Critical Radius of insulation in Heat Transfer

For the purpose of maximium heat transfer. Sometimes we added extra
surface area with heat transfered body ( i.e. insulation in case of
wire cable) so it can transfer maximium heat from the heated body to

But Here it should be noted that when we add the surface area for
increasing the heat flow. The conductive resistance of extra surface
area will also added to the body. And this will reduced the heat
transfer rate.

Hence there is two opposite and inversely phenomenon will happen this
will eliminates the advantage of surface area addition.

To reducing this problem it is necessory to examine radius of extra
surface area which can tranfer maximium heat. This radius of extra
surface called " CRITICAL RADIUS of INSULATION".

It can be found by differentiating the overall resistance equation
w.r. to outer radius of extra surface (i.e. By Maxima and Minima

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