 Okay, what we're going to do in this segment, we're going to solve another example problem using LMTD again for a shell and tube heat exchanger. So I'll begin by writing out what is known. Okay, so what we're dealing with is a shell and tube heat exchanger where we have one tube pass going through our shell and tube heat exchanger and we have the area given the overall heat transfer coefficient inlet temperature, exit temperature for the liquid being water coming through and then we have gas actually coming through on the other side and that is coming in at 260 degrees C. We don't know the exit temperature but we do know the mass flow rate. So things look okay in terms of what we have been given and what we're told is to find the mass flow rate of water. So what we're going to do, let's do this, try solving it using LMTD and we're going to have to look up an F factor as well. So let's begin with the temperature distribution. That can often bring some clarity to what is going on with a particular problem. Okay, so when we're looking at the temperature diagram we can say this is TC2, this is TC1 and this is T hot 1. Now we don't know the exit temperature of our hot fluid stream so it's going to be somewhere in here. So we'll put question mark equals TH2 and then that means that we're going to have some kind of line drawn and the fluid stream will assume that it's counter flow going in that direction. So that's a bit of a problem. We don't know what that temperature is on exit. Let's take a look now at what equations we have that we can work with. Okay, so those are the equations that we have. Now what do we know here? We know U, we were told the area A, we don't know F because we don't know one of the temperatures on the exit, that is for our hot fluid, and we don't know delta Tm, we can't evaluate that because we need that exit temperature. Now what else do we know? We know the mass flow rate of air. Now with that we cannot determine this because usually we have to get the average to get the value of Cp and for the air we know this, we don't know that, and then for the water fluid stream we know both temperatures, that's good, we can get the average value of this specific heat and we don't know the mass flow rate of the water, that's one of the things that we're after. So all of a sudden we're faced with a problem where we've got a lot of unknowns in here and our normal tools and techniques that we use in order to evaluate Q and then solve for mass flow rates and then go through are kind of blocked with this problem. So we don't know what mass flow rate of water is, that's what we're trying to solve in the problem. We don't know the exit temperature of our hot fluid stream, therefore we cannot get delta Tm, we don't know that, and finally if we do are able to get a correction factor for this we can't determine that either because we're missing one of the exit temperatures. So how do we solve this type of problem? Well unfortunately the only way to solve this is to guess a temperature on exit, so you would guess h2 or th2 and you would solve and iterate and this is going to be a bit of a problem for a number of reasons. The delta Tm, if you look in there we have the natural logarithm and so that's a non-linear equation, you have to do trial and error in order to get the root of that equation and so this is kind of a very laborious approach to solving a heat exchanger problem. There is a better way and that is what we will look at starting in the next lecture. Solution technique number two, so if we call this number one, solution number two is to use the effectiveness NTU which is the number of transfer units method and sometimes it's just called the NTU or number of transfer methods. I unfortunately call it epsilon NTU because this epsilon but it's really effectiveness. But anyways that's where we're going to go in the next lecture. We're going to look at this new method which enables us to solve problems that look like this where we have all of these unknowns and we cannot directly apply LMTD if we have no way of determining all of the inlet and exit temperatures of our fluid stream. So that's what we're going to be doing in the next lecture.