GATE 2022 ME (ME2) – Question 64
Saturated 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 $h_{fg}=2400$ kJ/kg). A fluid with $c_p=4$ 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).
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Correct answer: 1000
Explanation
The vapour condenses at a constant 200 °C, so the hot stream has an effectively infinite heat-capacity rate ($C_{max}\to\infty$) and the fluid in the tubes is the minimum-capacity stream.
**Step 1: actual heat transfer** (all of it is latent heat of condensation):
$$Q=\dot m_h\,h_{fg}=150\times2400=360\,000\text{ kW}.$$
**Step 2: maximum possible heat transfer.** The cold fluid can at most be heated to 200 °C:
$$Q_{max}=\dot m_c\,c_p\,(200-100)=\dot m_c(4)(100)=400\,\dot m_c\text{ kW}.$$
**Step 3: effectiveness.** $\varepsilon=Q/Q_{max}=0.9$:
$$Q_{max}=\frac{360\,000}{0.9}=400\,000\text{ kW}\;\Rightarrow\;\dot m_c=\frac{400\,000}{400}=\mathbf{1000\ kg/s}.$$