Question

A cross-flow heat exchanger used in a cardiopulmonary bypass procedure cools blood flowing at 4 L/min from a body temperature of 37°C to 25°C in order to induce body hypothermia, which reduces metabolic and oxygen requirements. The coolant is ice water at 0°C, and its flow rate is adjusted to provide an outlet temperature of 13°C. The heat exchanger operates with the blood flow unmixed and the water flow mixed, and the overall heat transfer coefficient is 750 W/m2.K. The density and specific heat of the blood are 1050 kg/m3 and 3740 J/kg-K, respectively. (a) Determine the heat transfer rate for the exchanger. (b) Calculate the water flow rate. (c) What is the surface area of the heat exchanger Physical Properties Mathematical Functions Step 1 What is the heat transfer rate, in W? w

Answer 1

P= 1050 kg / m3 Ati Thi Tc2=37-13=24°C solution blood: inlet temperature of blead (Thi) =374, 0) = 3740 kg kg-K The =250C volume flowrate of blood (Vb) = 4L/min = 4x 103 my min in water: To=0°C, Tcz = 13°c. (Cp) w = 4.18 / 1kg overall heat transfer co-efficient (U) = #solmak Step1 a) heat transferrate (8) = NASTM = m Cp (T2-T) Heat transfer mute (8) - Lov)g thi tho) blend 8 = (toyoy Mx103) x3740 ( 37-25) 9=31466 Walt Heat trans feroute () ix 314.6 watt B = [20 Go (On The Inland = PV GLTE-TE) weater 5) losoxu x 3740x( 37-23) XndX Vwx 4180x(13-0) Vw = 3.468 4min water volumetric flow rate (VW) = 3:468 Yomin 492=The-To=25-0=250 Tem, (F= 24-25 = 24.5 60 step2 C) ATEM, CF 4T1-412 45

Steps Capacity ratio (o = Comin - (Ce) min 60 Cmax (mp) max. for bleed: frio) = PVC = 1030X UY1034 3740=2618 W)k for water: 6mcy) = 1034 3,468X103, 84180 = 241.604 W/k ratio = 211.6ou 60 (c) Capacity = 0.923 2618 Stepy steps NTU = UA Hox0.9799 248 241.604 = 0.858 Cmin NTU=0.358 stepy : heat exchanger effectiveness (e) for coo88 flow in which Emax unmixed, mint mixed E = l-exp} -t [_explc-entuj] Esl- exp} -0.933 [-exp(-0.9380 308] E = 0.333 =0.353 effectiveness (C)=1283 Heart exchanger