 We're now going to take a look at a concept that is quite useful to use when you're solving problems involving heat transfer. It relates to the flux of thermal energy going through surfaces and what happens when you go from one surface or one material into another. And it's referred to as being the surface energy balance. So let's take a look at that now. And so what we're going to do, we're going to consider a scenario where we have a solid, so we have conduction, and then we have a fluid outside of the solid, we have convection, and then we have some surroundings. So we have radiative heat transfer. Okay, so what we have here is we have a scenario where we have a solid, and so the solid is shown here, so this here is all solid, and then we get to an interface where we then transition into a fluid, so there's a fluid outside of the solid, and then far away we get to some surroundings that is at temperatures surrounding. And when we're dealing with these types of problems, first of all we know that within the solid we have conduction, and we've shown the temperature distribution here, but we know that we have conduction coming through in this direction because it's going from the higher temperature to the lower T2. Now when we get to the wall, what's going to happen is the conductive heat transfer, or the energy flowing in, is going to leave via two mechanisms. One of these is going to be radiative, let me use a different color there, I will use red. So we will have radiative heat transfer, and we are also going to have convective heat transfer, and given that I put the fluid in green, what we'll do is we will put convection in green. So we have convection radiation, and so in solving these types of problems, it's often useful to draw a control surface right on the interface between where the solid transitions into the fluid, and so what I'm going to do, I'm going to sketch a control surface, I'll do that red so that it's easier to see. So what we're going to do, we're going to assume that these control surfaces exist on either side of the solid fluid interface, and we're also going to assume that they are infinitesimally large, so that the delta between them is sorry infinitesimally small, that they're right next to each other, they include no mass or volume, and so the control surface is going to be kind of a theoretical construct, but it's a very useful one that we can use for solving problems whenever heat is transferring from one media to another, and one material to another. So let's take a look at conservation of energy across the control surfaces, and so we know conservation of energy says Q in minus Q out is equal to zero, so we're assuming that this is a steady state scenario, so there's no build-up of energy, but even if it was, the control surface is infinitesimally small, so there would be no place for it to build up. But let's look back at our diagram here, so what is coming in? We know we have conduction coming in, and then what is leaving? Well we know we have radiation and we have convection, so those are the three things that we will put into this equation, so in here we can then rewrite what is coming in is Q conduction, and what is leaving is going to be heat transfer due to convection and heat transfer due to radiation, and those all need to sum to zero. So this is a very useful equation that can help you solve a lot of different problems. Basically it's an energy balance that you do on this infinitesimally thick surface, we call it a control surface, and we will use this while solving problems. Okay, so that is the idea, the control surface and the surface energy balance. What we'll be doing in the next segment is we're going to be looking at an example problem involving all three, conduction, convection, and radiation. We'll be using the energy balance in order to solve it.