Question

Water flowing at a rate of 10 kg/s through 50 tubes in a double-pass shell-and-tube heat exchanger heats air which flows on the shell side. The tubes are bras with outside diameter of 2.6 cm and are 6.7m long. The heat transfer coefficients on the inside and outside tube surfaces are 470 W/m2K and 210 W/m2K, respectively. Air enters the unit at 15°C with a flow rate of 16 kg/s. The entering water temperature is 350K. A) Draw and label a schematic for this system; find the relevant properties and state any assumptions B) Calculate the heat exchanger effectiveness C) Calculate the heat transfer rate to the air D) Calculate the exiting temperatures of the water and air streams E) If after a long period of operation, a scale has been built up inside the tubes resulting in an added fouling resistance of 0.0021m2/KW, calculate the new heat exchanger effectiveness?

Answer 1

ma=16kslo ے ج بيهندا * Tiowe win = 350k Heat Capacity of water 1 Cw-morews 10x4.187 = 41870 Jlsk Heat Capacity of air C Casma (pa = 16x 1.027 = 16112 Ilsk ca . (min (mat . 16112 = 4,5% = 0.355 Total area of heat exchonger. A= ADLxn. - A = F xo.o2646.785. = 27.35 m² Overall heat tronosfer Coefficient t & T I Neglecting fouling resistone R U u. It - - 145 W/m2K 4% + 1

NTUT Namber it Intoa Number of Transfer unit - UA 145x27:35 (min 10112 -0.246 . NU -0. 248 b) Effectueness of Heat Exchanger Ez 1-e Nuci-os VIU 1-ce-Nru (low = 1 - 80.246 (1-0.385) 1 -0.395 eu . -0.240 (1-0. 385) (3) c) Heat Transfer to air q = q (min ( Twin - Tan = 0.21 X 16112 (350-288) 12 = 209.778 K51 d) Heat rejected by water = net heat transfer to air Cw (Twin-Twout) = 209.778 41870 ($350-Twiont) = 209.778 Twisut = 350-5.02 Twout = 345 k) WAY

So exit temperature of Water is Twyout = 3456 - For air, Ca (Tasut -Ta, in ) = 209.778 16112 (Torout -288) = 209.778 1 Ta, out = 301.01k 1. Exit temp of air is To out = 301 x) de fouling resistanu , R = 0.0021 to m² klu So News Overall heat transfer Coefficiens Uen L +R + I Vi - 470 +0.0021 + L 210 U 6 m2 R Tu= 111.6 W/m2K NTU. VA - 118.6 x 27.35 (min 0.189 16112 se 1-NTU (-0 -0.189 (1-0.395) lace-NTOcio 1-0.385 e 0.189(1-0.305) Effecturness a 0.10 TE