Project ForgeA shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at 300 K at a rate of 100 kg/s. The overall heat transfer coefficient is 1500 W/m².K, and total heat transfer area is 400 m². Steam condenses at a saturation temperature of 350 K. Assume that the specific heat of coolant water is 4000 J/kg.K. The temperature of the coolant water coming out of the condenser is ___ K (round off to the nearest integer).
Explanation
Cmin = 100×4000 = 400,000 W/K. NTU = UA/Cmin = 1500×400/400000 = 1.5. Since the hot fluid condenses at constant temperature (Cr=0), ε = 1−exp(−NTU) = 1−exp(−1.5) ≈ 0.7769. Q = ε·Cmin·(Th−Tc,in) = 0.7769×400000×50 ≈ 15.54 MW. Tc,out = 300 + Q/(ṁcp) = 300 + 15.54e6/400000 ≈ 338.8 K.
Source: GATE ME 2021 Session 2 (ME-2) (2021)
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