 In looking at free or natural convection it is quite instructive to take a look at what is happening in terms of the fluid mechanics and so that is what we're going to do in this segment. And so before jumping into looking at the governing equations and things with the velocity profile and non-dimensional numbers, what we're going to do we're going to begin by looking at a fairly classic example of free or natural convection and that is one that deals with a heated or cooled flat plate flow. So what we'll be looking at in this segment is a vertical flat plate and we'll begin by looking at a flat plate that is cooled followed by one that is heated. So let's begin by looking at the cool flat plate and in order to do that what we'll be doing is we'll be looking at a video and what we have here is we're pouring boiling water and vinegar, water on the left, vinegar on the right, into a container that has ice water in the middle. So you can kind of see there's something in the middle that's a stainless steel tube that has ice water in it so we have hot fluid on the outside and you can see the index for fraction variations in the liquid, it's quite prominent. And then what starts happening you can see along the ice water surface or the cooled surface the fluid is descending and you can see it in waves and I've taken this, we're looking at about four and a half minutes of time here, convinced into shorter periods of time but you can see the cool fluid descending along the ice water, the stainless steel cylinder in the middle and as it warms up and the fluid on the outside cools then we come into equilibrium and the driving force goes away and that's why it becomes less and less pronounced with time. And so eventually you can see there are just small waves going through. So that's an example where we have vertical flat plate and we have a cooled surface and consequently the fluid on the surface becomes more dense and it then moves downwards. And so that is one application that we can have with the flat plate. Now the one that we're probably more used to is where we have the flat plate being heated and so that's what we're going to look at in this clip. And so here we can see a barbecue. There is the hot air coming up on the outside of the barbecue. It's going around a corner and so starting to separate and then eventually it merges with the byproducts of combustion coming out of the barbecue at the top and so you could see the thermal boundary layer in that case as well for that clip. So what we're going to do, we're going to take a look and we're going to look at the second video clip that we just saw and that is the case of a heated vertical flat plate. So let's examine that. So what I'm going to do, I'm going to sketch a vertical wall. So what we have here, we have a vertical heated wall. X is going in the vertical direction. Y is normal to the wall and the wall temperature we're assuming that is it is hotter or warmer than the ambient fluid which is out here. But what happens as we move upward along that plate, we do get a boundary layer forming and you could see that in the barbecue video, the one where we have a heated vertical plate. And you're looking at the index refraction variations within the air that is next to the hot vertical surface and it becomes at a higher temperature and consequently less dense and then that is what provides the mechanism that moves it upwards. But what will happen just like we saw for the flat plate with force convection, we go through a transition process where we go from laminar and then we move into a turbulent boundary layer that is on the surface. And so let me just sketch that out. And if we were to look at the temperature profile at any given location, now here what I've sketched, this is the boundary layer. And for now let's assume that the velocity boundary layer and the thermal boundary layer approximately the same thickness. That would depend upon the parental number just like we saw for force convection. But if you were to go and place a thermal couple along the wall and then do a traverse, so moving the thermal couple out in the Y direction, that would enable us to measure the temperature profile. And if we were to do that, the temperature profile in our boundary layer would look something like this. Remember the wall is hotter than the ambient fluid. And so eventually what we would find is that when you get outside of the boundary layer, you're going to get to a temperature that is T infinity. And as you move in towards the wall, what's going to happen is the temperature is going to increase. That's not a good curve. Let me redo that. So you're going to get something that might look like this. So the temperature as we move in towards the wall is going to get hotter and hotter. And eventually we get to a point when you reach the wall, the boundary condition on the wall is that the fluid temperature right at the wall surface has to equal the wall temperature. So we would have that at that location, T wall. And then we would have this profile, T of X, Y. And consequently the temperature profile is going to vary not only normal to the wall, but also as we move upwards along the wall. So it's a function of both X and Y. And if we were to look at the velocity profile, the velocity profile would be quite a bit different from what we saw for the boundary layer for force convection. And so I'm going to try to sketch that out. And what happens when you leave the boundary layer, you get into what we would call a quiescent fluid. And there the velocity is zero. And that's something new. We didn't see that before when we were looking at force convection. So the velocity has to go to zero outside of the wall. And then if you were to again place a probe that enabled you to measure velocity normal to the wall, you would find a profile that would look something like this. It would spike up and then it would come back down towards zero. And this then would be the velocity profile normal to the wall. And again it is a function of X and Y. And so that is the thermal boundary layer that we have. And this is going to be very important in terms of determining what the convective heat transfer coefficient is. And just like for the flat plate flows or any of the flows that we looked at for force convection, we'll be able to do a little bit of analysis for laminar. And we have a laminar flow. But when we go to turbulent, what we're going to be forced to do is rely on empirical or experimental data. So that is what the boundary layer flow looks like when we have free or natural convection.