 We're now going to take a look at the case of film condensation on the outside of horizontal cylinders and spheres. So the correlation that we'll be using is one that follows the correlation that was developed by Nusselt for the vertical plate. And if you recall the form that we had was the Nusselt number based on diameter. Here we will have the average heat transfer coefficient on be it a cylinder or a sphere and D is the characteristic dimension and you can see it there in the expression for the Nusselt number. And then there is a constant and that constant depends on whether we're looking at a cylinder or a sphere and from there then the relationship would be the same as what we saw for the flat plate. So that's the correlation and with this C is going to depend upon whether we're dealing with a sphere and if we're dealing with a sphere then C is 0.826. And if our problem is dealing with a horizontal cylinder then it would be 0.729. And again we have a modified latent heat of vaporization that's the one that is corrected using the specific heat of the liquid and the properties that are evaluated all properties are at the film temperature with the exception the density of the vapor and the heat of vaporization will be evaluated at the saturation temperature. So that is the expression that we can use for computing the convective heat transfer for film condensation on either a sphere or a horizontal cylinder. Now in the case of horizontal cylinders quite often what happens is these are packaged together into a tube bundle and that then forms condensing units which we saw an example of that in an earlier lecture when we're looking at engineering applications or real world applications. So taking a look at tube bundles so when we're looking at tube bundles typically we have n tubes horizontal so that would be the number going in the horizontal and we also have n tubes in the vertical direction and consequently this bundle would have n by n tubes. And what happens here is when we have condensation we would have film condensation coming around but then it drips and it goes down onto the next and so progressively the mass flow rate is going to build up and by the time that we get to the bottom we have a very high mass flow rate coming off of the bottom tubes and consequently the convective heat transfer coefficient for a single tube can be corrected for a vertical tier as we might have in this particular example here so this would be a vertical tier and the way that we correct for the convective heat transfer coefficient so we would have the convective heat transfer coefficient for n tubes in the vertical direction and in order to compute that what we do we begin by computing the convective heat transfer coefficient for a single tube and then we multiply it by the number of tubes in the vertical direction raised to the power minus one sixth and consequently that gives us a slightly modified convective heat transfer coefficient taking into account the fact that we had this vertical tube bundle and essentially what happens here is the convective heat transfer coefficient is going to drop down somewhat and the reason for that is if you think about the fact that as you get more and more condensate or condensed liquid forming around the outside of each of these tubes that then provides a bit of an insulating layer and consequently we would expect that the amount of heat transfer, convective heat transfer is going to be reduced as you get a larger and larger film forming around the tubes and so all of the tubes here would have this taking place and they would all then have a larger film developing around them so that is how you can handle or do calculations for the case of be it a single tube that is horizontal or a tube bundle or a single sphere and and so but this one here gives us the correction for the case of a tube bundle so what we're going to do in the next segment is we're going to solve an example problem of a condensing unit like we're looking here and and this would be referred to as being shell side condensation and the reason why we say shell side and sometimes we say tube side is because it is thinking of this in terms of a shell and tube heat exchanger where you have a larger cylindrical object and and that is essentially the shell and then on the inside you have all of these tubes and and and so in the case of shell side condensation that means the condensation is taking place outside of the tubes and it would be dripping as we have here now if it was tube side condensation then we would be looking at a condensing unit where we have the condensation occurring on the inside of the tubes and sometimes there'll be a little slope and the liquid will build up if you're to look at the cross section of this what's happening is you get the film building up on the inside it runs down the walls and then you get a layer of liquid forming on the bottom and so your film then is on the inside that would be tube side tube side condensation and this is shell side condensation so in the next segment what we're going to do we're going to take a look at the case of shell side condensation where the condensation is outside of our tube bundle