 Okay, we're going to finish up our treatment of fins by solving another example problem. Okay, so there is our problem statement, what we're dealing with here. We have a stainless steel square cross-section fin, we're told it's one centimeter by one centimeter. Eight centimeters long thermal conductivity is 18 watts per meter degrees C. The base temperature 300 degrees C, convective environment H is 45, T infinity is 50. We're told to compute the fin efficiency and heat loss by the fin. So those are the things that we're after and what we know. So let's begin by writing out what we know and what we're looking for. Okay, so we're after the fin efficiency as well as the heat being removed by the fins. So the analysis for this, what we're going to do, we're going to use our case three insulated tip solution, but we're going to correct the length. And so we're going to extend the length a little bit in order to approximate the case two, which was the more accurate solution, that with convection from the free tip. So analysis for this, so we have that for being the corrected length of the fin, the efficiency. And this is the advantage of being able to use case three solutions. It is much simpler. And so the only thing that we need to do in using case three is enter the corrected length instead of the normal length. And in their little M, if you recall, when we derived the solution from the fin equation, it's HP divided by K cross-sectional area AC. And so with that, we can plug in values. Now P, P is the perimeter and we're dealing with a rod fin. So sorry, a square cross-section. So if we look at the cross-section of our fin, perimeter is just going to be four times the length. And it's a square cross-section, four times the dimension of the fin, which we were told was one centimeter by one centimeter. So that's 0.01. Thermal conductivity was 18. And then the area is going to be 0.01 squared. And we take the square root of that. Okay, so there we have all the values that enables us to determine the fin efficiency. So let's do that. And this is where you have to make sure that you have the hyperbola tan function on your calculator. And make sure you know how to use it. So what we get, the fin efficiency, it's around 37%. And recall the fin efficiency was the heat removed by the fin divided by some theoretical max. So we said the fin efficiency was Q fin divided by some hypothetical maximum. That would be if the entire fin was at the base temperature. So from that equation, we can then evaluate the heat transfer from the fin as being the efficiency, the 37% efficiency times that Q max. Q max, that is if the entire fin is at the base temperature. So the wetted area of the fin is going to be the corrected length times the perimeter. And that's going to be multiplied by assuming the entire fin is at the base temperature minus the free stream temperature plugging in values. And you'll notice here I use the corrective length. And so there we don't have to worry about the area of the tip itself because we've used the corrected length. So from that we get the maximum heat transfer, the idealized case, 38.25 watts. And then the actual heat transfer from the fin. We're able to determine that this particular fin is capable of removing 14.1 watts. So that gives an example of how to use fin efficiency and using the Case 3 simplified solution for the case with the insulated tip by adding on this corrected length. And if you recall what I said last time in the last segment. So typically our Case 2 solution would have that and we'd have free convection from the end. What we're doing here is we're taking that length and we're adding on another corrected length. And so that is giving us our length corrected over the normal length. And it is assuming that this tip is then insulated so there's no heat transfer there. So it's through this addition of this small area here and here that we're able to make that approximation and use the Case 3 solution to approximate the Case 2 scenario which is the more accurate one where you would have Q convection coming off here. So that is solving a problem with fins and that concludes our coverage of fins.