 The last thing that we're going to take a look at in this lecture is the relationship between the new salt number, which we just saw, we came up with an expression for the new salt number for a vertically heated flat plate, and the relationship between that and the non-dimensional numbers that are important for free convection, a new salt number, obviously being one of them, but typically what we find is that the new salt number, and so let's assume that we're expressing this in terms of the length of a plate, it is going to be a function of a number of different non-dimensional variables, the Reynolds number being one of those, another one would be the Grashof number, and that is the non-dimensional number that fell out of our non-dimensionalization of the governing equations, and then finally the Prandtl number, that is an important number, again we saw that for a force convection, it pops up again with natural convection, it's basically a ratio of our viscous to thermal diffusion, and so what we have here is we have, depending upon the Grashof number and the Reynolds number in the ratio of those, we could be in different types of flow regimes, so to begin with, if we have the Grashof number, remember the way that we got the Grashof number, we multiplied our governing equation by Reynolds number squared, that's why we're dividing the Grashof number by Reynolds number squared here, but if this ratio is approximately equal to one, we have a flow regime that is referred to as being combined free and force convection, and consequently for this we know that the new salt number is going to be a function of all three, the Reynolds number, the Grashof number, and the Prandtl number, if we have a flow where the Grashof number divided by the Reynolds number squared is much less than one, that would be a higher Reynolds number flow, and that would mainly be force convection, and here what we could say is our new salt number would be a function of Reynolds number and Prandtl number, and then finally if the Grashof divided by the Reynolds number squared is much larger than one, that would be mainly free convection, and in that case the new salt number is going to be a function of the Grashof number and the Prandtl number, so those are some of the orders magnitude analysis that you can do when you're looking at this and finally one thing to say, we did come up with a correlation or a relationship for the new salt number for a vertically heated and constant temperature flat plate, but typically what we often do is we will use empirical relationships, and the reason why we do this is because quite often the shapes aren't as simple as just being a vertical plate at a constant temperature, and the relationship that we use here is you'll see the subscript after noting that you're evaluating the properties at the film temperature, so we use these coefficient C and M, and the film temperature is T infinity plus T wall divided by 2, or if you're using TS for the surface temperature and be divided by 2, same thing, and another thing that we have here C and M are in tables, so look in your heat transfer book and I'm sure you'll find them, and the final thing is notice that in the equation here we have Grashof times Prandtl, that is a non-dimensional number that is often appearing when we're dealing with natural convection, and sometimes what happens is that that is combined together into a new non-dimensional number referred to as being the Rayleigh number, heat transfer loves non-dimensional numbers, we have a lot of them in heat transfer, but it's the Grashof times the Prandtl and that gives us the Rayleigh number, and you'll see the Rayleigh number quite often in correlations for free or natural convection, so that's a bit of an order of magnitude analysis between free convection, forced convection, and combined free and forced convection, and it turns out that it is quite often difficult just to have pure free convection because you do often have mechanical forcing, people walking by, there might be ventilation in a room or something like that, and so it can be challenging just to have natural or free convection, you usually are in this combined mode, but anyways what we've seen here is the way to be able to figure out orders of magnitude, and when either the free convection or forced convection would be applying.