Optimal Heat Transfer From An Extended Surface

by James McClendon

Submitted : Spring 2016

In this project, a cylinder’s dimensions of volume were found to maximize the rate of heat transfer from the cylinder.  The process used a simple differential equation to find the rate of heat transfer.  From there, manipulation of the volume constraint allowed isolation of one variable.  The maximum of the function gave the value at which the cylinder had the highest rate of heat transfer.  This maximum was then plugged back into the volume constraint to give the second dimension of the cylinder. 

            The results showed that in maximizing heat transfer from a cylinder heated at the base, length was more valuable than radius.  This would make sense in a real life situation, where a greater surface area means more contact and convection with air.  A shorter cylinder with a greater radius will have less surface area to the air than a taller cylinder with a smaller radius to a point; this point is the maximization found in this project.   

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