Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
Milk (25°C) enters the inner pipe of a concentric double-pipe heat exchanger; hot water (82.5°C, 1.2 kg/s) flows countercurrently through the annulus. Inner-pipe diameter 60 mm, length 6 m, overall U = 2100 W/m²K. cp,water=4.18, cp,milk=3.95 kJ/kg·K. Effectiveness = 0.572, NTU = 1.01. Find the hot-water exit temperature (°C). (Rounded to 1 decimal place)
Official Answer Key:
66.9 to 67.5
Step-by-Step Solution & Explanation
Heat transfer area A = πDL = π×0.06×6 = 1.131 m². UA = 2100×1.131 = 2375 W/K. Since NTU = UA/Cmin, Cmin = UA/NTU = 2375/1.01 = 2351.5 W/K. Since Ch=(1.2×4180)=5016 W/K > Cmin, the milk stream is Cmin. Heat duty q = ε·Cmin·(Th,in−Tc,in) = 0.572×2351.5×(82.5−25) = 77,342 W. Hot-water exit temperature: Th,out = Th,in − q/Ch = 82.5 − 77342/5016 = 82.5 − 15.42 = 67.1°C.
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