Question

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\(^{-1}\).

• A. 0.016
• B. 42.5
• C. 62.5
• D. 310

Hint:

For heat exchangers, the overall heat transfer coefficient depends on the thermal resistances due to convection on both sides of the pipe and conduction through the pipe material.

Answer 1

The Correct Option is C

The overall heat transfer coefficient \( U \) for a double-pipe heat exchanger can be calculated using the following equation: \[ \frac{1}{U} = \frac{1}{h_i} + \frac{r_i \ln(r_o / r_i)}{k} + \frac{1}{h_o} \] where:
- \( h_i \) is the inside heat transfer coefficient,
- \( h_o \) is the outside heat transfer coefficient,
- \( r_i \) and \( r_o \) are the inner and outer radii of the pipe,
- \( k \) is the thermal conductivity of the pipe material.
Given:
- \( h_i = 100 \, \text{W m}^{-2} \text{K}^{-1} \),
- \( h_o = 200 \, \text{W m}^{-2} \text{K}^{-1} \),
- The thickness of the pipe is 1 cm, so \( r_o = r_i + 0.01 \) m, and the thermal conductivity \( k = 10 \, \text{W m}^{-1} \text{K}^{-1} \).
Substituting these values into the equation, we find that the overall heat transfer coefficient \( U \) is approximately \( 62.5 \, \text{W m}^{-2} \text{K}^{-1} \). Therefore, the correct answer is (C).