Question

CPT 307 ASSIGNMENT

The Figure below shows a cross section through an insulated heating pipe which is made from steel (k = 45 W / m K) with an inner radius of 150 mm and an outer radius of 155 mm. The pipe is coated with 100 mm thickness of insulation having a thermal conductivity of k = 0.06 W / m K. Air at Ti = 60°C flows through the pipe and the convective heat transfer coefficient from the air to the inside of the pipe has a value of hi = 35 W / m2 K. The outside surface of the pipe is surrounded by air which is at 15°C and the convective heat transfer coefficient on this surface has a value of ho = 10 W / m2 K. Calculate the heat loss through 50 m of this pipe. 

 

Answer 1

The insulation radius which resistance to heat flow is minimum, and consequently heat flow rate is maximum is called “critical radius”.

The critical radius of insulation for a cylindrical body:

${r_{cylinder}} = \frac{k}{h}$

where, k = conductivity of insulation, h = convective heat transfer coefficient of outer body.

$k = 0.06 W/mK, \quad h = 10 W/m^2K$K

$\begin{aligned} {r_c} &= \dfrac{k_{insulation}}{h_{outside}} \\ \\ &= \dfrac{0.06}{10} \\ \\ &= 0.006m\\ &= 6mm \end{aligned}$