Topic: Heat Transfer
The figure below shows a cross section through an insulated heating pipe which is made from steel ($k=45\text{ W/m K}$) with an inner radius of 150mm and outer radius of 155mm. The pipe is coated with 100mm thickness of insulation having thermal conductivity of $k=0.06\text{ W/m K}$. Air at inlet temperature $T_{i}=60^{\circ}C$ flow through the pipe has a value of convective coefficient $h_{i}=35\text{ W/m}^{2}\text{K}$. The outside surface of the pipe is surrounded by air which is at $15^{\circ}C$ and convective heat transfer coefficient on this surface has a value of $h_{o}=10\text{ W/m}^{2}\text{K}$. Find the critical insulation radius?
- A. 14.00 mm
- B. 3.00 mm
- C. 20.00 mm
- D. 6.0 mm
Answer: D. 6.0 mm
Explanation: The critical radius of insulation for a cylindrical surface is determined by the ratio of the thermal conductivity of the insulation to the outer convective heat transfer coefficient. Using the given values, $r_{c} = \frac{k_{outer}}{h_{outer}} = \frac{0.06}{10} = 0.006\text{ m}$, which equals $6\text{ mm}$.