 We're now going to take a look at a thing called the boiling curve, and this was based on an experiment that was done by a fellow named Nukiama back in 1934. And what this experiment enabled Nukiama to do was to identify the different regimes in saturated pool boiling. So if you recall that is pool boiling where there is no force convection, it's just natural convection, similar to the stove top experiment that we looked at in the first segment. However, the temperature of the liquid is at the saturation point or saturation temperature of the fluid at whatever particular pressure. Now what Nukiama did is he took a container, so he took a container and he filled it with water and he took the container or the water up to the saturation temperature. But there was a wire going across this container and through that wire he sent a current and by measuring the voltage drop and knowing the current he was able to get information in terms of the heat transfer with that particular wire. And if we recall power is equal to, that is going to equal the heat transfer from the wire is equal to IV, so the current times the voltage, P equals IV, power Q is equal to IV and also through Ohm's law we know V equals IR and from there we can obtain an expression for the resistance that is going to be the voltage divided by the current and so for his experiment he was able to measure the voltage, he was able to measure the current and from those two he was able to compute the resistance but with wires the resistance is fairly easy to figure out what the temperature of the wire would be once you know the resistance and so he used one of those relationships and that enabled him to get the wall temperature because the temperature of the resistor or of the wire I should say is going to be a function of the resistance and so he used one of those relationships and that enabled him to get the wall temperature and he also knew the power going in, Q and he knew the dimensions of the wire and so he was able to get heat flux that way so he was able to get Q over A as well and this experiment is what we would refer to as being a power controlled experiment and what that means is he was able to vary the current going through the system but he was not able to vary the temperature, the temperature just occurred based on the voltage and the current flowing through the wire and so he was able to control the power going in but he was not able to control the temperature of the wire so what we're going to do we're going to take a look at the boiling curve that Nukiyama was able to get by conducting this experiment and it will give us a lot of information about saturated pool boiling. Okay so this is a curve a boiling curve now Nukiyama was not able to get this entire curve he was actually unable to get this section here and that would only be you'd only be able to get that if you were to do a temperature controlled experiment instead of a power controlled experiment but a few areas or points that that I want to point out and we'll describe other ones throughout the rest of this segment but first of all this points up here at point C this is the critical heat flux and that had a value of Q max double prime another one is down here at point D this is where we have the minimum Q and this is called the Leidenfrost point and the Leidenfrost condition if you've ever taken a droplet of water and put it on a really hot stove you see that it kind of bounces around and skips around and it's because of vapor develops underneath the droplet and consequently it is free to move around that is the Leidenfrost point there where you have the vapor between the solid and the liquid and other things that I want to point out from a Delta Te remember that's the excess temperature if we look from one to five so in this range right here this is referred to as being free convection heat transfer and what is happening there just like the video we watched when we saw the natural convection taking place in the pot before the bubbles started to form that's what is happening between one to five with the excess temperature and then we go into a region that goes from an excess temperature of five up to 30 we get a new regime forming in there and so this would be where we have nucleate boiling and so what is happening there is bubbles are starting to form at nucleation sites and from five to ten those are isolated bubbles let me do that with a different color so from five to ten in this range here those are isolated bubbles and then from ten up to thirty that is where we get another process taking place and that's where the bubbles start to coalesce with one another and what we then get are jets and columns and so you could see that in the video as well the bubbles would start to communicate with one another and connect and they move up into pillar like structures now it when when you're watching in the high speed it didn't look that way and that's because you do have isolated bubbles going up but they do connect into one another with the weights that they have behind each of the bubbles so this is a region where we have jets and columns and then we get up to the critical heat flux point we then move into a regime that Nukiyama was not able to investigate and that is going up to the Leidenfrost point and I said that he wasn't able to do it because he did a power-controlled experiment he would have had to have done a temperature-controlled experiment in order to investigate that and this region is referred to as being transition and what's happening here is we're starting to get a film forming around our surface and so we get bubbles moving into a film and then finally when we go above the Leidenfrost point that's when we have film boiling and then radiation becomes very important but we'll be looking at that and describing it as we go on through this segment so what I want to do I'll refer back to this plot but this is the boiling curve and we're going to look at each of these different areas and I'll provide a description for each of the different temperature or differentials so to begin with we had free convection and that's for excess temperature less than five and here we saw that this is just natural convection taking place within our pool and then let's see did I put this on the curve oh and B I did good okay this is the onset of nucleate boiling that's what only B stands for and essentially what that means bubbles bubbles start to form and sometimes they make it to the top sometimes they don't but they start to enhance the amount of convective heat transfer on the surface because remember I said bubbles as they move up they train liquid from around them and and so we can move through isolated bubbles that's where we will start and we saw this in the video we had isolated bubbles forming and this is when we start our pot started to make noise and so you could hear it with the sound and what was happening is bubbles would form and sometimes they would then collapse if they didn't have enough of a temperature but the range here anywhere from excess temperature of five up to ten those are isolated bubbles and then we moved into jets and columns they appear to be jets and columns although they could be discrete bubbles like I said before you can see that with a high-speed video which Nukiyama obviously didn't have when he did this experiment back in 1934 got to give these guys credit for the amount of information they were able to extract with such rudimentary equipment they didn't have cell phones to distract them all the time so they're able to focus okay so those are jets and columns and then we get to point C point C was the critical heat flux point and in the next segment it will become a little more evident why we call this critical and this is for Delta TE approximately 30 and when Nukiyama was doing his experiment this is where his experiment went a little sideways and things didn't go very well for him and I'll talk about that in the next segment and then we move into transition boiling so we would only be able to get here if we were doing a temperature controlled experiment not a power controlled experiment like Nukiyama and this is Delta XS Delta TE from 30 to about 120 hopefully that's what I had on the plot let's see 30 yeah that's not too bad transition that looks like about 120 right there okay that is estimating a log scale which is hard to do and what is going on here is we're starting to get an insulating layer of vapor forming around our solid and what is happening is the bubbles are forming the vapor is forming and and they are coalescing and starting to form this insulating film of vapor obviously I was not able to get that on the stove top because we remained in jets and columns and individual bubbles going up and this is where on our boiling curve Q double prime or the heat transfer is actually reducing and this takes us to the Leidenfrost point but if you're to look at your wire what would happen is you start to get bubbles that are connecting with one another and so around your this is for Nukiyama's experiment we get this film and and so connected here might be the bubbles coming out but but they're all starting to merge with one another and when they do that you get this insulating film and this insulating film is the vapor itself and with that you're not bringing being able to bring in liquid in order to bring the surface back through the convective processes that we're looking at before and so convection becomes less and less being the main form of heat transfer we start moving into radiative heat transfer and and then eventually we go through transition boiling and as you increase the temperature the excess temperature we get film boiling and that would be for excess temperatures 120 degrees or more and so when we get up into this range what happens is any kind of increase in heat transfer looking at our boiling curve remember we came up we did this sort of a thing we come down and we do that where we're talking about this region in here going up and and so what's happening this is our critical heat flux this is where we were in transition and then here we have film and so what's happening in in this film region is the increase in heat transfer is due to radiation because if we look at our wire our wire would be completely blanketed with this vapor film and consequently the convective heat transfer has been minimized and the temperature of the wire is going up and then it becomes radiation radiative heat transfer and and so our temperature if you recall this is delta te here can start to go up relatively quickly as we increase the heat transfer watts per square meter so that is the boiling curve and what we're going to do in the next segment which will be the last one for this lecture we're going to take a look at what happens when you operate in this zone and and the troubles that it caused for new kiyama when he was doing his power controlled experiment