 In the last segment what we did is we took a look at the analysis that New Salt did for the convective condensation heat transfer on a vertical surface and what we're now going to do we're going to look at the correlation or the convective heat transfer coefficient that he was able to get out of that analysis and so he did make a number of approximations or assumptions in developing the relationship but what he was able to do is he was able to solve for the thickness of the film as a function of x and then he was able to get the convective heat transfer coefficient as well so he was able to get the film thickness the local convective heat transfer coefficient as well as integrate that to get the overall now looking at the film thickness this was the relationship that he came up with now keep in mind that this is for Reynolds number less than 30 so it has to be for laminar flow and that was raised to the power one quarter now we're going to see in a moment this value for the heat of vaporization it is going to be corrected so although this is what New Salt originally came up with he did correct that and we'll turn that into an hfg prime which we will see in a moment and so that is the one that you should be using for your analysis not just the straightforward heat vaporization you get in the tables but one that has been corrected and I'll get to that in a moment so that is the thickness of the film the local heat transfer coefficient is as follows and whenever there's a subscript L or V that refers to either the liquid or the vapor and the temperatures at which you evaluate these properties is important and we will see that in a moment so the local heat transfer coefficient now he was able to integrate that very much like we've seen for the in a collective heat transfer over flat plate for a lot of the ones that we've done we go through and perform an integration like this but if you look at the functional form hx is proportional to x to the minus one quarter and so with that you can go through and find that the average heat transfer across the entire plate is just four-thirds the local heat transfer at the end of the plate so what we're looking at here if I draw this in three dimensions we're looking at a plate of length l and quite often we will assume that it is unit or width b and so we have our film forming condensation forming like that and then delta obviously would be the thickness of the layer okay so that is the average convective heat transfer coefficient and then taking the value that we just had earlier basically you exchange x for l and so let me write that out and so this is for laminar flow and so this applies for the Reynolds number from 0 to 30 now you'll notice in here I put f that is denoting that the properties are being evaluated that that's the liquid properties but evaluated at the film temperature and and so I'll make a comment about that in a moment not all of the properties are evaluated at the film temperature the heat of vaporization is evaluated at a different one as is the vapor density so now the other thing that I had mentioned I said that this heat of vaporization that we see here and here new sold actually came up with a correction for that and and so I just want to make a comment on that but when you do your calculations use the corrective value do not use this value of hfg so when we do our calculations we replace the heat of vaporization that we get out of the steam tables with this corrected value hfg prime and the expression for that hfg prime is equal to hfg plus 0.68 times the specific heat of the liquid and then we have temperature saturated minus temperature of the surface or the wall temperature so this hfg prime is a modified value and again be careful it needs to be in joules per kilogram quite often the tables will listed in kilojoules per kilogram so you got to multiply it by a thousand when you pull it out of the table as the same exists for the specific heat of the liquid and that you would also get out of the tables but watch it is quite often listed as being kilojoules per kilogram kelvin so we have this corrected heat of vaporization and you use this in all of the equations that we have just looked at so which ones am I talking about here you would do hfg prime here you would do hfg prime so in new salt had done his analysis kind of simplified and this is a bit of a correction and then again i've already mentioned that they put hfg prime in that relationship so that is the modified heat of vaporization now where do we evaluate the properties well i was showing it here by putting the f the liquid property should be evaluated at the film temperature and so the film temperature is going to be your saturation temperature which would be the saturation temperature for the particular pressure that you're looking at plus the wall or surface temperature divided by two and the exception here except for hfg so the heat of vaporization and the density of the vapor those should be at t set so that is new salts correlation and quite often that would then be presented new salt let's see what would that be h l over k so h bar k that would be k the liquid l would be our vertical dimension that we would have for whatever we're looking at so if we're looking at a vertical plate that would be the length of the plate like that if we're looking at a big cylinder that would be the height of the cylinder so that is what l would be our characteristic dimension but anyways that is new salts correlation what we're going to do in the next segment we're going to look at correlations that in a way are based off of new salts analysis but they enable us to go to higher Reynolds numbers going into the wavy regime and then finally into the turbulent regime where you would have a turbulent condensation in your film forming on the cooled surface