 So, in this segment, what we're going to do, we're going to take a closer look at the configurations where we have enclosed space and we either have heating on the top or heating on the bottom. So, let's take a look at those. So, we said there are three different geometries, two horizontal one vertically, we'll focus in on the two horizontal ones. Now, we'll begin with the less interesting of the two, where you have a stably stratified flow field. And so, here is a case where the upper surface is heated. So, T1 is hotter than the lower surface, which is cool. And so, we have a quiescent thermally stratified fluid, meaning that the fluid is not in motion. And if we were to go in and measure temperature profiles, we would find that temperature profiles would be constant as at a given vertical position. So, as you move across horizontally, the temperature would not change. Gravity vector here is pointing in the downward direction. And the condition under which this would exist would be Grashof-Prandtl, less than 1,708. And for this condition, the Nusselt number is going to be equal to 1. And if we remember HL over K, what that is telling us is that H is just equal to K over L. And if we recall Fourier's law, we had H times, we had T1 minus T2. So, this is essentially plugging in the H value. We get K over L times T1 minus T2. That looks very much like Fourier's law. Remember Fourier's law, we had K dT by dx. Well, that's essentially what we're getting here. We have T1 minus T2 divided by the L's. That would get a gradient to the temperature. So, that is why we have the Nusselt number equal to 1 for the thermally stratified fluid. So, that one is only so interesting. Now, the next one, when we go above that critical Grashof number of 1,708, the fluid starts to go into motion. And that's where it gets kind of neat. So, here we get a cellular flow pattern. Remember we said that the fluid will be heated on the bottom. It will then ascend up. It gets cooled once it gets up to the top, and then it descends back down. And we then get these convective cells developing. And depending upon the geometry of the cavity that we're looking at, we can get slightly different types of cells developing. So, you get a pattern like that forming. And this is the case for T1 greater than T2. And here, this condition would exist for Grashof Krantl greater than 1,708. And the Nusselt number would be greater than 1. It's no longer 1. It's going to be greater than 1. And this cellular pattern that we're looking at here, it actually has a name. And it's referred to as being the Rayleigh-Bernard Convection cells. And so, let's just take a look at that. So, Rayleigh-Bernard Convection cells, and those are the cells that exist between the two horizontal plates with the heated surface at the bottom. Now, what we can do, we can do a little experiment here. And so, let's say you have a container that has a hot fluid in it. And if you take something like a Petri dish, and you put it on the top, and in the Petri dish, you fill it with a little bit of water. You have something like that. We would then have a condition where we have a free surface here. And if we were able to look at this from the side and do a cross-section, we would have cells that are forming. And depending upon the geometry, you'll get slightly different cells. But that, each cell would have fluid coming up and down. And these are the Rayleigh-Bernard Convection cells that we would see. So, what we're going to do is we're going to do this experiment. And so, what I did is I used the infrared camera, and I took a bowl of hot water, and here we can see there is the bowl of hot water. The one on the right is actually water. I put a lot of boiling water in there out of a kettle. And then I put that Petri dish with cool water in it. I'm putting a little bit of cool water in the one on the left there. And then we just watch what happens with time. Now, I've sped this up. And so, you'll see the Rayleigh-Bernard Convection cells start to appear. And they're really quite neat. And they're a little distorted there because I had a little bit of motion and the fluid. But the one on the right is much hotter. And you can see the evolution of the cells is drastically different from what we're seeing on the left. On the left, we have cells that aren't really merging. But on the right, we get this supercell forming. And that's just due to the fact that the water was quite hot underneath. And there you can see, for instance, cold water now. And that mixes it. Now, let's zoom in on what's happening with the one on the left. That was a lower temperature differential. This is over a longer time. And you can see the cells starting to reassemble. They're merging and moving around. This was probably about half an hour that I took this video clip from. And then you remove the Petri dish. And you can see the cells in the bowl of water in the bottom. And they started to go through a new transformation. So that's kind of neat to be able to see the Rayleigh-Bernard Convection cells in that configuration. I did do another experiment where the Petri dish was not perfectly level. And so the gravity vector was a little bit out of filter. And it's kind of interesting to watch what happens there. So let's move into that video clip. So here we can see I'm pouring in some boiling water into the, well, it's not boiling, but it's very close to boiling, into the bowl from below. And you see some mixing going on there. We'll speed up the mixing just so we can ensure that it's kind of uniformly mixed hot water in the bottom. And then we put the Petri dish on the top. And this is one where it was a little tilted. And I said the gravity vector is a little bit off. So watch what happens. We get a hot cell forming at the top. And it assimilates all of the other Bernard Rayleigh-Bernard Convection cells. It's kind of eating them. And it's kind of a neat thing to watch. At least it was neat for me. I hope it's neat for you as well. Anyways, that is Rayleigh-Bernard Convection. You pull it away. Again, you can see a cellular pattern in the bowl and they change with time due to the change in battery condition towards some more hot water. So those are Rayleigh-Bernard Convection cells. And now we do have a correlation for the bottom heating. And so this would be a case where we have two solid surfaces. So this would be hot. And this would be cool. And we said T1 was hot. T2 was cool. And the correlation for bottom heating is as follows. So this would not be with the free surface. We would have a surface on the top. So that's the correlation. It applies over this range of Rayleigh number. And in this, the properties are evaluated at the average temperature. So that's either T bar or T average. But that's defined as being T1 plus T2 divided by 2. So that's a correlation for the case of a horizontal and closed space with the bottom hot and the top cool. In the next segment, what we'll do, we'll move into looking at vertical confined spaces and closed spaces with natural convection.