Project ForgeSaturated vapor at 200°C condenses to saturated liquid at the rate of 150 kg/s on the shell side of a heat exchanger (enthalpy of condensation hfg=2400 kJ/kg). A fluid with cp=4 kJ·kg⁻¹·K⁻¹ enters at 100°C on the tube side. If the effectiveness of the heat exchanger is 0.9, then the mass flow rate of the fluid in the tube side is ________ kg/s (in integer).
Explanation
The condensing shell-side fluid has Cmax→∞ (isothermal phase change), so Cmin equals the tube-side fluid's heat capacity rate. Actual heat transfer Q=ṁ_shell·hfg=150×2400=360,000 kW. Q_max=Cmin(Th,in−Tc,in)=Cmin(200−100)=100Cmin. Effectiveness ε=Q/Q_max: 0.9=360000/(100Cmin), so Cmin=4000 kW/K. Since Cmin=ṁ_tube·cp: ṁ_tube=4000/4=1000 kg/s.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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