GATE 2022 ME (ME1) – Question 65
During open-heart surgery, a patient's blood is cooled down to 25 °C from 37 °C using a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at 4 °C and leaves at 18 °C. Blood flow rate during the surgery is 5 L/minute.
Use the following fluid properties:
| Fluid | Density (kg/m$^3$) | Specific heat (J/kg-K) |
|---|---|---|
| Blood | 1050 | 3740 |
| Water | 1000 | 4200 |
Effectiveness of the heat exchanger is _________ (round off to 2 decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.41 to 0.43
Explanation
The blood flow is $\frac{5 \times 10^{-3}}{60} \times 1050 = 0.0875$ kg/s, so its heat capacity rate is $0.0875 \times 3740 = 327.3$ W/K. The heat taken from the blood is $327.3 \times 12 = 3927$ W. The water heat capacity rate is $\frac{3927}{14} = 280.5$ W/K, which is the smaller one, $C_{min}$. The maximum possible heat transfer is $C_{min}(37 - 4) = 280.5 \times 33 = 9257$ W. The effectiveness is $\frac{3927}{9257} = 0.42$.