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GATE 2022 BT – Question 13

Fundamentals of Biological Engineering · Bioreaction Engineering: Kinetics of cell growth, substrate utilization and product formation, structured and unstructured models · 1 mark · Multiple choice

For a double-pipe heat exchanger, the inside and outside heat transfer coefficients are 100 and 200 W m-2 K-1, respectively. The thickness and thermal conductivity of the thin-walled inner pipe are 1 cm and 10 W m-1 K-1, respectively. The value of the overall heat transfer coefficient is ___________ W m-2 K-1.

  1. 0.016
  2. 42.5
  3. 62.5
  4. 310

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Correct answer: (C) 62.5

Explanation

For a double-pipe heat exchanger with a thin-walled tube, the overall resistance is the sum of the three resistances in series (per unit area):

$$\frac1U=\frac1{h_i}+\frac{t}{k}+\frac1{h_o}.$$

**Numbers.** $h_i=100$, $h_o=200$ W m⁻² K⁻¹, wall thickness $t=1\text{ cm}=0.01$ m, $k=10$ W m⁻¹ K⁻¹:
$$\frac1U=0.01+\frac{0.01}{10}+0.005=0.01+0.001+0.005=0.016\ \text{m}^2\text{K/W}$$
$$U=\frac1{0.016}=\mathbf{62.5\ W\,m^{-2}K^{-1}}.$$