 In the last segment we took a look at the solution to the 2D heat diffusion equation in the case of a square plate. In one case we had an unrealistic boundary condition and it resulted in a nice solution. In the other one we had a more realistic boundary condition and the solution that came out of that was an infinite series. What we find is if we look at a lot of different solutions to the heat diffusion equation there really are not that many for complex geometries that we would find in real world applications. Given that the net result is that if we are studying complex shapes numerical solutions are typically used to determine the temperature distribution in three dimensions within an object. You can also do time as well, it can be a transient solution but that is typically what is done if you have a complex shape. There are some cases where there is an in-between area that we can use things in. This is referred to as being shape factors. Shape factors still do have use in certain things. If you are looking at pipe flowing you do not want to do as an example pipe flowing and you do not want to do full complex numerical solutions along the pipe to model the heat transfer you could use something like a shape factor. That is what we are going to look at in this segment. Shape factors have been tabulated for a number of two dimensional shapes that are too complex to use the heat diffusion equation to solve. The nice thing about a shape factor is it gives us a quick and dirty way of being able to calculate heat transfer from one object to another. Let us take a look at shape factors now. What the shape factor is, it is a technique or a method that enables us to compute heat transfer between a certain geometry and its surroundings. The way that we do this is we have an equation q equals ks delta t. It is kind of like a Fourier's law but delta t is overall. What we have in here, k will be the thermal conductivity of the material that we are looking at. S is the shape factor and so S itself is the shape factor and k is the thermal conductivity of the material that we are looking at and delta t overall is the temperature difference between the two systems that we are transferring the heat between. It will make more sense when we look at an example problem. I said that this looks like Fourier's law but looking at it closer does have thermal conductivity but also looks like Newton's law of cooling so it is a bit of a mix between the two. But anyways that is the shape factor and so values of the shape factor are tabulated. You can find them in books for different shapes. I should call it objects because they are shape factors we are talking about but for different objects for example. So it might be a sphere buried below a surface and it is not very far below the surface. So here obviously we would not have only radial conduction going on. We have the presence of this surface and that is going to cause this to become a two dimensional problem versus just a one dimensional problem. So that can be an example of what you find with the shape factor. But what we will do next in the next segment is we are going to take a look at solving a problem using the shape factor but look at any textbook and you will find many, many different shape factors tabulated within the book.