 Okay, so you've been talking about the convective heat transfer over a cylinder, and we said that the valangular has implications, and consequently the Reynolds number has implications into the nature of a heat transfer. What I'm going to do now is provide an equation that enables us to determine the convective heat transfer coefficient from a cylinder. So this is the case where we have heat transfer over a cylinder in cross-flow, so the flow is coming along like this, and depending upon the boundary layer, we saw that the separation could either be up here or down here, but anyways, we have this flow field coming over a cylinder, and the equation that we have, we express it in terms of a new salt number with the length scale being the diameter of the cylinder, so that would be the diameter there, and it's hd divided by kf, and I will define what f is. That's the film temperature, but I'll give you that later. You can express this in the following manner. What we have here, u infinity d over the kinematic viscosity, and that, again, is evaluated at the film temperature, and so this term in brackets here, you'll recognize that as being the Reynolds number based on diameter, and we raise this to the power n, and then we multiply this by the Prandtl number, again, evaluated at the film temperature, raised to the power one-third. So looking at this expression and this equation, what we see is we have these coefficients, c and n, and these would be obtained by conducting experiments, so what I'm going to do now is just write out the values, and we'll assume this here is red, evaluated at the film temperature. Okay, so that there is a table that you can use to determine the values of c and n that you then apply in the expression up here, and the thing that you can note is that these coefficients are a function of the Reynolds number coming over the flow over the cylinder. Here we have u infinity, a couple of other things to note. We have f, and we'll talk about that in a moment. That denotes the film temperature, but the main thing is just as the flow around the cylinder changes, the convective heat transfer characteristics will change, and like I said at the end of the last segment, there are expressions that can enable you to determine the value of h as a function of position as you go around the cylinder, but just like for the flat plate. If you recall for the flat plate, we looked at a situation where we could determine h as a function of x. Usually we're more interested in the average heat transfer across the plate, so same thing pertains or applies to the cylinder. We're usually more interested in the average convective heat transfer around the entire cylinder because that's what we use for engineering calculations. So the last thing that I want to comment on here is just the case of the subscripts. So the subscripts that we see, there's infinity, and that usually refers to free stream conditions, and what free stream means is that you're so far upstream of the cylinder that the presence of the cylinder, that the flow has not yet responded to it. So as far as the flow is concerned, there is no cylinder there, that's free stream conditions. f, that denotes the film temperature, and we'll use this quite a bit in heat transfer. Oftentimes properties were told to evaluate them at the film temperature. The film temperature is just the wall temperature plus the free stream temperature divided by 2, and I just said it w, that is the wall temperature. Okay, so those are some of the different subscripts that we have, and you may see R, E, D, F, that pertains to the fact that you're evaluating Reynolds number based on diameter with properties evaluated at the film temperature. When we look at Reynolds number, there are a couple of different ways that you can express it, roll U, D over mu. The properties where you have to worry about temperature then would be the density and the viscosity, or we can also sometimes see it expressed in this manner like I did on the previous slide. There, the only thing that you need to do is that would have to be evaluated at the film temperature. That is our kinematic versus the dynamic viscosity. So anyway, that is the equation that you can use to calculate the connected heat transfer on a cylinder. There are other equations that you can find in different textbooks, but the one that I gave you is one that is quite often used, and it's quite simple and straightforward to apply.