 Good afternoon. We will get started with the last topic of this course, which is essentially related to phase change heat transfer. So, during the interaction with coordinators, they express the desire that you know please include boiling and condensation. So, the both boiling and condensation are essentially related to two phase heat transfer, which is actually a little bit more involved complicated than single phase heat transfer. So, what we are going to do is in about 1 hour, 1 hour, 10 minutes we are going to talk whatever we can about boiling. Tomorrow morning in another hour or so, hour, hour and a half we will talk about condensation and that is probably what you will need as far as an undergraduate curriculum in heat transfer is concerned. But equations and all those solving of problems is not what we are aiming to make you understand here. What we are trying to say is whether it is boiling or condensation, when I have two phases of either the same substance or a different substance. Let us say air water, water and steam or if you take oil pipelines for example, it will be crude oil, it could be water, it could be vapors of crude oil, it could probably even be some air. So, I could have multiple two phases of different substances and the liquid phase could also be consisting of two different substances. So, such flows necessarily exist in nature, they are very involved complicated to deal with if you want to go from first principles. We are not going to deal with solid liquid or solid gas kind of flows, we are not going to deal with that sublimation or anything like that. What we are going to do is deal with liquid vapor kind of flow situations. By liquid vapor kind of flow I mean it could be air water, it could be water and steam or any fluid and it is corresponding vapor that is going to be involved. So, two fluid one is the liquid phase, other is the gas phase. So, we are going to deal with liquid gas phase heat transfer. So, let us with that brief introduction let us get started. So, liquid vapor heat transfer, so liquid vapor heat transfer is what we are going to deal with. I will spend the next 5 to 10 minutes maximum to give you see the aim is not to say oh this is so difficult. So, you know so hard to deal that is not the aim, but I want you to appreciate the difficulty or the complexity involved in this whole scheme of things just by the presence of one additional phase. So, what is liquid vapor heat transfer where you have and in this course we will restrict ourselves to situations where the vapor corresponds to the same physical substance. So, water and steam is what we are going to. Boiling. Boiling that is why I have told 310, 310 is what I have told them. So, what do we understand where are these situations condensation is one extreme, other is boiling. All of us have seen condensation in during winter months you will see that you will have condensation of dew. Dew is liquid droplets you will see condensation of dew on in your glasses so on and so forth. If you go into a hot like you know if you go to a room which is very hot from a cold environment there you will have condensation. So, condensation is one branch where you would see on a surface there could be several droplets which are formed and these droplets eventually will slide down like a film. So, it will glide down the surface like a film. What we will cover now is related to boiling, but the physics meaning the complexity related to both these are similar in nature. Boiling is a little bit different from condensation but whatever we are saying is the same. Boiling is of two types. One all of us would have boiled water for making a cup of tea. So, that geometry is essentially what we call as this is there here already is of two types one is pool boiling and other is flow boiling. Pool means what? I am just having a stagnant liquid and I am changing its temperature by some external heating which is causing it to boil. Now, what is boiling? What is evaporation? These are two different things. Evaporation is happening even at room temperature meaning if you go to the lakes for example, the lake water will decrease during summer. It is primarily because of evaporation. It is not reach boiling point, but it is there is a what we call what we understand as evaporation. There is no bubbling, there is no agitation of the water or anything like that. Just it is a surface phenomena whereby water is going to get transformed into vapor phase. Boiling on the other hand all of us when you make tea we would have seen water at 30 degrees from the tap you put it on a vessel and start heating it. If you keep the gas sufficiently low let us do it let us do experiments slowly. So, you will see the water is starting to boil water is starting to get hot after a while you will start to see some vapors coming out. You will not see any bubbles or agitation of the liquid. So, this vapors coming out even after the temperature has reached hardly 50, 60 degree centigrade that is what we observe normally. Then if I proceed to heat it further at some point of time during this heating process what I will get? I will if you have not done this experiment I urge all of you to go and make tea one day and let there be sufficient time to observe this. If this is my liquid and I am supplying heat and if you have a transparent vessel you know this thick baking vessels that you get if you can keep that on a stove or the electric induction heater that will that way you can observe what is happening, but even a stainless steel vessel is ok. So, what you will see is initially you will see some kind of vapors coming out and within the fluid also you will start to see some kind of currents like thing. After this is that initial some time next after some time you will start to see one small bubble which will be formed. This small bubble will be there for some time and then it will just collapse. All of us have seen this then another bubble will be formed somewhere else it will also collapse. So, I am continuing to heat I am not change the boundary condition. Then what will happen after some more time if you have continued heating if you are measuring temperature we are going to see the temperature bulk temperature of the liquid is going to increase. What is happening? Natural convection only is happening whatever we studied in single phase natural convection is what is there water here is becoming hotter water here was cooled there is a convection pattern which is set up natural convection is set up here because of which ultimately when you see everything is at uniform temperature. When you make tea also when we cool tea in a room in a room we just leave it we think it is cool when you just take the first sip ok, but bottom is still hot because the convection pattern has not made the temperature uniform. So, when you start having this first before the bubbles are formed this will continue even when the small bubbles are formed it is not the natural convection is dying of it natural convection will be there. What will get started is that as temperature of the liquid increases tea increases with time with supply of heat you will have this bubble form this bubble will collapse another bubble will be formed it will collapse little more time you give you will see that if I take the top view of this vessel I will see bubbles forming leaving forming collapsing and this frequency will increase quickly they will start forming collapse will happen then suddenly what you will see there is no more collapse will happen you will see one bubble which is becoming slightly large rising to the surface and then collapse some which is just formed there nucleus we will call this nucleation it will just nucleate and it will collapse after some other time when the bulk mean temperature bulk temperature of the fluid is increased a little bit more this bubble will rise up some bubbles will rise up and will travel to some height and then collapse collapse means what it is getting condensed why it is getting condensed because this temperature is higher than this this liquid here is somewhat still lower than saturation temperature. So, when this interface meets a cold liquid it is going to get condensed it will collapse this is what happens here initially, but now because the bulk fluid temperature has increased with time the lower temperature regions are only primarily up and when it rises up it encounters one such layer and it collapses. So, many such locations you will see this bubbles forming and suddenly after a while you will start that the entire vessel surface you start getting bubbles. So, this essentially all of us are observed now if you have turned the gas on very high you want to make it very quickly. So, what you do you take the turn the gas on very quickly you will suddenly see the same water which was at 30 degrees you will see suddenly you will see lot of bubbles generated at the same time basically all these things you do not allow to happen you quickly raise the temperature the region here becomes very hot very quickly. Another thing that we have seen is this is all this comes under what we call as pool boiling there is no bulk movement of the fluid. Boiler condenser all these devices heat exchangers which we are talking about where you have a flow which is occurring. So, the liquid this water is getting heated let us say in this pipe either by electrical heating or there is coal which is getting whatever it is whatever be the source of heat liquid which is coming in eventually gets converted to steam inside a pipe and then you have a two phase mixture two phase mixture means liquid vapor mixture. So, I have pool I have flow boiling this is also called as convective boiling convective or flow boiling pool boiling means no bulk motion ok. What other things are there complexity that we see now all of us we have seen this example I give though it is not liquid vapor it is never the less very useful to understand I have if I if I have a tap and I have a hose pipe transparent tube which is carrying water connected and this tap is closed you have gone out of town for a few months or few weeks and you come back and you open that tap to allow water to come out. So, you will see this sound and air and all starts coming out first. So, after a while when the flow happens you will see large bubbles a large air spaces which are going to be formed and water will come out and eventually only water will start coming out. So, if this tube was held horizontal what you would see is bubbles which are the air which will which is there will sit on the top water will flow at the bottom. Whereas, if the same pipe same water if the tube was made vertical all of us would have seen that you would have these kind of what we call as slugs air which is there flowing like a bullet in the water stream. So, I have water in this air will be occupying a space in the center like this it will go like this and water will also sorry it to draw like this water air is going like this water is also going like this. So, what we are seeing even for the same mass flow rates of liquid and mass flow rate of vapor depending on the orientation of the pipe of the geometry my nature of flow how it looks to you what is the flow distribution or flow pattern this is going to change. So, this complexity is very very important why is this important because in vertical or horizontal flow depending on what we take let us take a pipe where fluid is flowing vertical pipe I take a horizontal pipe same m dot same m dot I am just telling this all qualitatively this is help us understand things a little bit better that is all. So, I have the same m dot and uniform same heat flux if I have a vertical pipe what I will see is a different set of flow pattern let us do horizontal first cold water is coming in it will start evaporating and what will happen if the pipe length is not of concern to us you will start to see an interface which is going to go like this is liquid this is vapor meaning water will settle liquid phase will settle if this is the cross sectional view this will be the liquid phase this will be the vapor phase and this is getting heated uniformly in all from all the sides. So, this is called as a stratified let us not worry about the names what I am saying is this surface is completely covered with touching vapor this surface is completely liquid and this area in contact is with the liquid very nice who will give me this distribution I do not know is it half is it 270 degrees I do not know why is this important this is important because what is wall shear stress we cannot forget our basic fluid mechanics d u by d y at r equal to r d u by d r at r equal to r whatever form you write wall velocity gradient do what do we know about the densities liquid density is we should take water it is about 1000 steam is 1000 of that roughly 1. So, what are we saying velocity is going to be much higher for the gas phase than for a liquid phase. So, this is going to accelerate and this is going to be much slower in magnitude if I am going to heat further more steam is generated same mass is getting converted to steam it is going to move fast why the area allowed is small is the same. So, I am pushing more of vapor through a similar amount of space it is going to accelerate even further when I accelerate a fluid what happens to my friction shear stress is going to increase this shear stress is going to be very different on the liquid side because it depends on the velocity gradients on the at the wall liquid interface who gives me this I do not know, but what I know is one average or mean velocity when I measure something on the outside that is a very poor estimate of what is happening inside because mass flow rate is mass is conserved it is m dot which is coming in it is not gotten converted to m dot f plus m dot g does not matter it is conserved, but I do not know anything about the relative areas what is m dot given by m dot is rho a u or rho a v and if I write at the exit it will be rho f a f u f plus rho g a g who gives me all this who gives me a this u u who gives me all this I do not know. So, there itself lies a problem second thing what happens at the interface. So, what are the problems what is this man teaching only problems are there because of orientation first thing areas occupied by each phase and velocity of each phase then last thing which I want to add before I go further is what happens at the interface at this interface we know from intuition without knowing any heat transfer fluid mechanics when you boil water for a making tea the interface is not smooth it will never remain smooth it will be lot of there will be lot of agitation. So, this interface is also going to be agitated. So, what is going to be transferred energy mass momentum everything is going to get transferred across this interface how do I account for that God only knows what about shear stress there has to be a force balance. So, the velocity profile should adjust itself if I take the velocity at a given cross section this is going to be much faster this is going to be much slower liquid the velocity will adjust itself such that the shear stress is going to balance at the interface. So, mu f d u by d y I am not putting the signs. So, the complexity occurs because of this so called interface interfacial shear stress and interfacial heat transfer what is causing heat transfer evaporation or condensation whatever be it this liquid vapor there is energy heat is when the liquid gets converted to vapor it carries m dot h f g associated with it. So, minus k d t by d y d t by d r at liquid vapor interface is minus k gas d t by d r for the gas phase this is for the liquid phase similarly mu d u by d y for the liquid is mu d u by d y for the gas. So, this interfacial conditions have to be balanced first of all I do not know the velocity I do not even know the average velocity how am I going to get velocity distribution then worry about the gradients. So, just the presence of an additional phase of the same substance where I can at least do an energy balance is giving me so much complexity in vertical flow I did not tell I will just tell and then we will proceed further in vertical flow what will happen this issue of stratification liquid settling down and gas going up is not there one other thing sorry when the gas is on top if I am supplying it is uniform wall heat flux condition the gas heating is going to produce a very different amount of effect then what what happens in liquid heating because liquid is going to use that energy to sensibly heat and get converted to vapor, but vapor which is already hot is just going to get super heated more and more. So, that also is there these bubbles will give rise to what we call as what we call as this vertical annular flow where the liquid will be pushed to the wall and vapor is very much in the center these will be chunks of vapor in the middle of the liquid with time this is what will happen with length rather this is what will happen to the flow. So, this is vapor which is going to accelerate this is liquid which is going to go much slower. So, this will shear this will pull away the liquid along with it and eventually you will get only liquid droplets these droplets eventually will get vaporized and you will get completely single phase liquid. So, what I am saying is cross sectional view will look something like this gas or vapor and liquid at this location at top location there will be very less amount of liquid and more amount of vapor. So, all this is the problem. So, what we have to tell our folks is that it is not very easy we are just introducing you to boiling and your condensation and this part actually what happens is let me just tell for completeness this is all boiling when I have bubbles and all those things bubble is formed bubble collapses all this thing we call as boiling, but here when this vertical channel especially it is very easy to observe there will be no more bubble formation it will be only evaporation this liquid film eventually will evaporate. So, in the same vertical pipe I can have boiling and evaporation both occurring at different location. So, this region will be evaporation this region will be boiling there why and how and all we do not care about what happens at higher quality is boiling is suppressed evaporation takes over. So, we have thermodynamic quality we have three qualities I am not going into all those things one is h minus h f by h f g in thermodynamics we took everything as the same other one is this is called as equilibrium quality other one is flow quality m dot g divided by m dot f plus m dot g thermodynamics everything we said was the same we did not bother. And third one is static quality that is in a given control volume fixed mass how much is the vapor and how much is the liquid. So, that x static is nothing but m g by m f plus m g. So, this is a different definition you do not worry about it I am just telling you that these three are very different. So, at thermodynamic equilibrium these two are the same otherwise they are different. Another quantity which you might come across when you read books is what is called as this void fraction this is again very important parameter alpha which is void fraction this refers to volume of vapor phase divided by volume of vapor plus volume of liquid. So, it can if you take a a times d z as the volume I can write when d z cancels of a g by a f plus a g this is very very important. And why is this important is because this represents the space occupied by the vapor phase with respect to the liquid phase we said density is very very high for liquid very low for vapor. So, even if one gram of liquid has evaporated it occupies a large volume. So, this fraction even though quality is may be small void fraction can be very very high. So, if now let us just go to friction delta p f l v square by 2 g d what is f let us say it is some turbulent flow some c times r e to the power minus m what is r e rho some average velocity some diameter divided by some mu raise to minus m single phase no problem rho mu everything we knew what about here what is rho what is mu what is u what is d let us say this somehow I get total pipe diameter and some average velocity I do not care if you are sipping cold ring through a straw there is gas also coming in. So, that gas is travelling at the same velocity as liquid that is ok I can use the same velocity, and what is rho is it liquid plus vapor by 2 I do not know density also somehow I can relate because I know thermodynamics specific volume I will say v is equal to v f plus x times v f g. So, I can get density, but viscosity I do not know. So, this thermodynamic properties which are there rho mu all these things they can be weighted in very different ways. So, mu bar could be weighted in terms of alpha mu f mu g or quality mu f mu g. So, each of these definitions will give you a different functional form. So, my pressure drop expression will be different. So, my two phase pressure drop consists of not just frictional pressure drop this is another very important thing frictional pressure drop is f l v square by 2 g d if it is a vertical channel you have gravitational pressure drop Bernoulli equation you write p 1 by rho g plus v 2 v 1 square by 2 g plus z 1 equal to something plus z 2 that z 1 minus z 2 is the gravitational pressure drop plus head loss you write. So, this also we know in single phase. So, this is also single phase studied this is also single phase studied except that how we deal with density viscosity I do not know, but it is ok. In addition to this because of this phase transformation that is because of area change or quality change area change quality change or just compressibility effect because when the velocity of steam is going to be very high it is density is also going to change compressibility effect will come come in. So, compressibility effect it is not because it is going at supersonic speed it is because of the nature of the flow this compressibility effect will come in all these will cause what we call as acceleration pressure drop physically why is it there it is there because a slow moving liquid has suddenly now gotten converted to something else and is moving fast. There is a transfer of momentum what is pressure drop it is again Newton's second law only we are writing. So, this transfer of momentum has caused this so called acceleration pressure drop in condensation a fast moving steam when it condenses it becomes a slow moving liquid. So, in condensation this quantity is going to make the total pressure drop lower because it is just an addition and this has a negative sign whereas, in evaporation or boiling in boiling this is also a positive quantity and this will increase the total two phase pressure drop and we cannot cannot neglect this quantity in two phase flow. So, it is a very very important complication this depends on void fraction flow pattern etcetera. So, with this let me just quickly in another half an hour finish whatever I am supposed to on what you will have to teach. So, we said liquid solid liquid liquid oil water immiscible miscible gas liquid all kinds of two phase flows are there we are going to deal with steam water or air water only in this simple half an hour lecture. So, boiling refers to a situation where liquid gets converted to vapor where T L is greater than T sat at a given pressure this is common sense T V greater less than T sat at a given pressure you will get condensation latent heat of vaporization H F G is involved and as you progress along the length of the pipe for example, if steam is condensing as you progress along the length of the pipe what is going to change is your thermodynamic quality. So, if I am going to have boiling from here let us say it has reached T sat at this location as I move along the length of the pipe thermodynamic quality will be greater than X at inlet how do I relate that simple energy balance I do not have to do anything see this is E in Q is coming here and E out. So, E dot in minus E dot out equal to 0 E dot stored and E dot generated as 0. So, what is coming in M dot H F M dot H let me call it enthalpy some enthalpy it is H H plus X 1 H F G plus Q double prime P B Z area is equal to M dot H plus B Z increase in enthalpy has happened. So, therefore, if I change this bring it to this side M dot H M dot H will cancel off I get D H by D Z is equal to Q double prime P by M dot what is H H F plus X times H F G. So, derivative would be D H is equal to H F G times D X. So, this will give me H F G D X by D Z is equal to Q double prime which will give me quality variation D X by D Z D X by D Z is equal to Q double prime perimeter M dot H F G. So, if I have a constant wall heat flux condition I know this I know the dimension I know M dot I know H F G at a given pressure I can plot X as a function of Z Z if it saturated liquid at inlet I will have from here itself a linear variation X is equal to 0 at Z equal to 0 and some exit quality at X is equal to exit. So, I can get the quality variation from that at every location I can get the appropriate weighted properties rho mu etcetera I can get I can then calculate pressure drops one and so on. Latent heat of vaporization therefore is weighted by the quality surface tension very important again because it is involving two phases properties of fluid in each phase. Then what we are saying these are something which we we should know in the form of numbers at least ballpark single phase we have going to have much lower heat transfer coefficient whereas in case of convection boiling and condensation it is you know getting 8, 10, 1000, 15, 1000 watt per meter square Kelvin is not at all a big deal. So, boiling process of addition of heat such that generation of vapor evaporation occurs evaporation is a surface phenomena boiling is a bulk phenomena P vapor pressure less than P sat at of the liquid at a given temperature involves no bubble formation or bubble motion I said that already boiling occurs we have seen all this when a liquid is brought in contact with the surface as a temperature above the saturation temperature of the liquid. So, this is this is when boiling can occur now many of us you have seen that boiling when you made when you try to boil water if you it will bubble will be formed somewhere another location and the vessel third location it is not formed uniformly everywhere you keep a different vessel it is formed differently you keep a different shape vessel it is formed differently why is it so it is because before boiling to occur you have to have entrapped gases or air. So, any surface when you take my microscopically there are pits and cavities in those pits and cavities there are entrapped air and the liquid that you put also will have some dissolved gases. So, not getting into that details of it just because there is a pit boiling will not occur at that pit. So, let us not have that misconception. So, if I have a have a surface which is like this it has some pits and cavities like this any shape arbitrary every each one of these is not going to become a site at which boiling is bubble is going to be formed no. So, nucleation site is what is the word for this nucleation site refers to a particular site at which a bubble can be formed and it can be sustained. So, when there is air entrapped depending on the shape size of the cavity amount of wall heat flux that is put all these things surface tension depending on all this a particular cavity may choose to behave like a may support nucleation or may not support nucleation. If a cavity supports nucleation what you will see is you will have this kind of a interface of vapor liquid with more heat this interface will grow further and further it will grow I will just draw it on the next page because this is quite interesting. And if I take a cavity like this way beyond this but nevertheless this is in this is a liquid vapor interface vapor liquid this is at next time I am drawing this with respect to time another time the interface will be like this. Now, this is the solid right we are supplying heat like this and this is a blown up view of the cavity. So, this surface is getting heated there is a temperature profile for the fluid remember we have this kind of a temperature profile. So, this layer of fluid suppose is at a temperature which is sub cooled then what will happen this interface will get collapse and it will come back it will become the bubble will collapse what is generation. Now that is why you saw some small bubble and then it just collapse after some time what will happen to the temperature the temperature of this layer would have increased. So, this layer is now ok this the interface is ok to pass through this layer because it is not cold anymore. So, it the bubble will grow another layer it will grow. So, what will happen it will keep growing and there will be a point when what are the forces involved surface tension buoyancy. So, pressure surface tension and buoyancy when this balance is broken this bubble will depart from that particular surface ok. So, after some time you saw this bubble coming out of the surface then immediately why bubble is not formed it is not formed because this cold liquid which was surrounding it came and sat in that cavity again it has to get heated it will take some time. But now with progress of time the cold liquid is now slightly warmer water which was at 40 degree now second instant when the bubble is left is now at 60 degrees. So, it is going to take less time for it to go through this process surrounding layer has also become hot. So, the chances of it surviving or more finally what will happen the bulk liquid itself has re saturated. So, this whole thing of the cold the surrounding liquid coming in and this whole cycle repeating itself the frequency will increase that is why you just see this agitated motion that is happening. So, this something which all of us have seen we have not been able to understand it. So, I just thought we will tell that now. So, force free convection depends on density specific heat thermal conductivity boiling heat transfer depends on all these properties surface tension at the liquid vapor interface so on and so forth. Bubbles exist because of the surface tension at the liquid vapor interface due to the attraction force on the molecules at the interface towards the liquid phase we have studied in fluid mechanic mercury water what is happening to the size of the shape of the droplet. So, surface tension decreases with increase in temperature and no bubbles are formed at supercritical pressure and temperature. So, that is why you will see direct conversion from liquid to vapor classification pool and flow boiling pool boiling bulk fluid is stationary motion is due to natural convection currents motion of the bubbles because happens because of the influence of buoyancy flow boiling fluid is forced to move in a heated channel or a surface by external means such as a pump ok. So, this has where does this have application I just want to spend couple of time power plants of course, boilers condensers definitely in cooling of reactors etcetera where you are talking of very high temperatures which are associated with the reactor fuel you have to cool it continuously if you have seen there will be it is always enclose in a pool of liquid that is a moderator which is there for some other reason, but it also provides some amount of cooling. So, in that case natural convection natural circulation is always there force force convection cooling involves use of a pump. So, many times nowadays if you are seeing in reactors especially if there is a power outage then things do not flow cannot happen things cannot be cool. So, emphasis is more on natural circulation cooling ok. So, it has wide relevant application cool and flow boiling can be classified as sub cooled and saturated boiling I am not going to details I am just going to say saturated boiling all of us will understand when the bulk fluid temperature is equal to the saturated temperature water will start to boil, but actually in reality that is not the case boiling will happen your bubble that is formed and which is leaving the surface of the vessel when you are trying to make tea water does not reach saturation temperature if water had reached saturation temperature it would have gotten converted to vapor immediately. So, what this sub cooled boiling is the sub cooled boiling refers to boiling that is occurring when the bulk fluid temperature still is sub cooled remember our single phase we have to remember again and again what did we say when I have a pipe there is a temperature profile correct this temperature profile we have converted pseudo to a bulk mean temperature T m of x correct, but this portion this portion the circumference close to the wall the region close to the wall could be at a higher temperature than saturation temperature locally because what we say when T is equal to T sat we are referring to the bulk mean temperature. So, for locations what this small bubble that is formed I said it is formed it leaves it collapses all that is occurring in this part only attach the wall. So, when the wall temperature becomes greater than the saturation temperature liquid will still the first layer of liquid will still not be at T sat it will be at lower than T sat, but when T wall is greater than T sat if other conditions what they are I do not know at this point I am not going to tell when T wall is greater than T sat at that given pressure conditions can be favorable for what we call as sub cooled boiling to occur sub cooled boiling means bulk fluid temperature is lower than T sat, but phase transformation due to boiling can occur. So, heat transfer coefficient can be high even in sub cooled boiling situation and of course, when when bulk temperature reaches T sat that is easy to understand everything with a T sat. So, you will have phase phase change occurring. So, that is saturation and a sub cooled boiling this is bulk fluid less than T sat T bulk fluid greater bulk of fluid is equal to T sat that is what it would be surface would be at a higher temperature than T sat the surface temperature would be higher than T sat I just so that this registers in your mind I just want to show this one thing. If I plot temperature variation the wall see this is exactly what we did in in our single phase heat transfer wall and fluid parallel lines a fully developed flow if I am assuming the wall temperature would show some such profile and this is the bulk fluid temperature this is T sat this this line refers to T sat. So, always a super heat delta T sat is needed for boiling to occur always wall is going to be at a temperature greater than saturation temperature. This wall has crossed this point this point onwards even though the liquid is still T m at this location is less than T sat it is below this line right it is below the saturation line conditions can be such that in this portion in this portion this is where the liquid has reached T sat in this portion I can have sub cooled boiling. So, I can divide the region of a pipe flow situation into three parts one where a single phase single phase convection heat transfer force convection in this case one where there is sub cooled boiling this is what that you see bubble form collapse all these things and this is where saturated nucleate boiling nucleate because of this concept of nucleation birth growth leaving that is nucleation.