 Okay, in this segment what we're going to be doing is we're going to be looking at systems involving conduction where there is heat generation within the solid. And to begin with what I'm going to do is review the heat equation or the heat diffusion equation. So that there is the heat diffusion equation that we derived in an earlier lecture. And what we're going to do that will be the starting point that we will examine systems with heat generation within them when we look at conduction. But I'm also going to write out the other forms of the heat equation that apply to other coordinate systems because depending upon the problem sometimes the starting point would be either the heat diffusion equation in cylindrical or in spherical coordinates. So there is the heat diffusion equation expressed in cylindrical coordinates. And what I have done here is I've introduced a new symbol and this is one that we will find quite often with transient conduction and that is the thermal diffusivity. And it has the symbol alpha and it is defined as being our thermal conductivity of the solid divided by the density of the solid and the specific heat capacity of the solid. So that is the thermal diffusivity. We put it into the equation as 1 over alpha. And then finally looking at the heat equation in spherical coordinates. Okay, so that is the heat diffusion equation in three different coordinate systems. That's a partial differential equation and consequently in order to solve it we either use numerical methods or we reduce it significantly and solve it analytically. But that will be the starting point by which we will be looking at heat generation systems. So when we're talking about heat generation or heat source systems. So when we have heat source systems looking back at our equation, the heat equation, the place where we have the heat generation is the q dot over k term. And consequently for heat source systems or heat generation systems, q dot is not zero but it exists. So that is the heat generation rate. And the units for that are typically expressed in watts per meter cubed in Si. And the source of that internal generation could be from a number of different sources. It could be from a nuclear process. It could be from a chemical reaction. And the heat generation rate could be either positive or negative. So it could be an exo or an endothermic reaction. Electrical resistance heating or dual heating. And there could be others and I will just leave that as etc. So any any kind of process that exists where you have this generation, you need to address that in the way that we address it is through this q dot term. So what we are going to do now is we are going to work an example problem that considers a system with heat generation in a slab. And so that's what we'll be doing in the next segment. And then we'll plug in some values and take a look at what it looks like to see if it makes sense. But the place where we're going to start looking back here, we will start with a heat diffusion equation. Given that we're looking at a slab, we're going to be dealing with the one in rectangular coordinates. So that's where we're going in the next segment.