A countercurrent concentric heat exchanger receives milk at 25°C and water at 82.5°C. Water flow is 1.2 kg/s. Inner-pipe diameter is 60 mm, length 6 m, and overall U=2100 W/(m²·K). Water and milk specific heats are 4.18 and 3.95 kJ/(kg·K). Effectiveness is .572 and NTU=1.01. Use π=3.14. Find water outlet temperature in °C, to one decimal.
Area is $A=\pi DL=3.14(.06)(6)=1.1304$ m²,so $UA=2373.84$ W/K. Since $NTU=UA/C_{min}$,$C_{min}=2373.84/1.01=2350.337$ W/K. Heat transfer is $q=\epsilon C_{min}(T_{h,in}-T_{c,in})=.572(2350.337)(57.5)$. Water capacity rate is $C_h=1.2(4180)=5016$ W/K. Thus $T_{h,out}=82.5-q/5016=67.0888$°C, rounded **67.1°C**.
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