Heat Transfer of Sphere Geometries

Heat transfer calculations are very important in engineering and various shapes are used in heat transfer calculations. These shapes are cylinders, spheres, etc. Furthermore, here we explain the conduction heat transfer of spheres and how to calculate this heat transfer phenomenon for sphere shapes with a calculator.

Check: Most Used Textbooks About Heat Transfer In Engineering!

How to Calculate Heat Transfer in Sphere?

Heat transfer of sphere geometry
Image Source: Youtube.

Firstly, the calculation of heat transfer of the sphere shapes is very simple. Before starting the calculation of heat transfer of spheres, you need to calculate the total thermal resistance of the sphere. 

Thermal Resistance of a Sphere

The heat transfer resistivity of a sphere is calculated via this formula; 

So, in this formula, r2 is the outer radius and r1 is the inner radius which has the unit of m or in. ‘k’ is the thermal conductivity of the material of the sphere shape. The unit of the thermal conductivity is W/m·K or BTU/h.ft.F. 

With this formulation, the unit of the obtained thermal resistivity is °C/ W.

Effect of Wall Thickness on Heat Transfer

As you see above, if the difference between the inner radius and outer radius increases, the thermal resistivity of the sphere increases. This is because the wall thickness of the sphere increases. Also, there is an inverse proportion between the wall thikness of the sphere and the total conduction heat transfer. 

Effect of Thermal Conductivity on Heat Transfer

With the increasing thermal conductivity value, the thermal resistance of the sphere decreases. With the decreasing thermal resistance, the total heat transfer increases. So, with the increased thermal conductivity of the material, the total conduction heat transfer through this shape increases.

Total Conduction Heat Transfer Calculation of a Sphere

After the calculation of the thermal resistivity of this shape, we can use the formulation below to calculate the total conduction heat transfer of the sphere. 

Conduction heat transfer formula of the sphere.

So, here, we just need to divide the temperature difference between the inner wall and outer wall with the calculated thermal resistivity value. The calculated total heat transfer value will be in W or BTU.

Conduction Heat Transfer Calculator for Sphere

We prepared a calculator to calculate the thermal resistivity and conduction heat transfer for this shape in an easy way. 

Conduction Calculator for Sphere

Furthermore, the use of the heat transfer calculator for the sphere is very simple above. You just need to enter the inner radius, outer radius, the thermal conductivity of the sphere material, inner wall temperature, and outer wall temperature of the sphere inside the brackets and click on the ‘Calculate!’ button. So, thermal resistivity and conduction heat transfer of these shapes will appear. Also, if you want to make additional calculations, just click on the ‘Reset’ button and reenter the new values. 

The conduction heat transfer calculator for these shapes will be very useful for you. You do not need to bother yourself with time-consuming hand calculations. You just enter the values inside the calculator and calculate them. 


Above all, these are the general aspects of the total conduction heat transfer of sphere shapes. 

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

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

Finally, do not forget to leave your comments and questions below about the total conduction heat transfer of a these shapes and calculator. 

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