 In this lecture, what we're going to be doing is taking a look at some of the correlations that exist for quantifying the amount of heat transfer, the connective heat transfer coefficient when we have condensation occurring on vertical surfaces. And so what we're going to do, we're going to begin with a model that was developed by Nusalt. And we'll refer to this as being Nusalt's model. And then in the next segment, what we'll do is we'll go through some of the analysis that Nusalt did to come up with an expression for the connective heat transfer coefficient. So Nusalt came up with a model to be able to characterize what was happening with film condensation. And this developed a relationship for the connective heat transfer coefficient as well as the Nusalt number. And consequently, that is part of the reason why we name it after the fellow. But it was a very insightful type of analysis and it has enabled a lot of other researchers to use his functional relationship in order to collapse their experimental data. Now, obviously Nusalt's analysis only applied to laminar flow but what we're going to do, let's begin by drawing a schematic of what the problem looked like from Nusalt's perspective. And then we'll work a little bit looking at some of the relationships that were existing. And so we'll begin by looking at Nusalt's model. Now, he was doing a combination of force balance and as well, he was looking at dimensional reasoning, so dimensional analysis. But let's begin with the schematic for how Nusalt envisioned the flow field for when we have film condensation on a vertical plate. So what we can see here, this is the model that Nusalt used to come up with a relationship that enabled him to come up with a connective heat transfer coefficient. And first of all, just like before with our model, we had a representation for the thickness of the film, the condensation film, and that was denoted by delta. But another thing that he did is he looked at a differential element of fluid that would have been on the surface and he would have assumed that to be at some y location. So we'll have that at location y and then the thickness of that element he denoted as being dx. And and the depth here is B. So what we're looking at, if I was to draw this in three dimensions is we have a plate like that. The film is forming and coming down this way. And so that would be our film. Here is our plate and delta was the thickness and B was the width. Sometimes we assume it to be unit width here. We will assume it to be width B. A couple of things that he assumed. One was that there was no vapor drag. And so what does that mean? What what that is implying is that there is no shear on the surface of the film as it is forming and moving down. And so he assumed there is no vapor drag. Another assumption that he made was that the temperature profile. Let me do that in red. They the temperature profile was linear with position. And so that was another approximation that enabled him to simplify this scenario of what was going on. Last thing, I haven't drawn this yet, but he had the no slip boundary condition along the wall. And so what he was assuming there was velocity equals zero at y equals zero. So that was the model that new salt came up with in terms of developing an equation. And so what he did is he considered the differential elements. What we're now going to do we're going to zoom in on this little differential element here and we're going to look at the forces that are occurring on that differential element. So what we have here looking at the differential element. There are a number of different forces that are acting on the element to begin with. We have the weight of the element and that could be characterized by the density of the liquid. And then multiplied by the volume. And so we have delta minus y being the width or the thickness of this little differential element, the unit with B and then DX being our vertical and that was the weight buoyancy force is expressed in that manner. And then finally shear, there is viscous shear in the fluid and I'm going to assume that you is only a function of y and that's why I'm putting this as an ordinary differential. U is actually evolving and so it could be a partial as well depending on how you're looking at the analysis. But just giving kind of an order of magnitude perspective here in terms of what was involved. So what he then did is he looked at the downward force and said that that was equal to the upward force. And with that, he had a balance between weight and viscous shear plus buoyancy. Now I'm not going to go into details of how New Salt did his analysis, but you can look in many, many different textbooks on heat transfer and they will probably go through some kind of treatment in terms of covering how New Salt did his analysis. But what we're going to begin with in the next segment is some of the results that he obtained from this model and what it enabled him to do is start coming up with a relationship which then enabled him to build up and evaluate the convective heat transfer coefficient and then finally the New Salt number which is named after his analysis and that's the non-dimensional number that we use for convective heat transfer. So that's what we're going to be going in the next segment.