Critical radius of insulation for a cylindrical pipe is given by [where k = Thermal conductivity of insulating material, h = External convective heat transfer coefficient]:

Explanation:

Critical thickness is the thickness up to which heat flow increases and after which heat flow decreases.

• The insulation radius at which resistance to heat flow is minimum and consequently heat flow rate is maximum is called “critical radius”.
• Note that the critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h.

The critical radius of insulation for a cylindrical body:

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

The critical radius of insulation for a spherical shell:

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

Additional Information

1. If the radius of insulation is less than the critical Radius then the rate of heat transfer from the cylinder increases with the addition of insulation. 
2. If the radius of insulation is equal to the critical radius of insulation rate of heat transfer from the cylinder reaches a maximum when the radius of insulation is equal to the critical radius of insulation.
3. If the radius of insulation is greater than the critical radius of insulation then the rate of heat transfer from the cylinder decreases with the addition of insulation.