubes. (10 marks) 80 tubes 1.5 m 1 cm Water Figure 1. Shell and Tube heat exchanger

Answer 1

Algo power required will be: P- Ap.8. po tfQ - 983.17549.8140.9189.3x15710 ip 132.965 W pimping powder er riquired. 6 thickness of Scale - Wilds up it imm roughness R=0.4mm radius ; r = 1/2 - 1 =orem smn Calculate foiction factor using nilusada leque ☆ = 2.0logo (YIRD+ 1.74 alog,o (slow) +1.74 - 3.93383 If = 0.06462) let v be Pipes the flow velocity across single head loss as v2 tf calculate 29

HH = 0.06462x1.5x uz PX 9.81 XBX ( d-di-2t = 1cm-260.1) -0.3cm. 3 mm = 8x10 3m Hf =0.617542 but pumping power required is same => P pg hf 0. pg HP (Av x80) 2) 132.945 = 983,17587.81X0.617542x I(8x100)? X VX80 -) 132.945 23.05106 v3 Hence V= 17705 mis T flow velocity addoss single pipe calculate total - AVX80 - TT (8 x (0-3)*x117705 XBO flow rates = 7.1196 x 10-3 m/s Q': 7:1196 L 131 Calculate y reduction in total flow rate as y. AQ x 100 Y, 15-71196 Хоо. Y.40 = $2.536 : 7. reduction in flow sate due to scale builds up. 30.010
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ST flow rate a 15 x 10-3m3 Ls NU = 80 using peace software, properties of water = flow velocity through each pipe Temprature T= 60°c is ils No. of tubes inner pipe diameter ozlem = 0.0m Pipe length d=1.5m at 60°C density D: 983, 195 18g Im3 dynamic viscosity , M = 0.000466 Pa-s calculate velocity of flow as flow area 190.985.0 m/s A :1:55x103 x 10.01) va Va 190.9859 ak 80 2.3873 m ܥܐܕ calatate No. Reynolds Re = VDS so. using relation.

2.3873 XOOIX 783.25 [o di 11 0.000486 =) R 50367.675 e Sime Re >4000 ... The flow is turbulent y Calculate friction factor for turbulent flow using relation 0.316 fa 0.316 (Re) ily 50367 67.675)%4 16:002109 I calculate head loss through Åpe given by Elu² p> 0.02109x1.5*(2.3873.)2 29 di 2*9.81*0.01 + HA -0.91893 m Acrass now T =983.175*9.81 X091893 Pressure drop each pipe is given by Apa Pg HF 42 : 8863.03 8.863 La pa pressure doop across single tube . Pa