In the previous article, we looked at the basic concepts of heat transfer and heat conduction. Taking the discuss forward, in this article, we will study the Heat Conduction in a cylindrical body. The most common case of heat conduction in a cylinder is that of heat transfer through a pipe with a fluid flowing inside. This system can be shown as per the figure below, by radial heat flow through a cylindrical shell. 

In this analysis, we will find out the temperature distribution and the heat transfer rate in a long hollow cylinder of length L, given the inner and outer surface temperatures are  and , respectively and there is no heat generation. The temperature at the boundaries is not a function of time, so the conduction equation in this case will take the form:  

Integrate the eqn (1) once with respect to radius gives us,

 or 

A second integration of the above equation will give us,

Now let us apply the boundary conditons to find out the constants of integration:

 at   

Similarly for 

 at 

Therefore, 

The temperature distribution can be written in a dimensionless form as,  

The rate of heat transfer by conduction through the cylinder of length L is given by, 

 

In terms of thermal resistance, we can write, 

Now the value of thermal resistance in this case will be, 

The principles for a plane wall with conduction and convection in series can also be applied to a long hollow cylinder like a pipe or a tube. Check out the figure below to understand a thermal circuit of such nature. 

Now if we follow equation (4) and find out an expression for the rate of heat flow, we will get the following expression.

 

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