Question #180888

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.

Expert's answer

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}"

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