 up until now we've been looking at free convection in rather open spaces where the fluid is unconstrained but what we're gonna do in this lecture is we're going to take a look at free convection within enclosed spaces. So for these applications the fluid is confined and consequently it is in enclosed space and it is restricted in terms of where it can go. So when we're looking at free convection in enclosed spaces essentially what we're looking at is two surfaces. They could be vertical or they could be horizontal where there's a temperature differential between those two surfaces and there is a fluid between the two surfaces and and that fluid due to natural convection can heat up and it can be put into motion and so that's what we'll be looking at when we look at free convection in enclosed spaces. So what we're going to do we're going to begin by looking at three different geometries two horizontal and one vertical. So let me sketch those out and then we'll discuss them. So what we have here are three different geometries two of them horizontal and one vertical and these are the plates that are either heated or cooled and I've indicated the temperatures blue would be a cooler surface red would be hotter and there is a fluid in the space between these two plates being them horizontal or vertical. So let's begin and take a look at what is happening over here in the case of bottom heating. Now what is going to happen with bottom heating is the fluid adjacent to the wall is going to heat up and when it heats up it will become less dense and consequently becomes buoyant and it moves upwards and so it'll move up like this and when it gets up near the upper wall it starts to cool and when it begins to cool it becomes more dense and consequently it then starts to descend and what we then find and that's not a very good error let me redo that what we then find is we get these cells developing and we refer to those as being convective cells that exist within the enclosed space and so that's what happens with bottom heating and there there's a certain temperature differential before that begins to take place below it it won't take place we'll be talking about that in the next segment. Now looking at vertical space so this might be something like the cavity between windows or in the cavity of a wall of a house where you have studs and then drywall and plywood on the outside and what is happening again the fluid on the right hand side surface here is going to heat up and it's going to move but we usually with the cavity we're going to have some sort of confinement at the top and the bottom and consequently the fluid can't hit the top it's going to have to start to come around and when it comes around it comes against this wall which is now at a lower temperature and it becomes more dense and then it descends down to the bottom but it can't hit the bottom it's got a turn again and when it starts to turn it starts to come back up and that is the convective cell that develops within a vertical cavity and then finally let's look at the last one here over on the right hand side and here we have the case where the heated plate is on the top and the cool plate is on the bottom and this one nothing exciting happens it's just straight conduction and that's because this is what we refer to as being stably stratified and and so we go just from hot down to cool and that follows straight conduction going through that so the fluid does not go into motion when you have a stably stratified system like the one on the right so with that those are the three different geometries that we're going to be looking at in this lecture and when we're dealing with this we have a Grashof number and the Grashof number with the characteristic length is l and l in all of those cases hopefully I did that and I didn't put it here let me put it there l sometimes you'll see delta depending on the the textbook sometimes they'll use a a delta there but that can get confusing because that's what we said was the boundary layer thickness so we're going to use l here l is the separation between the two plates and expressing that as a Grashof number and then the temperature difference is going to be the hot surface minus the cooler surface the length scale is l and then we divide that by our kinematic viscosity which is squared new salt number that is going to be evaluated again using l as the characteristic length scale and then through this we have through Fourier's law the double prime would be watts per square meter and then it would just be h times t1 minus t2 so what we're going to be doing in this lecture is we're going to be finding ways just like we've been doing with all the others to estimate h and we'll do that using Grashof number, Rayleigh number, new salt number, things like that so that is reconvection and closed spaces what we'll be doing in the next segment is we'll begin with the horizontal where we either have bottom heating or top heating and we'll take a look at that flow field