 We're now going to take a look at some of the correlations that exist for pool boiling. And if you recall, in the last lecture we introduced the boiling curve and that will be the basis of what we will be looking at here. We have delta Te on the bottom. We have our heat flux, so that was the excess, that was T wall minus T sat, where T sat is a saturation temperature. And we started off, let's see, in here we would go up and then we hit onset of nucleate boiling and that was point A on our curve and then we would curve up and over, down and then up again. So that was the boiling curve that we looked at. And then we said that this here was point B and then this was point C where we have our maximum heat flux or the critical heat flux. This down here was point D and then when we go up here that becomes film boiling. So now if we operate down in this region here, this region would be prior to the onset of nucleate boiling and so the convective heat transfer correlations there would just be simple natural convection. So we're not going to cover that, that was covered in another section or other lectures of the course. But that would be natural or free convection. What we will do, however, is we're going to look at relationships that enable us to determine what is going on in this region here, we'll also come up with a relationship that enables us to determine the critical heat flux there. We will have another relationship that enables us to get the minimum, so that is Q min, that's the Leidenfrost condition, and then up here we have Q max. And then finally we will have relations that enable us to determine what is happening when we have film boiling occurring, which would be up here. So we're going to look at correlations for those different regions and we will begin with nucleate pool boiling. So for nucleate pool boiling we're from A to C on the boiling curve and the relationship for the heat flux in the nucleate pool boiling region is as follows. So this equation is referred to as being the Rosenau equation and it is one of the most widely used equations for pool boiling and in this equation all properties are evaluated at the saturation temperature and what you'll be doing is you'll be using steam tables in order to find all of the different properties because you need both the liquid and the vapor and so the steam tables are convenient for that. L in this equation denotes liquid and then V denotes vapor and you're going to have to do a little bit of a mental gymnastic when you go to the steam table because steam tables will have different subscripts for either a gas or the liquid. And delta Te, that was our excess temperature, which is T wall minus T sat, where T sat is the saturation temperature at the operating pressure. And the other thing that we have in this equation, notice we have this CSF and we have N, those depend upon the material, so the solid material as well as the liquid, and you get those from tables in your heat transfer book. So a few things to point out about this equation, sigma that is the surface tension, but the things that you might want to be careful with, H F G, H F G, when you put it into the equation and put it in joules per kilogram kelvin, you'll probably read it out of the table in kilojoules per kilogram and it will mess you up if you don't use it in joules per kilogram kelvin. Another one, the specific heat capacity of the liquid, again use that in joules per kilogram kelvin, if you don't it will mess you up. And those I think were the main things, G is the gravitational constant, and yeah, that's probably all that we need to worry about for that equation. So that is the equation for a nucleate pool boiling going back, so that enables us to handle anything in this region here. We now want to look at the critical heat flux, so let's look at what correlation exists for that point. So this is the equation for the critical heat flux, and as before, all properties are evaluated at T sat, and notice in this equation that we have this constant C, so let's make a comment about that. So C is going to vary between 0.13 and 0.149 depending upon the shape that we are doing the calculation for, and again like before, be careful with HFG, make sure that it's in joules per kilogram kelvin, and surface tension, gravitational constant, those are all pretty straightforward. Now the next point that we're going to look at, let's go back, we're going to look at the minimum heat flux which is occurring down here, so let's look at the correlation for that. So this is the equation that we have for the minimum heat flux, and if you compare this to the max heat flux, the equations look very, very similar, flip back and forth. The only thing different is with the minimum heat flux we're dividing by the sum of the liquid density and the vapor density and then squared, and however it is a little bit more restrictive in terms of the types of shapes that it applies to. As before, all properties are evaluated at T sat, and the equation, the value of C is 0.09, and that is for large horizontal plates. Okay, so those are some of the correlations that exist. We looked at, from the onset of nucleate boiling all the way up to the maximum heat flux, and that was for just a straight nucleate pool boiling in that region. We looked at the maximum heat flux, and we looked at the min. In the next segment what we're going to do, we're going to be looking at the heat transfer in this region here. We're not going to do it in this segment right now because it's a little bit more complex, but that is what we will cover in the next segment, and then we'll have completed looking at the correlations for boiling heat transfer.