 so we're talking about the physical mechanisms of heat transfer and we're looking at conduction the first method of heat transfer and what we're going to do now is we're going to write out one of the equations that we quite often use when we're examining conduction and it is referred to as being the conduction rate equation and the equation that we use is Fourier's law and writing it out this is written in one dimension we can have it in three dimensions but we're writing it here in one dimension and that's why if you look here we have the little x that denotes the fact that we're in the dimension or direction x and we have this constant k a is the area and then dt by dx a gradient so what we're going to begin in looking at this equation we're going to write out a little schematic showing the temperature with diff the distance in a solid so let's assume that we have some solid and we have temperature and then we plot distance along the horizontal and if we could measure the temperature let's say we measure t1 here and then a little further into the solid we measure t2 and what we find is for one-dimensional conduction oops I didn't do a very good job of that this should be a linear line straight line so there we go that's a straight line connecting x equals 0 to x equals l t1 to t2 and then remember the heat is going to flow from the hotter to the cooler and consequently the heat transfer is going in this direction here and we will take a look at the different terms in Fourier's law we have qx that's referred to as being the heat transfer rate and that could be in watts or joule per second we already talked about that in an earlier segment the next term that we have is k k is the thermal conductivity of the solid that we have for the material that we have the heat transfer going through and the units of k are going to be watts per meter degrees C or it could be watts per meter kelvin and the next term that we have is the cross-sectional area through which the heat is being transferred through because that's the area of the surface and that will be in units of meters squared and then finally we have dT by dx that is the temperature gradient in the direction of heat transfer and that is what is driving the heat transfer to take place and the units there are degrees C per meter or could be kelvin per meter given that we're looking at a difference it doesn't matter if it's degrees C or kelvin so that is the Fourier's law it's a law and equation that we're going to use over and over and over again when we are analyzing many many different systems in heat transfer especially when we're looking at conduction so the different terms in Fourier's law and then that is for one dimension we'll get to a little bit more of a complex form of this equation when we look at the heat diffusion equation and there we would have it in multiple dimensions but for right now we'll consider it only in 1D