Question

2. (40 pts) A simple cross-flow heat exchanger consists of a thin-walled copper pipe that carries cold water and is exposed to side flow of hot air. You can neglect entry length effects. a) (10 pts) What is the heat transfer coefficient on the air side? b) (10 pts) What is the heat transfer coefficient on the liquid side? c) (5 pts) What is the overall heat transfer coefficient for this heat exchanger? d) (10 pts) What is the mean outlet temperature of the water? e) (5 pts) Please suggest routes that the heat exchanger could be changed to improve the heat transfer. Please list the options in terms of increasing complexity (i.e. probable cost so that decision could be made given some budget). Bonus (2.5 pts): Comment on how you think the answer to c) changes throughout the lifetime of the heat exchanger. Pipe: d=1 cm, L = 1m, thickness: neglect Water: Mean flow velocity: 0.1 m/s; Mean inlet temperature: 10°C Air: Free-stream velocity: 5 m/s; Free stream temperature: 80°C

Please help with the following problem and show work thank you

Answer 1

Coppere pipe d=1cm Cold water Vw = 0.1 m/s L1m Ti = 10°C Į q Shot aire Vasmis Too - 80°C 353k X 350k a) Thermophysical properties of air at Top = 80° - 80 +273 = V = 20.92 x 1050 mg Kave 0.03 W/mK Per=0.7 Rep= - 2 390.057 5X 0.01 20.92 x 10-6 2 we use for cylinder in cross flow, churchill & Bernstein relation 12 1/3 Per <0.01 0.62 Red Reg 1 + Nuo = - had - 0.3 + 10.4 243 282000) Kair [1 + ent j3 14 سے 0.03

Rep & Pe in above Eq. air side M = 1.225X10 ON.S/m2 After putting tha 74.586 W/m²K imk b) Thermophysical properties of water at 10°C po 1000 kg/m3 Cp=4.18 kJ /kg k 1 Kw= Per 0,59 w 8.81 M Red = PVND 1000 x 0, 1 X 0.01 816,328 1.225X1o-3 < 200 » Laminar flow Assuming constant surface temperature, Nusselt number Nuo = 3.66 hwD asi is given = 3.66 Kw hare o.ol -3.66 0.5 ho - 183 w W/m²K c) overall heat transfer coeff.cu): 1 1 + 오 ha 1 no + 74.586 183 는 u= 52.989 ²53 W/m²K

d) Thermal resistance cieceuit Too Tinsideo tube 1 I howas 7 ha As outlet temperature is given as: UAS mcp Too -e To. Ti To As - XDL = Txo.of X1 -0,0314 m2 in = ( Ac Vw = 1000 x (4xo.olx 0, 30,00 0785kg / 52.989 X0,0 3/4 e 0.00785x4186J/kg* To = 10-80 To = 13, 461°C D) has muen Instead of of air, water could be used which better heat capacity Bonus : 0 (c) paket: with time impurities settles on the surface of pipe, called fouling, it will reduce overall heat transfer coefficiera.lu)