GATE 2022 CH – Question 30
A perfectly insulated double pipe heat exchanger is operating at steady state. Saturated steam enters the inner pipe at 100 °C and leaves as saturated water at 100 °C. Cooling water enters the outer pipe at 75 °C and exits at 95 °C. The overall heat transfer coefficient is 1 kW m$^{-2}$ K$^{-1}$ and the heat transfer area is 1 m$^2$. The average specific heat capacity of water at constant pressure is 4.2 kJ kg$^{-1}$ K$^{-1}$. The required cooling water flow rate is __________ kg s$^{-1}$ (rounded off to two decimal places).
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Correct answer: 0.14 to 0.16
Explanation
The temperature differences at the two ends are $100 - 75 = 25$ K and $100 - 95 = 5$ K, so the log mean is $\frac{25 - 5}{\ln 5} = 12.43$ K. The duty is $Q = UA\Delta T_{lm} = 1 \times 1 \times 12.43 = 12.43$ kW. Then $\dot{m} = \frac{12.43}{4.2 \times 20} = 0.148$ kg/s, which is 0.15 kg/s.