Critical radius of insulation of a hollow cylinder is

Explanation:

The critical radius of insulation:

The critical radius of insulation can be defined in many ways. Let's see them all together.

• The value of Router for which the heat transfer rate is maximum is called the critical radius of insulation.
• The thickness up to which heat flow increases and after which heat flow decreases is termed as critical thickness.
• 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

The rate of heat transfer from the cylinder increases with the addition of insulation for r2 < rcr, reaches a maximum when r2 = rcr, and starts to decrease for r2 > rcr. Thus, insulating the pipe may increase the rate of heat transfer from the pipe instead of decreasing it when r2 < rcr.