The critical radius of insulation for asbestors with k = 0.125 W/mK surrounding a pipe exposed to room air with h = 2.5 W/m²K is

Concept:

Critical radius:

The insulation radius at 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:

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

The critical radius of insulation for a spherical shell:

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

Critical thickness:

The thickness up to which heat flow increases and after which heat flow decreases is termed as Critical thickness.

(rcr)thickness = rcr - r

Calculation:

Given:

k = 0.125 W/mK, h = 2.5 W/m2K

The critical radius of insulation for a cylindrical body:

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

\({r_{cr,cylinder}} = \frac{0.125}{2.5}=0.05\;m=50\;mm\)