 Ok, in the last segment what we did is we solved a problem involving a heat source system. And what we did is we solved a problem where we had a planar slab. It was insulated on the left hand side. We were told that the right hand side there is natural convection taking place. T infinity and H describe that natural convective environment. The thickness of the slab or of our wall was L. The heat generation rate in watts per meter cube was Q dot. K was the thermal conductivity. And what we did is we came up with an expression for T of X. And that expression came out to be the following. And T1 here was the boundary condition of the temperature on the external surface of this wall. So what we're now going to do, we're going to pick some typical values that you may have for a wall with heat generation. And one area where heat generation often occurs is the curing of concrete. When you pour concrete it cures and the curing process is exothermic. So what we're going to do, we're going to pick some typical values, plug them into this equation and then we're going to plot up that function and see what it looks like. So let's write out the typical values for concrete. Now the curing rate we can say the heat generation is on the order of about 20 watts per cubic meter. We're going to assume our wall is 30 centimeters thick, so about 12 inches. The thermal conductivity for the cement mortar that we're looking at is 0.72 watts per meter degrees C. And the last thing we're going to say is the temperature on the right hand surface is about atmospheric temperature 25 degrees C. And if you recall when we came up with the formulation for this equation, we didn't use this boundary condition, we used this one. Had we used this boundary condition, we would have had to then input the conditions for the convective environment into our equation. But what we're going to do, we're going to take these, we're going to plug them into the equation. And when we do that, the following plot results. So let's take a look at that. This is what the temperature distribution looks like, resulting for our equation. Okay, now T1, that was right here, T1, and we can see that is 25 degrees C as it should be. So if I draw a line over, we can see that matches up there. Another thing that we can determine, and so this is going from, let me write it out here. This here was x equals 0, and this was x equals l, which was 30 centimeters. So the left hand surface here, this was the insulated wall. And if you recall when we derived the equation going through solving the problem, we said that if the wall is insulated, that means that q is equal to 0 in this direction. So if q is equal to 0 through Fourier's law, that then tells us that dT by dx at x equals 0 is equal to 0. So what does that mean mathematically, dT by dx is equal to 0? Well, that means the temperature does not change with spatial location. And consequently, you would then expect this to be a flat line or zero slope at this location. So dT by dx at x equals 0 is equal to 0, and that's what we're seeing in the plot. So that's good. The final piece of information that we can extract out of here is if we look at this point here, so if we were to take this slope here and then apply Fourier's law, that would equal, that would be q conduction. But if I was to put an energy balance there or do one of those infinitesimal surfaces and do the surface flux balance, what we could say is that that conduction then has to equal q convection, which we haven't done anything with here. But that would then go into q convective heat transfer, assuming that there's no radiation at 25 degrees C. There wouldn't be any radiation there. But anyway, so that gives us an example of applying energy generation. We derived this equation having the internal heat source. And once we had that knowing our boundary conditions, we're able to come up with the temperature distribution inside of a wall. And what we can see essentially what happens is the energy generation inside the wall causes the temperature to go up within the wall. And so that's essentially the net impact of the thermal generation that is taking place inside of a concrete wall while there is carrying going by. So that gives us an example of energy generation in a planar wall.