 Alright, so we're continuing looking at the correlations for pool boiling and the last one that we're going to look at is the film boiling region. So we're looking at film pool boiling. And if you recall from our boiling curve, we had Qs double prime, delta Te for excess, and that's T wall minus T sat. And our curve, we go up, we hit onset of nucleate boiling, we go up, Q max down, and then up again. And this is the min, that's Q max, which we solved for in the last segment. And we also had something that enabled us to go from onset of nucleate boiling up to Q max, and that would be nucleate pool boiling in there, where you have discrete bubbles, and then you get jets and columns going up. But what we're going to look at now is what happens when you get up into this region here, where delta Te becomes quite large, because remember that this is a log scale here. And consequently, it might not look that large, but it is logarithmic, and consequently the delta Te's can be very, very large. And that's why when we get above the Q max, if you are in a power control versus a temperature controlled experiment, you could burn out. And we talked about that in the last lecture. But for film boiling, what we want to do is we want to come up with a way to be able to estimate the convective heat transfer coefficient in this region. And so the equations, if you're calling we have film boiling, we said that what happens is the bubbles start to coalesce along whatever surface we're looking at. But it's that coalescence that then gives us a film of vapor over the surface. And consequently, the mechanisms of heat transfer become mainly radiation. Radiation does dominate. But we're going to look in a regime where we both have convective as well as radiative heat transfer. And I'll show you an equation that you can use in order to estimate the amount of heat transfer that would be in this film region. So let's take a look at that. Now the equation that we use, that this is, we're looking for h bar. That would be the average convective heat transfer coefficient. Now we have an equation that combines the convective heat transfer plus the radiative heat transfer. And again, h bar appears. So in order to solve this equation, we're interested in that and we're interested in that. But we can't solve for it directly. So what we need to do, we have to do an iteration. So we have to iterate. But the first thing that we need to do, let's find out what this is and what this is. And then we would know that we can put them in there and go through and iterate in order to get the convective heat transfer coefficient in film boiling. So what we're going to do, we're going to begin with convective heat transfer. And for this, we have a new salt number. And you know what I'm going to do? I'm going to put it on the next slide just because I'm running out of space here. I don't want to have it all in one space. There we go. Okay. So very similar to the other expressions that we've seen for Qmax or even in nuclear boiling. But it's a little bit different. And first of all, this equation applies only to certain geometries. So it applies to cylinders and spheres. And the value of C, notice we have this constant here. And so a C depends upon the geometry. And it is 0.62 if we're dealing with the horizontal cylinder. And it is 0.67 if we're dealing with a sphere. Now the properties here, notice that we have both vapor as well as liquid. So let's begin with vapor. Vapor properties are evaluated at the system pressure. So be careful with that. And the reason why I say be careful about that is because if you're at atmospheric pressure and the temperature is 2, 3, I don't know, it would be higher. It would be let's say 400 Kelvin, 500 Kelvin, something like that. You need to have a table that would have the properties of steam or vapor in this case at that high temperature and atmospheric pressure. But you evaluate it at the system pressure and at the film temperature, which we saw quite often when we looked at natural convection as well as force convection. We've seen that many times before. So that is how you get the vapor properties. Again, be careful with HFG. We have a prime, which I'll define in a moment. But make sure that you work in joules per kilogram Kelvin. And I don't see the specific heat, but it is in here. I'll show you. It's in the modified value of HFG, which we just wrote out here. And nu is your, that would be the kinematic viscosity for the vapor. K is the thermal conductivity. The other properties that we have here, HFG and roll liquid are at the saturation temperature of the liquid that we have. I assumed it's water. It's not always water. And then HFG prime, that's a modified value of HFG. And is it expressed in the following manner. And that's where you have the specific heat of the vapor. And make sure you use that in joules per kilogram Kelvin. Or it will mess you up. Okay. So that gives us an equation that we can use to solve for the convective heat transfer coefficient. Remember, that's what we're after. Because if we come back here, we were looking for this right here. So we have an expression for that in this equation. And the radiation, that is the other term that we have in the equation. And so the way to determine radiation is with the following expression. That is the Stefan-Boltzmann constant. It is not the surface tension. Don't get that mixed up. Epsilon is the emissivity. And remember, when we're dealing with radiative heat transfer, these temperatures need to be in Kelvin. So that is how you determine HRAD. You take both of those. You take the value of H convective. And then you plug it into this equation here. And you need to iterate in order to solve for the value of H bar. Because that's what we want. And when you get that, you have then estimated the convective heat transfer coefficient in the film region, where we said that we have a combination of both convective heat transfer as well as radiative heat transfer. Okay. So that covers things for pool boiling. Now there is also force convection boiling. We're not going to cover it in this course because it gets quite complex. You're dealing with multi-phase flow. And as essentially the typical one that we would look at would be pipe flow. And there you would have fluid flow going through a pipe. But you would start with liquid flow. It would probably be turbulent. But you would have your liquid flow. But then eventually you're going to start getting bubbles forming. And then multi-phase flow is going to go through different regimes. And so we can have bubbles, dispersed phase bubbles. We can then go into slug flow, plug flow, where you might have vapor here and then a liquid. And then you can eventually get to a point where you have a corannular flow, where you might have a liquid on the wall and just vapor in the middle. And then you can get to a point where you get a missed flow and then you have entirely vapor. So it's a very complex process going through the transition for multi-phase flow. And consequently we're not going to look at it in this course. That would take quite a bit of time. And that could be a course unto its own. And then if you look at vertical multi-phase flow, the dynamics would be slightly different from what we just talked over here for horizontal. So anyways, that is force-convective heat transfer with boiling. We won't look at it. We only look at saturated pool boiling and the correlations are the ones that we've looked at in this segment and the previous one. So that concludes boiling heat transfer. From here we're going to be going into condensation, which is the flip side of looking at heat transfer where you have the phase change. Whereas in this case we're going to be going from the vapor back to the liquid. And that will be condensation heat transfer. That's what we'll be doing in the next few lectures.