 Okay, we're continuing looking at pre-convection and closed spaces, and now what we're going to do, we're going to consider the case where we have enclosed vertical space. Okay, so we haven't closed vertical space. What we're going to do, let's assume first of all that this here is insulated as is this, and consequently there is no heat transfer and no surfaces. But what happens, the fluid heats up, we were saying earlier, and then it gets to the top by continuity, it has to turn, it has to go somewhere, and then it gets near this wall and it starts to cool and it goes down, and we get this circular pattern developing and that is our convection cell. And that leads to enhanced heat transfer over if you have no fluid motion within the cavity at all. Example applications where we can find this are the following. So example applications, double pane windows, and so with double pane windows sometimes they'll put a gas that has lower thermal conductivity inside of the cavity, but it is the process of having these convective cells in the double pane that actually leads to increased heat loss, be it heat loss in the winter in northern climates, or it could be heat coming in in warmer climates if you have air conditioning on the inside. Wall cavities, that's another area, and that is why we put insulation in the walls of our homes. The purpose of putting the insulation there, first of all the insulation, the glass fiber is typically low thermal conductivity, but it also prevents the air from being able to go either through the wall, in the case of cold drafts from outside, but also the convective cells that might develop in the wall cavity. And then finally, solar collectors, that's another example, but here you would have your solar collector at an angle, but you can have convective cells that are developing within solar collectors. This would be a case of solar thermal collection, not solar photovoltaic. Solar thermal really has some sort of working fluid within the solar collector itself. So those are example applications. Now it turns out the correlations, there are a number of different ones, and the correlations vary by the aspect ratio. Now the aspect ratio here is defined as being H over L, and so you can imagine if H over L is 1, we're looking at a square cavity, and if H over L, another aspect ratio, let's say it's 10, and this was 1. If it was 10, that would mean that we would have to be 10 times the width, and so that would be 1 there in 10. This is 1 to 1, so that would be the aspect ratio of 1. So a window aspect ratio would be very, very high, because windows tend to be very large, tall, and not much of a gap between them, but other applications may have a lower aspect ratio. So that will have an influence on the new salt numbers, so let's take a look at the correlations now. What I'm going to do is I'm just going to write them out for either small aspect ratio cases or for larger aspect ratio. So we'll begin with small aspect ratio. Okay, so if you have small aspect ratio, so remember we said that that would be something like a square to something like that, where this would be 10 times that, there it's 1 to 1. So if you have small aspect ratio, these are the different correlations that you use and there's restrictions there in terms of the Prandtl number and the Grashov number. Okay, so those are the equations that you can use to calculate the convective heat transfer coefficient for an enclosed vertical space where you have a cavity. Now if you have larger aspect ratios that you might have in the case of a double pane window and the correlations are a little different. Okay, so different correlations that exist for the case of larger aspect ratios, so things that you might find I said in double pane windows and those are the relations that exist again for different Rayleigh numbers, different Rayleigh number ranges and different Prandtl numbers. So that is how to handle enclosed vertical spaces and what we're going to be doing in the last segment of this lecture, we're going to be working an example problem that uses one of the correlations for an enclosed vertical space.