 We're now going to conclude this lecture by looking at correlations where the film thickness is unknown. If you recall from the previous segment, we were looking at correlations for either a vertical plate or for a vertical cylinder where the radius is much larger than the film thickness. We needed to know the film thickness in order to compute the Reynolds numbers. What we're going to do here, we're going to come up with alternative correlations that enable us to handle problems where we may not know delta. What we have here is a different definition for the Reynolds number, and you'll notice there is this capital P that I have in here. I haven't talked about that yet, but that is a dimensionless parameter, and it is defined in the following manner. So what we have here, within this, this is the thermal conductivity of the liquid. These are length scales. Remember, if we're dealing with a vertical plate like this, the length of the plate would be like that, or if we're dealing with a very large cylinder, the length would be the vertical extent like that, and the diameter here, and this would be the case where r is much larger than the film thickness that would occur at the bottom of the plate. So when you solve these problems, you have to double check to make sure that that assumption is appropriate, if you're using this for a vertical cylinder. But that is what L is, and then we have our modified heat of vaporization that has been corrected with the specific heat of the liquid, and the other thing we have, we saw this earlier, this was in the New Salt Number relationship, and remember, that is our kinematic viscosity, which is mu L divided by rho L. Okay, so we have this value of P, and now what we're going to do, we're going to look at relationships for laminar, wavy, and turbulent that use this, and so we get that relationship there, and this, remember for the Reynolds number, it applies if the Reynolds number was less than 30 here, P needs to be less than 15.8, and that would indicate that we have laminar flow. For the wavy flow region, P is going from 15.8 up to 25.30, and then finally, we have turbulent, and just like we saw in the previous segment when we got to turbulent, it included the parental number, and so this applies if P is greater than 25.30, and it also applies for parental number of the liquid greater than or equal to one. So those are three different relationships that we can use to determine connective heat transfer, or other things that we might be trying to solve if we have a problem of condensation on a vertical surface, be it a plate or a large cylinder, and where the axis is aligned vertically, and this is going to be used with the following equations. So we have Newton's law of cooling, and we saw this earlier on, and be careful with the area there, remember that is the wetted area, and so what I'm referring to, that would be the perimeter times the vertical length, whatever the length scale is, and the perimeter would be pi times D if it's a vertical cylinder, and it would be D if it is a vertical plate, so perimeter equals B for plate, or pi D for cylinder, and that's vertical cylinder. We'll look at horizontal cylinders in the next lecture, that is for the vertical plate. Okay, so that's Newton's law of cooling, the other thing that quite often we're asked to solve for, or we might be interested in, is the mass flow rate of the condensate coming off of our condensing system. So for that you take your overall heat transfer, and you divide by the modified latent heat of vaporization, and then that is equal to the following, okay. So what we've done, we've looked at Nusalt's derivation, his model came up with any expression that enabled us to calculate the connected heat transfer coefficient for condensation on a vertical plate for laminar flow, and then what we did is we've extended that from laminar into wavy, and then finally turbulent. We have different relations depending on whether or not you know the thickness of the film. So that is coverage for the vertical plate and the vertical cylinder, and what we'll be doing in the next segment, we're going to be looking at horizontal objects, mainly cylinders and then two bundles, which would be quite common if you have shell side condensation in a condensation unit. So that will be what we'll be looking at in the next lecture.