 We're now going to take a look at a couple of different shapes with free convection. We're going to begin by looking at a horizontal cylinder and then we'll look at the correlation for a sphere. So what we're doing is very similar to the vertical plate that we've looked at before. We're considering the case of isothermal surface on an isothermal cylinder and just like the other ones we've looked at, properties will be evaluated at the film temperature and the correlations. There are a couple of different correlations that exist for horizontal isothermal cylinders. The first one is the relationship with the Rayleigh number and here I have the subscript F for properties evaluated at the film temperature, D is the diameter of the cylinder and what we have is C and I guess we could do Grashhoff-Prantle to the N, I'll do M, it doesn't matter. Or you could do C, Rayleigh number based on diameter to the M. And here C and M are from tables, I'm not going to go through what the values are. Any heat transfer book, you can probably find those values. So that is one correlation, similar to what we saw for the vertical plate and we also do have a relationship that applies and so let me give that correlation and this one applies over a wide range of Rayleigh numbers and looking at this form it is very very similar to what we saw for the vertical isothermal plate where we had the either the laminar or the turbulent correlation functionally very similar Rayleigh to the one sixth and then squares that gives us one third. So that gives an indication that this one will apply to a turbulent layer on the cylinder. And when you look at it what's going to happen, we have a cylinder and we'll have a stagnation point here but then we're going to get this film coming up and around and that is where the heated fluid is and so it's going to depend on the differential in terms of what the nature of that flow is going to look like but essentially that's kind of what the stream lines would look like if you were to look at the cylinder and the diameter here D and then T wall would be T wall or sometimes TS those are the same and then out here we have T infinity the free stream temperature. So that is the case of the cylinder now let's take a look at a sphere and for spheres for the case of a sphere the correlation that we have this one looks a little bit more like the laminar one so let me write it out. So there's the correlation and this applies for Rayleigh number based on diameter less than equal to 10 to the 11 so not exactly the 10 to the 9 that we saw for the vertical flat plate and parental number error and above so is 0.7 so anything above 0.7 and you'll notice the reason why I say that this is similar to the laminar is because we have the power of the one fourth on the Rayleigh number and that was what we saw for the vertical plate we saw with the power of one four that typically indicated that the correlation was for a laminar flow when we look here 10 to the 11 that's close to 10 to the 9 that we had for the flat plate but anyways. Now what would the flow feel look like here just sketching it it would be very similar to what we just saw for the cylinder so you're going to have a stagnation point there and then the flow is going to come up and around and depending upon the temperature differential you're going to have slightly different isotherms and streamlines coming along T infinity is out here and then obviously we're assuming that this is a constant surface temperature around the perimeter of our sphere so those are two correlations horizontal cylinder and a sphere