## What is critical radius of insulation?

The critical radius of insulation is the thickness of insulation at which the rate of heat transfer through the body is maximum.

It means that the rate of heat transfer increases with an increase in the thickness of insulation up to the critical radius of insulation.

If we increase the thickness more than the value of critical thickness then the rate of heat transfer starts to decrease.

The value of the critical thickness of insulation depends on the thermal conductivity (K) and convective heat transfer coefficient (h) at the surround of the insulation.

## Critical radius of insulation graph:

This plot indicates the change in heat transfer with the increase in thickness of insulation.

**For** `(r_{1})<(r) <(r_{cr})` :-

The increase in a layer of insulation on a cylindrical surface up to the radius `r_{cr}` results in an increase in the rate of heat transfer through the insulating body.

Therefore for the increase in insulation thickness from `r_{1}` to `r_{cr}`, the rate of heat transfer also increases.

**For** `(r) =(r_{cr})` :-

At the critical radius of insulation, the resistance to the heat transfer is lower hence at the critical radius the rate of heat transfer is higher.

Up to the critical radius, the increase in conduction resistance is dominated by an increase in convective heat transfer as the outside area exposed to the surrounding increases.

**For** `(r) > (r_{cr})` :-

If the radius of insulation increases further of the `r_{cr}`, the conduction resistance also increases therefore the rate of heat transfer also decreases.

Now in this case the increase in the rate of convective heat transfer is dominated by an increase in conductive resistance.

## Critical radius of insulation significance:

The critical radius of insulation has different significance based on its purpose.

**1) For thermal insulation:**

The use of thermal insulation is to avoid or lower the rate of heat transfer from objects.

hence the thickness of insulation should be greater than the critical thickness of insulation.

**2) For electric insulators:**

The insulations used for the electric conductors are good insulators for electricity and good conductor for heat.

Therefore in this case the radius of insulation should be less than or equal to the critical radius of insulation.

So that it will resist only the flow of electricity but allow the transfer of heat generated while conduction.

## Critical radius of insulation for cylinder:-

The critical radius of insulation for the cylindrical surface is given by,

`r_{cr}=\frac{K}{h}`

Here,

K= Thermal conductivity, w/mK

h= Convective heat transfer coefficient, w/m^2.K

## Critical radius of insulation for sphere:

The critical radius of insulation for the spherical surface is given by,

`r_{cr}=\frac{2K}{h}`

## Why rate of heat transfer increases till the critical radius of insulation?

As we increase the layer of insulation on a cylindrical or spherical surface, the area exposed to the surrounding also increases.

The increased surface area increases the convective heat transfer. Up to the critical radius, the conductive resistance of the insulation is dominated by rising convective heat transfer.

Therefore up to the critical radius of insulation, the rate of heat transfer increases.