 In this lecture we're going to consider the topic of flow across two banks. The area of flow across two banks is of engineering interest mainly for the case of cross-flow heat exchangers. Now we are going to be looking at heat exchangers more extensively later on in the course, but for now what we'll be doing is we'll be looking at the case of external flow over two bundles or two banks. So it turns out that when you're looking at two bundles or two banks, there are two different types of configurations that you can have. You can have a case where the two bundles are aligned or you can have staggered. So let me just draw it out and that will help illustrate the difference between one and the other. So first of all what we have drawn here is the case of aligned or inline two bundles. And the second case is that where we have a staggered arrangement. So let me draw that. Okay, so what we can see here, some of my tubes don't look that good. Let me re-draw that one. Anyways, these are all supposed to be of the same diameter. But what we can see with the inline arrangement, all of the tubes are organized in a nice pattern where they all line up with one another. Whereas in the case of the staggered two bundles, what we find is that we do have rows and columns, but they are staggered with respect to one another. And that guy there is in the wrong spot. There we go. So with this, we can have very different flow fields. Before we look at the flow field, however, what I'm going to do, let me define a few things. On the diagram I've shown SP and SN. That is basically the spacing in the normal and the parallel to the flow direction. So SN is spacing normal to flow direction. And SP is spacing parallel. And in all of these diagrams, we're assuming that the diameter of the tube, each tube in the tube bundle is D. So D equals diameter. So with that, we can have two bundles with either arrangement. And what we're now going to do, we're going to take a look at some flow visualization that helps us understand or appreciate the differences in the flow in either the aligned or inline or the staggered. So what we're going to begin with is the case where we have the aligned or inline. And so there you can see two cylinders. We're adding two more. And we continue to add more and more cylinders. But what you'll notice for the inline or aligned, we have kind of a centerline jetting occurring between the tubes. And there we can see under different arrangements. It's quite prominent and evident that we have this jetting going on between sets of tubes. And then when you zoom in, you can see there's strong recirculation zones between the tubes themselves. And consequently, that has a fairly large effect upon the convective heat transfer that occurs. Now moving on, we can then look at what happens when you have staggered. So here we have one single tube that would be in a flow. And then we add two very similar to what we saw before. But then we add one in the middle. And you can see it starts to distort the wake of the previous two tubes. There we add two more and then another on the inside. And so the flow here is very, very different from that of when we had the inline or aligned tube bundles. And when we zoom in, we can see that the flow is undergoing fairly significant changes in direction. And again, there are strong recirculation zones behind the tubes, but not as large themselves. It then becomes instructive and interesting to look at comparing the aligned on the left and the staggered on the right. And that's where you can see more prominently the recirculation zone for the aligned between the tubes and smaller recirculation zones and significant changes in the flow direction for when we have the staggered tube bundles. So that gives us some appreciation for what is happening with the fluid mechanics and tube bundles. And consequently, we can expect that the convective heat transfer coefficient will be heavily dependent on the arrangement, the spacing, and the diameter. And so that's what we'll be looking at in the next couple of segments as we study tube bundles and convective heat transfer in tube bundles.