What is the critical radius of insulation for asbestos (thermal conductivity = 0.17 W.m^-1.°C^-1) surrounding a circular pipe and exposed to room air at 20°C with heat transfer coefficient 3 W.m^-2.°C^-1?

Concept:

The critical radius of insulation for a cylindrical body:

\({r_{cr,cylinder}} = \frac{k}{h}\)

The critical radius of insulation for a spherical shell:

\({r_{cr,sphere}} = \frac{{2k}}{h}\)

Calculation:

Given:

k = 0.17 W.m-1.°C-1, and h = 3 W.m-2.°C-1

The critical radius of insulation for a cylindrical body:

\({r_{cr,cylinder}} = \frac{k}{h}\)

\({r_{cr,cylinder}} = \frac{0.17}{3}\times 100=5.67\;cm\)