 Okay, so in this lecture we've looked at a lot of different correlations. What we're now going to do, we're going to solve an example problem and that will be for the isothermal vertical flat plate. Let me write out the problem statement. Okay, so what we have, we have a fireplace with a glass door, a fire screen. So that is what contains the fire within the fireplace itself. And we're told that the height of this glass screen is 0.71 meters by a width of 1.02 meters. We're told that it gets up to 232 degrees C, so it's very hot. The room temperature, the ambient room temperature is 23 degrees C and then we're told to estimate the convection heat transfer from the fireplace to the room. And so let's begin by going through the process of writing out what we know and what we're looking for. So that's what we know and what we're trying to find as we're trying to find Q due to convective heat transfer. Okay, so let's begin with a schematic of what we're looking at. Okay, so we have our fire. The surface temperature is TS and we have the dimensions here. And this is where we have to be careful to make sure we get the right dimension for the vertical extent or height. And so that is L, whenever we're dealing with vertical flat plate with natural convection and the width. We'll assign W and that is 1.02 meters. And out here we have our ambient fluid. And so that is going to be moving adjacent to, you know, what I'll do, I'm not going to put those arrows. Really the only place we would see that is right up next to the fire screen. This is cool. It is 23 degrees C. So what's going to happen is we're going to get the boundary layer going on there. Okay, so this is obviously a case of natural convection. We don't know if it is a laminar boundary layer or a turbulent boundary layer on the vertical surface. We're assuming that it's a constant temperature and so we'll use the isothermal relationships for constant temperature. So another thing that we're going to assume is that the room itself, there really is no bulk motion of the fluid. So the only thing driving the fluid is going to be the natural convection, which is going to occur right along this surface here. So in reality, is it going to be a uniform screen temperature? Probably not, but that will be the assumption that we're making here. The other one is that the room is quiescent or the room air. Remember that means that there is no bulk motion of the fluid in the air. Okay, so where do we begin? Well, we have an indication that this is going to be a natural convection on a vertical flat plate, isothermal, so that gives us a hint where to look. But whenever we're doing these problems, the first thing to do is to evaluate the properties. And for this particular case, for a vertical isothermal plate with natural convection, we know that we evaluate the properties at the film temperature. For this case, it's 127.5. It comes out to 400K. So going into the tables of your book, hopefully you don't have to do interpolation at 400K. That always makes the problems more interesting and more enjoyable. I'm joking. KF, and finally beta. Beta we can get directly. I'll put it there, but it's one over the film temperature. We don't have to go to the tables for that. That's for dealing with air. So that gives us that value. Okay, so we have our properties. The next thing that we're going to want to do, we'll look at the correlation that we're going to use. And we'll want to calculate the Rayleigh number, the Grashov-Prandtl number, in order to determine if we are in the laminar flow regime or in the turbulent flow regime. And for this particular problem, what I'm going to do, I'm going to use the correlation. I'll write it out here. I'm going to use the one with the C and the M. So what we need to do, we don't know what C is, nor do we know what M is. That's unknown, and that's unknown. We need to evaluate this to determine if we're dealing with the laminar or with the turbulent flow. So let's go ahead and evaluate the Grashov number and then the Rayleigh number. So when we do that, we get 1.88 times 10 to the 9, and that is greater than 10 to the 9, and therefore we're dealing with a turbulent flow. So you could either use the more involved correlation for a turbulent flow, or you could find the values of C and M for turbulent, and we said C would be 1.10, and M, remember we said, was one-third, it's one-quarter if it's laminar, it's one-third if it's turbulent, and C would change as well if it was laminar. So with that, what we can do, we can come back to this equation here. We have everything that we need in this equation. In order to evaluate, first of all, either the Nusselt number or directly the value of the connective heat transfer coefficient. So with that, we can evaluate H, and this would be the average value of H across our fire screen, and we get 5.85 watts per meter squared Kelvin, and just realize when you're dealing with natural convection, that's typical, you'll get numbers between 2 and maybe 7 or 8, so 5, 5 to 6 gives us an idea that this is a natural convection type problem. Numbers much higher, 50, 60, if you're getting a number like that and you're dealing with natural convection, you might want to think about it a little bit more, because it may be incorrect, but this is the right ballpark range that we should be expecting. So with this, the question, remember, asked us to determine what is the convective heat transfer from the fire screen, and so with that, we can then just use Newton's law of cooling, and when you plug in values here, we get convective heat transfer equals 886.03 watts. So that's good, we've solved the problem, we've been able to determine the value of the heat transfer. Now, a question that we could ask, remember that this fire screen was at 232 degrees C, and if you've ever sat next to a fireplace, you are benefiting from both the natural convection that is coming off of the fire screen, you're also benefiting from radiation, we have radiative heat transfer going on, just check and see what about radiation. They didn't give us anything about the emissivity of the fire screen, I'm just going to assume that it's one, obviously it would be lower than that, but that's just going to be a starting point. And so I'm putting an emissivity of one, the area, the Stefan-Boltzmann constant, and then remember, when you're dealing with radiation, these temperatures need to be in Kelvin, and with that, we get that the radiative heat transfer assuming an emissivity of one is quite high. It's actually higher than our convective heat transfer, so that is an indication that in order to solve this problem, we really should be taking into account the fact that we have radiative heat transfer as well. And the amount of radiation that's coming off would be a little lower because we've assumed emissivity to be one, which is a little bit on the optimistic side because it would be lower than that. But anyways, what it does is it demonstrates that radiation would also be important in this problem, not just natural connection. So that's an example problem involving natural connection from a vertical isothermal plane.