Critical Thickness of Insulation

[Ali Durrani]

< Mentor Note -- thread moved to HH from the technical engineering forums, so no HH Template is shown >[/color]

What do you understand by the term "Critical thickness of Insulation"? What is the critical thickness of a plane wall? Derive an expression for the critical thickness of insulation for a cylinder?

 

[stockzahn]

Imagine a cylindrical or spherical geometry you want to insulate thermally. The heat transfer at the outside due to convection increases with a larger surface of the insulation, whereas the heat conduction in the insulation decreases with the thickness of the insulation. For small thicknesses the increase of the convection due to the larger surface outweighs the insulating effect against thermal conduction due to the increase of the thickness. From a certain thickness of the insulation the thermal resistivity against conduction increases faster than the heat transfer at the outside of the insulation due to convection.

There shouldn't be a critical thickness for the insulation for a plane wall, because it doesn't increase the surface of the insulated object.

You can derive an expression for the critical diameter starting with the heat flux calculated with the u-value.

 

[Ali Durrani]

Imagine a cylindrical or spherical geometry you want to insulate thermally. The heat transfer at the outside due to convection increases with a larger surface of the insulation, whereas the heat conduction in the insulation decreases with the thickness of the insulation. For small thicknesses the increase of the convection due to the larger surface outweighs the insulating effect against thermal conduction due to the increase of the thickness. From a certain thickness of the insulation the thermal resistivity against conduction increases faster than the heat transfer at the outside of the insulation due to convection.

Is it the right approach by taking the derivative over the total resistance of a cylinder and then again taking the derivative over the answer, if the answer is positive, you get a minima over the curve so the conduction heat transfer has decreased over an optimum value of convection heat transfer

 

[stockzahn]

Is it the right approach by taking the derivative over the total resistance of a cylinder and then again taking the derivative over the answer, if the answer is positive, you get a minima over the curve so the conduction heat transfer has decreased over an optimum value of convection heat transfer

Basically yes, but you have to set the 1st derivative zero to find the critical thickness/radius and then plugging it in the 2nd derivative (I'm pretty sure you implied that in your post).

 

[curious-iman]

Also tubes or pipes are critically insulated to decrease the heat transfer rate. And wires are insulated to increase the heat transfer rate.