GATE Chemical 2012 | Question: 45

Question

In a 1-1 pass floating head type shell and tube heat exchanger, the tubes (od = 25 mm; id = 21 mm) are arranged in a square pitch. The tube pitch is 32 mm. The thermal conductivity of the shell side fluid is 0.19 W/mK, and the Nusselt is 200. The shell-side heat transfer coefficient (in W/m$^{2}$.K), rounded off to the nearest integer, is

• A. 1100
• B. 1400
• C. 1800
• D. 2100

Answer 1

For shell-side flow across a tube bank, the diameter to be used in the Nusselt relation is the equivalent diameter (D_e), not the tube outside diameter.

For square pitch:

[
D_e = \frac{1.27,(p^2 - d_o^2)}{d_o}
]

Given:

• Tube OD (d_o = 25,\text{mm} = 0.025,\text{m})

• Pitch (p = 32,\text{mm} = 0.032,\text{m})

[
D_e = \frac{1.27,(0.032^2 - 0.025^2)}{0.025}
= 0.02027 ,\text{m}
]

Using the Nusselt number relation:

[
Nu = \frac{hD_e}{k} \Rightarrow h = \frac{Nu \cdot k}{D_e}
]

[
h = \frac{200 \times 0.19}{0.02027}
\approx 1875 ,\text{W/m}^2\text{K}
]

Rounded to nearest integer → 1875 ≈ 1800 W/m²·K

✅ Correct answer: 1800