I mean, it's the ratio of actual heat transfer to heat transfer if the material had infinite conductivity.
How is it of any practical, or even theoretical use? How does it help, in saying one fin is better over other?
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If the material has infinite conductivity, the entire fin would be at the base temperature.
This represents an ideal scenario. If the temperature of the fin were the same as the base all the way through, that would mean the heat transfer between the fin and cooling medium would be a theoretical maximum. In reality, you will lose some of that efficiency, because the imperfect conduction means that the further from the base the fin is, the lower the temperature, and thus heat transfer is reduced.
There's some level of tradeoff between increased area of fins, and the decreased temperature due to non-infinite conduction; but the "ideal" fin the efficiency compares to does not have that tradeoff.
Well, think about a heat sink with one small fin. You could model the heat transfer to a convecting fluid with a bit of work.
Now think about a larger heatsink with multiple fins the same size as the first one. You'd expect it to transfer more heat to the convecting fluid, right?
So we can simplify things a bit by assuming that the material of the heat sink conducts perfectly. So now it is only the size and shape of the heatsink that governs how much heat is moved. Now we can compare two heatsinks and see which one moves more heat. That ratio is just a convenient way of doing this.