 In the last segment we took a look at the flow around a cylinder in connective heat transfer and we found that the separation point varied depending if we had a laminar or a turbulent boundary layer. So what we're going to do in this segment is we're going to take a closer look at what is happening with the boundary layer. So with the boundary layer on the cylinder I'll draw a Y normal to the wall. So this is looking at a section of wall assuming that it's normal to the cylinder itself. So let's see here. Let me sketch out. If this is the cylinder what we're doing is we're zooming in on a section and Y would be normal to the surface of the cylinder. So that's kind of what we're looking at here. And in this region of the cylinder here is our stagnation point but in the upstream region here what's happening is we have what we call a favorable pressure gradient and so the boundary layer may look something like this. It's going to vary depending if it's laminar or turbulent. Let's assume here it's laminar. U infinity is the free stream velocity far away. So U infinity here. Now I should be careful because U infinity is going to change depending upon where you are. That would be U external I guess because what we have done originally is we said U infinity was up here. But the velocity outside is going to change and it's going to be a function of theta for angle as you go around the cylinder. So remember theta was our angle here. So this would be the case of what we would call a favorable pressure gradient. And what is going on here is we have a situation where dp by dx where what I've done is I've defined x as being parallel to the surface of the cylinder. It is less than zero. So the flow is going from a region where the pressure is getting lower and lower and lower and consequently the flow is accelerating as it's going. So that is easy for the flow to navigate. Now if we go further along we'll get to a region. We'll call this region one. This here would be region two. And again I'm going to draw a section of the wall normal. Now we're going to get to a location where dp by dx is equal to zero. And x is the direction here. I should have drawn x there. And our boundary layer is going to look a little bit different. It might start to look something like this. And then that would be U external. I should have written that as being external. And so that's the case where we have no change in the pressure as the flow is going along. So what's going to happen here is the fluid will still have inertia so it will continue to move. And then you're going to eventually get to a location. We'll call this region three. Where we have what we would call a critical adverse pressure gradient. And so looking again at what's going along along the wall or what's happening. Why it would be normal. Our velocity profile may start to look something like this. And this would be dp by dx greater than zero. But this is what we would call a critical adverse pressure gradient. And the reason why we call it critical is because what has happened here is the velocity right at the wall has gone to zero. So well we know that we always have the no slip condition. But I guess that would be at a point above the wall. It really comes down to the gradient of the velocity. But what is happening is our fluid right along the wall is losing the ability to overcome the pressure gradient. And if we go a little bit further downstream, what we'll find is a bit further downstream. We have a scenario like this. And we actually have backflow along the wall. And when you get that backflow, that is when you have a separated boundary layer. And you can see kind of it in the flow biz in the first segment. You can see what looked like the boundary layer lifting off the wall. And that is when this is taking place. And so that would be separated flow. Okay. And so what we said is that that separation point is going to vary whether or not we have a laminar. I think I said 82 degrees. And then for turbulent, I said 120 degrees. That would be the separation point. And it would vary if it was a laminar boundary layer, it's 82 degrees. And if it's turbulent, it's 120. Why is there the difference? Well, the reason is it has to do with the mechanisms of the boundary layer itself. What is happening in the turbulent boundary layer, we have very large scale structures and they provide energy to the flow. And that helps energize the boundary layer. So let me just make a comment along those lines. So what is happening here is the laminar boundary layer has less energy or inertia, I guess you could say, than the turbulent boundary layer. Turbulent, we have these large scale structures. And they are able to overcome the adverse pressure gradient more than the laminar boundary layer. And so the fluid is moving into a region of increasing and increasing pressure. If there's turbulence, it can overcome that more. And that's why we have the separation point further downstream. So the implications of all of this in terms of heat transfer, and that's what we're interested in, that the main thing is that separation, a separation point has an impact on the collective heat transfer coefficient on a cylinder. And so with that, you can expect that the heat transfer characteristics of the cylinder will be dependent upon the Reynolds number of the flow over the cylinder. And you can compute convective heat transfer on a compute measure. You can measure it as a function of theta, but usually we don't really get into that level of detail. Usually what we do is we come up with a new salt number for the entire cylinder, which gives us an average convective heat transfer coefficient for the cylinder. And that's what we'll be taking a look at in the next segment. I'll give you some equations or an equation that we use, and it enables us to get the convective heat transfer coefficient for flow over a cylinder. So the main thing though, the boundary layer has an importance in terms of where the separation point is, and that has an impact on the convective heat transfer characteristics.