 When you're looking at heat exchanger problems, quite often it's beneficial to write out the temperature distribution as a function of position within the heat exchanger and acknowledging there are different types of configurations that we have. Quite often this is assuming that we have a double pipe type configuration, but it does help the student of heat transfer get an idea in terms of what is happening within the heat exchanger. So we're going to sketch out a couple, one with parallel flow and then the other with counter flow and take a look at what is happening to the temperatures as the fluid goes through those units. So what we have here is a schematic showing the case of parallel flow and we have a couple of different temperatures on here and first of all you'll notice the inlet to the heat exchanger is over here and we have our hot fluid coming in and a cold fluid coming in and typically what we'll do is we will label this t-hot in and this t-cold in and then this will be t-hot out and t-cold out and we will also have different temperature differentials one here and sometimes we will call that delta t at the beginning of the heat exchanger and then this delta t over here is delta t at location l. So that is the case of parallel flow with a parallel heat exchanger. Now let's take a look at what happens with counter flow. Now when we have a counter flow heat exchanger a couple of things that you will notice. First of all if you look at the cold fluid so it's coming in over here it can actually exit the heat exchanger at a temperature that is higher than the exit temperature of the hot fluid. So that is one thing when you have counter flow and if we look back on parallel flow that is not possible. The temperature of the fluid exiting for the cold stream is never going to rise above the temperature exiting for the hot stream. If you have a heat exchanger of infinite area they will come to the same temperature you'll get thermal equilibrium you never have a heat exchanger that way but theoretically you could think of it. However when we look at counter flow we actually can have the cold fluid going to a higher temperature than the hot fluid exiting and again we have temperature labels and nomenclatures. So for this one I would call this one t hot in and this would be t hot out and then this would be t cold in and t cold out and so that's a nomenclature that you'll see up here when I'm solving problems in an upcoming lecture and again we have temperature differentials here this would be delta t at zero and this here would be delta t at l. So those are cases of parallel flow counter flow. There are two other conditions that we can have when we're looking at the temperature distribution and those pertain to whether or not we have the fluid going through a phase change. So let's take a look at those two right now. So the first unit that we're going to look at this is a condensing unit and you recall from earlier lectures we've looked at the process of condensing and what is happening here is our cold fluid stream is entering so that would be t cold in t cold out and as our other fluid is going through a phase change process the cold fluid is heating up and consequently again we can have so and what you'll notice is t hot in t hot out could be an either one but it's not going to change because we're going through a phase change whenever we go through a phase change the temperature is constant so that's what a condensing unit would look like and I guess this could also be t hot in and that could be t hot in as well so it could be either way what we have here this is our delta t at zero and then this here is our delta t at l so that's a condensing unit and then finally the last one that we'll look at for the temperature distribution is that when we have boiling and so we can see when we have boiling what is happening is we have a fluid and it's losing energy so that would be t hot in t hot out and it is losing energy which is causing the phase change of the other fluid stream and so that would be at the saturation temperature I'll just do t sat but that would be the cold fluid stream in or out and what do we have we have temperature differentials here just like before so those are temperature diagrams sometimes it helps to draw them out I don't always do it because after solving a lot of these problems you start to just kind of you get a little sloppy I guess you could say but I will write them out when I solve the problems in the lectures okay so those are different temperature diagrams again they're helpful when you're trying to figure out what's going on in a heat exchanger and I do realize that when you get to the different types of arrangements like shell and tube heat exchangers or if you have aerial cooling units cross flow exchangers things can be a little bit more complex but still these diagrams do kind of give you some help in terms of understanding how the temperatures are with respect to one another for what we call the hot fluid and the cold fluid as well as the inlet and the exit temperatures for both of those fluid streams so those are temperature distributions what we're going to do in the next segment we're going to take a look at the overall heat transfer coefficient which is quite often used in heat exchangers and we will use it later on when we do the NTU analysis effectiveness NTU analysis but that will be what we'll be covering in the next segment