 Okay, in this segment what we're going to do, we're going to continue looking at the flat plate. However, what we're going to be doing is looking at that for a turbulent boundary layer. So if you recall from the end of the last lecture we talked about a fluid friction analogy or the Colburn analogy, that is the best thing to use if you're trying to determine the convective heat transfer coefficient for a turbulent boundary layer over a flat plate. And if you recall the relationship looks something like this. And what it enabled us to do was rely on a wealth of information that currently exists in terms of the friction coefficient for flat plate turbulent boundary layer flows. Okay, so what we're going to do, let's take a look at using the Colburn analogy for a turbulent boundary layer on a flat plate and this will be the case of an isothermal flat plate. Now for the turbulent boundary layer we have no analytical solution for the velocity profile. The only thing we have are basically curve fits for different types of turbulent boundary layer flows. You can take a look at my fluid mechanics course. I do have some information on how to try to determine the velocity profile for the turbulent boundary layer but we run into what is called the closure problem with turbulence and it has to do with terms that arise in the Navier-Stokes equations that we are not able to solve for the velocity profile when we have turbulence. And so this is an approximation that is sometimes used. It's a 1-7 power law and you can take that and you can couple it with a momentum, integral momentum analysis and use it to predict the boundary layer thickness. And there are a number of different ways that you can do this. In my fluid mechanic course I do this using a functional fit that von Karman came up with and I can't remember if it was a square or a cubic but anyways if you look there I go through a process of coming up with the boundary layer thickness but doing a similar sort of thing but using the 1-7 power law delta can be approximated to be. And remember this is a case where what we're assuming here is that we have a turbulent boundary layer starting right from the beginning. So in order to do that you would have to trip the boundary layers. Maybe you put a sandpaper or a wire on the front that would be X measured from that location there. So that gives us an expression for the boundary layer thickness but we're really after here we want to know the convective heat transfer coefficient and so for that what you do is you go and you use cold burn analogy and you find relationships that have been collected experimentally that characterize the friction coefficient. And so I'm just going to put one here and we'll work with that with the cold burn analogy but here is one for a skin friction coefficient and this is for a turbulent boundary layer and so CFX that denotes that it's the friction coefficient at a spatial location from the leading edge and we have a minus one fifth and so you can see they would use things we have similar sort of functional form that we had here but anyways that that is experimental data and this particular data set it turns out that it applies from the transition point up to a Reynolds number of 10 to the 8 so if you recall the boundary layer it's going to begin with the laminar boundary layer we go through transition and then it becomes turbulent and the turbulent boundary layer grows at a faster rate than the laminar boundary layer so this is our laminar boundary layer turbulent boundary layer and in this case what we're saying is that it only applies from the transitional for a flat plate typically we use 5 times 10 to the 5 for being the critical Reynolds number where we go through the transition process from laminar to turbulent but anyways that's not critically important what we're going to do here though we're going to take this skin friction coefficient and we're going to plug it into the cold burn analogy and we're trying to determine the new salt numbers so let's take a look at that so writing out the cold burn analogy that this is an expression that we had at the end of the last lecture and this was equal to it was equal to CFX divided by 2 so taking our friction coefficient and dividing by 2 we get 0.0296 so what I'm going to do now is I'm going to take these terms here and this term and bring them over to this side of the equation and what we then obtain is we get a new salt number that looks like this so that would then be an expression that we could use to determine heat transfer when we have a turbulent boundary layer and an isothermal plate and obviously isothermal the plate is going to be higher than the fluid temperature or lower but we're going to have heat transfer so there's some temperature differential driving the convective heat transfer process so that is an example of what you would do if you want to determine the convective heat transfer coefficient for a turbulent boundary layer you basically use cold burn analogy and you use the friction coefficient values plug it into cold burn analogy and then you obtain your expression you could do it experimentally as well and you curve it but why do it if you can easily get the values of CFX so that is the boundary layer what we're going to be doing in the next lecture is we're going to be looking at external flows on bluff bodies so cylinders spheres things like that and then after that we'll be looking at two bundles so multiple cylinders arranged in various patterns so that's where we're going for external force connection flows