A few lectures ago we looked at how for the case of a cylinder we could, in fact, increase the rate of heat transfer by adding insulation (i.e., making the diameter larger). Upon reflection, we realized that this happens because by adding the insulation (or making the diameter larger) we increased the area available for convective heat transfer! When we figured that out it seemed that everyone was happy with what was a confusing issue.
If we had instead resorted to thinking about finned surfaces (like the radiator in your car, the little do-dads in your computer, etc.) we may have realized earlier that sometimes adding material increases heat transfer (as long as the increase in surface area is sufficient to cause the convection to overcome the added conductive resistance). This will be our topic for a short while.
Having said that, I am sure that it is perfectly clear that often, when we need to increase the rate of heat transfer through a material, we may add fins! Some typical fin configurations are shown below.
As I am sure that you can imagine, fins are tremendously technologically important items (as Chem. E's we would certainly be interested in their use in heat exchangers!). So, how do we handle these things?