 Alright, in the last segment what we did, we took a look at a conical section with one dimensional conduction. We used the alternative method which uses Fourier's law for 1D conduction. What we're going to do now, we're going to look at cylindrical, so a system involving cylindrical coordinates, and for this what we have is a cylinder. Conduction is radial, which is what gives us the one dimensionality, so it's not going in the axial direction. We're going to assume that it is steady state, 1D, no heat generation, and the last thing, thermal conductivity is a constant, so it's not a function of temperature. So those were all the things required for us to use this alternative method. What I'm going to do, begin writing out a schematic and then we're going to apply it and see what we get when we look at doing this for a cylindrical coordinate system. Okay, so here we have our cylindrical coordinate system. We have some object and we're trying to determine the temperature at radial location r. The area, so what's happening, we have the center, the internal radius is ri, the outer radius is r0, so there's r0 and there's ri, and we're trying to determine temperature at some given location. Our thermal conductivity, we're told, is k in the material and ti and t outer are the boundary conditions for the temperature. The area in terms of what the heat flux is going through is going to be the circumference of this cylinder at a given radial location r, multiplied by the length, and usually you do per unit length. But anyways, that is the scenario that we have. Now what we want to do, we're going to follow a very similar procedure to what we did in the last example where we're looking at the conical section and we're going to write out Fourier's equation and we're going to introduce the area function that we have here and then we're going to integrate that from the inner radial location to this arbitrary radial location that we're determining things. So let's go ahead and do that. So there is Fourier's law, what we're going to do, input the area, we'll bring it over the left hand side. So we get that equation there, now we want to integrate that. So we have that and now, oops, I forgot a r, sorry about that. There should be an r there. So we're going to integrate that dr over r, the integral, that's natural logarithm. So we get that equation and just like before what we want to do, we want to isolate to get our t, an arbitrary radial location, r. So let's go ahead and do that. Once we get this equation here, now we're not quite home free yet and the reason is, is we still have the qr in there. So we need to determine that, how do we determine that? Well, we have our boundary conditions. We have ti at ri and we have t outer at r outer. We've already used this one. So now we're going to use that boundary condition. And when we apply that, we get for qr, we get this relationship here. So that then enables us to determine the temperature distribution and the heat flux in a cylindrical coordinate system. In the next segment, what we'll do, we'll take a look at applying this to a spherical coordinate system.