Critical Insulation Radius in Heat Transfer?

Insulation is a very important thing in heat transfer to reduce the total energy that is expended to make the system hot or cold. Also, staying hot or cold in that system is very important. Because additional energy consumption is required to hold the system hot or cold as intended. In this case, optimum insulation must be designed. You will see that, the general logic of the critical insulation radius is very simple.

Check: Most Used Textbooks About Heat Transfer In Engineering!

What is the Critical Insulation Radius?

Critical insulation radius in heat transfer..
Image Source: Researchgate.

Firstly, there is a belief that with the increasing thickness of the insulation, the total rate of insulation increases. But it is not like this. There is a critical radius of insulation where the insulation becomes the maximum. Insulations bigger than or smaller than this value, make the total insulation rate smaller compared with the critical insulation thickness. 

But this situation is only valid for the cylindrical or sphere heat transfers. Heat transfer for the flat surfaces such as the wall, the total heat transfer decreases. 

With the addition of an insulative layer to sphere or cylinder shapes, the conductive resistance of heart transfer increases. But at the outer surface of the insulation layer, the total area for the convection heat transfer increases. After a critical thickness, the total heat transfer increases with the increasing outer area because of the convection heat transfer. 

How to Calculate It?

So, the calculation of the critical radius of insulation is very simple. But the calculations of the critical radius values for sphere and cylinder are quite different. 

For cylinder; 

Rcritical = k/h (ft or m)

‘k’ is the total thermal conductivity of the insulation material which has the unit of BTU.h-1.ft-1.℉-1 or W.m-1K-1 in SI units. ‘h’ is the external heat convection coefficient which has the unit of Btu/(hr-ft2°F) or W/(m2°C) in SI units. 

For sphere; 

Rcritical = 2k/h 

The only difference between the cylinder and the sphere is the multiplication by 2. 

And also as you understand from these formulations to calculate critical heat transfer radius for sphere and cylinder, with the increased thermal conductivity, the total critical radius increases. Because with the higher thermal conductivity, the total conduction heat transfer will be higher. 

With the increasing heat transfer coefficient of the external environment, the total critical insulation radius decreases. Because, with the increasing heat transfer coefficient, the total convection heat transfer decreases, and the requirement for additional insulation thickness decreases.

Critical Radius of Insulation Calculator

Critical Radius of Insulation Calculator for Cylinder

Critical Radius of Insulation Calculator for Sphere

The use of the critical radius of the insulation calculator is very simple. After the selection of the shape that you want to calculate the this, you just need to enter the thermal conductivity of the insulation material and the heat transfer coefficient of the environment. Then click on the ‘Calculate!’ button to calculate the this. Also, if you want to make additional critical insulation radius calculations, click on the ‘Reset’ button to re-make calculations. 

Furthermore, you can use this critical radius of insulation calculator in the complex heat transfer calculations. Because you will probably calculate lots of calculations related to the critical radius in the complex designs, you will not bother yourself with these simple calculations by hand. 


Finally, the general aspects of the critical radius of insulation in heat transfer can be explained as above. 

Above all, Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

Also, you can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

So, do not forget to leave your comments and questions below about the calculation of this topic.

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One response to “Critical Insulation Radius in Heat Transfer?”

  1. Duff Harrold Avatar
    Duff Harrold

    I’ve commented before but it seems nothing has changed. You seem to be implying that the critical radius is the radius beyond which added insulation will increase the rate of heat transfer. You use the term “insulation rate” which I can only assume means “thermal resistance”. The critical radius is NOT the radius of maximum thermal resistance but rather MINIMUM thermal resistance. If the radius of the system is less than the critical radius then adding insulation will increase the rate of heat transfer UNTIL the critical radius is reached. Insulation after this critical radius will increase thermal resistance and decrease heat transfer. PLEASE fix this or tell me how I’ve got this wrong.

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