 So, what is the boiling curve? The boiling regimes and boiling curves. So, I have told now already, single phase, some sub cooled boiling and then saturated boiling. So, what is what is so great? Well, something more is going to happen. If I go back to my, if I take a vertical pipe going beyond what is there here, but again this way I think we will understand better. If I have a vertical pipe, I have a certain m dot. Remember, you think of your water geyser at home. So, you keep reducing the, you want hot water, hot water, hot water, you keep reducing the flow rate. You start to see intermittent hot vapor coming out and liquid coming out. What is happening at that time is sudden burst of liquid and vapor is coming out. So, if my mass flow rate becomes very, very low, my water is going to get very hot. Now, let us use this analogy and say my mass flow rate and heat flux combination is such that I get, I go through all this region bubble formation, this sheet formation and so on and so forth. I come and reach this annular flow business. This is called annular flow. Annular means liquid is surrounding and vapor is in the form of a central annular core. Liquid is in contact with the heated wall. So, if I look at this from top, it is going to look like this. Afterwards, if the pipe is still long, somebody asks this question, boiler, I will, after I have evaporated, then in my diagram I go to this, this portion. Temperature is not constant. This portion is what super heated vapor in our diagrams. We have seen thermodynamic. What is this? Liquid has gotten converted to vapor. There will be some dispersed droplets because interface will always be agitated. I am drawing nice smooth. It is not smooth because vapor is shooting at a high velocity. Liquid is still sluggish. So, the interface is going to be pulled and you will have some liquid droplets entrained. Entrain means carried away by the fast moving vapor. So, after a while, even if then the length is long, this water droplets will evaporate. So, you have single phase vapor. What will happen to my heat transfer coefficient? My h, what is h q double prime divided by T s or T wall minus T this one. What do we expect? Forget two phase, single phase. What do we expect? Common sense. I expect, what is, what is removing the heat here physically? Liquid. When liquid is there, I am relaxed. I know heat will get removed very nicely. So, my heat transfer coefficients will be defined very nicely because I have a surface temperature. This is C-pack. The moment I start to lose touch with liquid, what will happen? All of us would have eaten dosa at some point of time and probably some of us would have made also. If you put on the pan and you have forgotten there is a phone call, you are just going and talking and the pan has become red hot after that. It has become very hot. What do you do immediately? First reaction is you know seeing your mother or grandmother, if you put the batter and try to make dosa, nothing will come. It will just stick around and there will be no pattern formed. So, you will immediately sprinkle splash cold water on it. When you splash cold water, what you see? You will see the small droplets which are dancing all around. Even in the roadside stall that guy will do, he does not know heat transfer, but he is very smart. He will sprinkle water and he will use this spoon to spread the water so that everywhere temperature becomes nice. So, when the temperature has gotten down because liquid has come in contact, you can then pour the batter and you get this shape, but when this temperature is very, very high, when liquid is not in contact, when vapor comes in contact, you keep your hand on top and see it is so hot. Why? Because the same heat flux, you are not seeing the gas settings or anything. The same heat flux, because vapor is a poor thermal conductor, it cannot take away heat very nicely, wall temperature will go up tremendously. Because wall temperature goes up, heat flux is fixed, temperature difference drops, your heat transfer coefficient drops. So, which came first, we do not want to argue, but what I am saying is when liquid is there in contact, my heat transfer coefficient is good. The moment I lose contact with liquid, I am going to have very, very poor heat transfer coefficient. If I continue to keep heating, what will happen? The surface, the material will get completely degraded. So, many times you will see this as if you are not cooling anything, if you are immersion heater, people would have used in olden days, a bucket which will be there and there is water and there will be a coiled heater which is there. So, if you do not have enough water or you have put it on and forgot and the water has gone, immediately what is going to happen, this is going to burn off. So, this concept of burning off of the heated surface, because it is unable to throw away the heat that is being supplied. That concept has led us to understand what is called as burnout is used. Again, these are all used loosely, but we will also use them loosely for now. Critical heat flux C H F, we call it critical. That heat flux, that value up to which I can operate safely without the sharp decrease in heat transfer coefficient, that is called as critical heat flux. For undergraduate, this definition is more than enough, critical heat flux. So, if I have a pan of, if I am making tea and the water, you have forgotten, you have gone to sleep, water is gone, evaporated and you are still continuing to heat, what will happen to the surface? Sometime or other you would have seen somebody do this, the surface would become totally black, milk you keep and forget, the milk is just evaporated completely. That degradation of surface you see in the kitchen is very different, but in industry if you see, in a nuclear reactor that you see, this material characteristics of this material will get degraded. So, critical heat flux burnout, another thing, when does this occur? When there is complete vapor which is covering it, here also there is vapor only. So, dry out burnout, dry out, dry out means what thing is dried, there is no more liquid present. So, dry out burnout critical heat flux are all used interchangeably, we will not go into the specifics. So, that is another big, big, big concern to us. So, these regimes which we are talking, going to talk about are based on what happens to the flow or boiling as you are going to supply heat to a given situation. So, Nuki Amai in 1934 was the first person to do that, he did this experiment where he tried to generate Q versus delta T kind of curve which we call as the boiling curve. This is there in all textbooks, what is boiling curve? Boiling curve for water at one atmospheric pressure, this boiling curve is essentially a graph of heat transfer coefficient. How is it heat transfer coefficient? Q on the y-axis, it is a log log scale, 10 to the power 3, this is y-axis is wall heat flux, 10 to the power 3 going to 10 to the power 6 representative numbers and this is delta T, T wall minus T sat. One atmospheric pressure T sat is fixed, T wall is going on increasing, this is a heat flux controlled experiment, I am controlling this, this is constant, this is going to keep changing, T sat is fixed, T sat is fixed, T wall is changing, slope of this curve Q divided by delta T is heat transfer coefficient. So, the slope of this curve gives you a measure of the heat transfer coefficient, you see single phase natural convection etcetera is here. So, this one when I make a plot of I am supplying heat, given I am supplying heat I have the power to control the heat and the fluid has reached. Now, after supplying heat for sometime in a pool, it has reached T sat, I am measuring the wall temperature for a given heat supplied, I am maintaining constant pressure. What will happen? Initially, what we have seen while making T is going to happen, single phase natural convection, you will have some slope which is typically H for natural convection. Then once sub cooled boiling starts, nucleate boiling region, this is what? Sub cooled boiling start because this local boiling small bubbles formed, it is carrying large amount of energy m dot h f g. So, because of that you will see a rise in slope and then you see here, you notice here T minus T sat is of the order of 5 degrees this position of the order of 5, meaning if T sat is 100 this is about 105 wall temperature. So, that is these are typical numbers conditions at which sub cooled boiling will start, roughly at about 107, 110 degrees that is when 10 degrees super heat is there, you will reach nice nucleate boiling where bulk fluid has reached T sat. I continue heating, what will happen? I keep increasing the heat flux, my experiment is such that I am increasing the heat flux. I will reach a situation where T sat remains fixed, T wall will keep increasing and I will reach this location of so called maximum heat flux. At this point, what is going to happen? In this pool water would not have boiled, but what happens is what we told in the Tawa experiment. The surface is become so hot that there is a liquid, there is a vapor film which is going to be formed on the heated surface. There is a vapor film that will be formed, liquid will if I blow it up, I will have bubbles which are formed and coming out, but they will be coming out at such a fast rate that it will look as if there is a vapor film that is going to be in contact. Because of that what will happen? I will go to a situation where there is a sharp decrease and actually you will traverse this, we will go to point E. Point E refers to a film boiling region that means the heated surface is covered by a vapor film. Liquid in contact with heated surface is very good, vapor in contact with the heated surface absolutely unacceptable. You see here, rise in temperature of the order of 1000 degree centigrade, evolve minus T hat is just jumped up by almost 1000 degree. So, for the same heat flux, this is just like a trigger. You go from a very good heat transfer region to a very poor heat transfer region and then when I start reducing the heat flux, I will not go back here. I will traverse this portion of the curve that means I will still have a film. Finally, I will reach a point where the film no longer exists. Basically, I am cooling, but the heat is so high, heat flux is still so high that liquid will still not be able to come in contact and this point D refers to Lirenfrost point which is the end of film boiling. What about C to D? Between C and D, we do not get this region in case of all heat flux controlled experiment. You will get this in case of wall temperature controlled experiment. Nevertheless, it is sufficient to say that this region which is called transition boiling is a nightmare because it will be oscillatory flow. Liquid will come, vapor will come, alternating temperatures will be there. Suddenly, the temperature of the wall will go very high. Suddenly, it will go to very low value just about E sat. So, this region, what is drawn so beautifully? This portion of the boiling curve is never drawn, never so nice. So, I can broadly separate the boiling curve into natural convection, nucleate boiling, film boiling and transition boiling. This peak is called critical heat flux. This is called Lirenfrost point or minimum film boiling temperature. You can write this down, minimum film boiling temperature. Lirenfrost point is because it was first identified by Lirenfrost, but it is referring to the point at which the last phase of film boiling will occur. Beyond that, you will go into this oscillatory transition boiling. So, pressure drop, imagine when you are in transition boiling, suddenly you have liquid, suddenly you have vapor. So, you have an oscillatory pressure drop also. Everything becomes a problem. So, natural convection governed by natural convective currents, heat transfer from heating surface to fluid is by natural convection. Nucleate boiling, stirring and agitation, I have talked all this. I do not want to go into this. These are all given in textbooks. Transition boiling, this is unstable film. Film boiling, presence of vapor film between the heated surface and the liquid is responsible for low heat transfer rate. Heat transfer rate increases with increase in excess temperature as a result. So, radiation becomes very important here. See here, radiation we neglect in boiling, but when I have a film, that film between the heated surface and this between the heated surface and the film, between the heated surface and the film. Let us say this is the liquid and this is the vapor and this is the heated surface. I am going to talk of T surface of the order of 1000 degree centigrade or 500 degree centigrade. This interface to here, there is definitely radiative heat transfer. You coming in by radiation is going into sensible heating of the liquid and phase change. So, what is coming at this interface from the wall by radiation and probably even conduction, because it is gas. This will go into this interface. If I do an energy balance, some of it will go in sensible heating of the liquid. If the liquid is still lower than T sat or it will go, let us say sensible heating and some portion which will get converted to vapor. But who will give me this split? Who will give me this? It is very difficult. All I know is for a given control volume, q double prime perimeter at d z gives me the heat total q. How it is going to be distributed? Nobody knows. So, that is the difficulty associated with this. Anyway, so that is film. What are the various regimes? Nukeyama did this methanol with 1 centimeter diameter horizontal steam heated copper tube and these are textbook representations of what you see by natural convection, natural convective current onset of boiling, 1 or 2 small bubbles. Individual bubble regime, regime of slug and bubble you will see long bubbles formed sometimes. Transition boiling which you do not want and film boiling these two you do not want. This will be observed when I increase the heat flux very rapidly. Bubble nucleation or boiling inception, I told you cracks and crevices do not themselves constitute site of bubbles. They must also contain dissolved gases or pockets of gas entrapped air within the vessel when the vessel was filled with liquid. From these pockets of entrapped air bubbles begin to grow. If there is no entrapped air that is why in micro channels you will basically take away, you will deionize the water so much that when you supply it there is no dissolved gases present in the water because dissolved gases when you heat will expand. So, that will go and sit in that cavity and you will start to boil. So, that is one thing. So, heat transfer in nucleate boiling this is what I think most undergraduate books cover and this is there in most textbooks. Nuclear boiling heat transfer is a function of Reynolds and Pantel number, Nusselt number is h L f by L by k f, R e is rho u L by mu f, P r is mu C p by k. What is this velocity scale in boiling? So, I want to calculate heat transfer coefficient. So, velocity scale is the liquid velocity towards the surface which is this which is to supply the vapor that is being produced. So, when this velocity what is this velocity as the vapor is formed it leaves. So, liquid is going has to replace it by the same velocity. So, that is the velocity what is it given by Q double prime where did this come from this is just come from a simple energy balance. This is come from simple energy balance energy balance would give me Q double prime means heat flux. So, Q times area which is nothing but what is m dot that is evaporating rho u A correct that A I am going to divide here. So, I will get heat flux. So, m dot h f g is Q latent heat of vaporization times the mass that has evaporated is the energy that is carried out by the fluid because of phase change. This m dot is rho A u this velocity is what I want this area if I am going to divide it is going to be Q double prime is equal to Q double prime is equal to h f g rho f m dot is rho u u f this velocity is like. So, this one then length scale what is this length scale who gives me this length this length scale is taken to be of the order of these are not equal please again we are talking of a scale we are talking of an order of magnitude is roughly of the order of sigma by g rho f minus rho g to the power half what is this this has come from instability criteria. So, sigma is related to the surface tension force this relates the buoyancy force. So, for a bubble to be formed and to leave surface tension buoyancy force balance when one of them becomes more than the other surface tension is doing what it is holding the bubble when surface tension and buoyancy balance broken and buoyancy takes over the bubble will have to leave what is the size up to which why that is why you will see some bubbles in certain liquid will be small before they come out whereas, in certain case it will come to a large diameter before they break and come up this coming up flowing of the bubble through the liquid is essentially the buoyancy force related phenomena. So, this length scale this has been found if I remember right I think this is Taylor length scale I am not sure. So, do not quote me on this, but sigma by g rho f minus rho g under root during boiling disturbances of all wavelengths are present there will be some small wavelength disturbances and long wavelength disturbances that will cause the interface to be unstable this is what we are we are told now we are putting it in words condition for the interface instability of a motionless liquid is given by this one. So, alpha is nothing, but this rho f minus rho g times g divided by sigma r h to half this condition is called as yeah it is Taylor Rayleigh Taylor instability this wave number which is there is called as the critical wave number which is given by 2 pi all these things all these things essentially I have related to the buoyancy and the surface tension effect. So, now what I am going to do is I am just going to substitute everything I want a scale why do I want a scale because I want Nusselt number because I want h what is h related to h is related to heat flux here. So, I will just blow this up Nusselt number is h l f by k which is h times for l I will substitute this k remains as it is Rayleigh Reynolds number rho u l by mu rho by mu is as it is u is q double prime rho f h f g length scale again is the same thing p r is mu c p f by k and what Rosenov one of the pioneers in boiling heat transfer what he did he said this functional form I am going to assume for Nusselt number 1 divided by c f times r e to the power 1 minus n we called it m and n he has taken it 1 minus m and 1 and minus m just for convenience why he has done that you will see this Nusselt number when I open the brackets here and recast all these things Reynolds number is rho f q double prime mu h so on and so forth substitute that here Prandtl number substitute that here 1 over c f I do when I do all that I come up with a nice relationship which looks like this this looks like a messy relationship it is not so messy it has forgetting everything what is it q double prime heat flux T wall minus T sat everything else what are they sigma property rho f property rho g property c p property mu property k property h f v all these things are thermo physical or thermodynamic property related to the fluid and the pressure correct c p everything so this c s f is one black box but essentially slope of this q divided by delta t boiling curve definition is what q on the y axis delta t on the x axis so I am going to be able to get this relationship for a particular fluid and surface combination that fluid surface combination is exemplified by this coefficient c s f so water on copper versus water on tin water on aluminum it is going to behave differently correct all of us appreciate the stainless steel vessel it will be different if you use copper bottom vessel it is going to be different if you aluminum vessel it is going to be different correct so that difference all the things related to the surface fluid combination has come and fallen in this c s f and n and m are given typically one for water 1.7 for other fluid c s f is a surface fluid constant depends on the surface in the fluid typical values are given in the table for a given delta t sat heat flux is proportional to c s f to the power minus 3 so this will be a graph generated this graph is essentially what q double prime time some constant some things h f sigma all these things t wall minus t sat times c p f by h f g p r where did I get this t wall minus t sat c p f h f g p r. I brought this in here this is the other quantity which is there q double prime under root sigma blah blah blah blah everything what is left which is unaccounted is this what is what is this if I take log on both sides this is going to become the slope so this quantity is basically c c s f is embedded here. So, for by rosin of method what I am getting is for various pressures if I plot there is a curve that has been obtained and rosin of did something very nice he has done this for various combinations of surface and fluid combinations. So, water on scoured paper emery polished copper water copper water brass tabulated various c s f value. So, this is available in almost all under graduate heat transfer textbooks most significant variables affecting c s t are surface roughness of the heating element determines the number of nucleation sites at a given temperature angle of contact between bubble and the heating surface which is a measure of wettability wettability is very important mercury wets very little compared to water. So, if it does not wet boiling characteristics are going to be different what is wettability dependent on it is dependent on the surface tension. So, these are there these are available we can use it and try to estimate what are we estimating we will get let us put this in perspective rosin of gives you this part of the boiling curve it is not giving you here it is not giving you anything here it is giving you nucleate boiling region giving you this part of the boiling curve that is that too another thing that is valid only for pool boiling stagnant pool one other thing which we forgot to mention which I will tell you now what is I said typical boiling curve we did not classify pool or force convective or force convection boiling. Boiling curve nature will be identical only thing in case of flow boiling or convective boiling the heat transfer coefficient will be little bit more enhanced because of the flow effect convective effect whereas in a stagnant pool if this is the curve the slope of the boiling curve would be slightly different the nature would be the same the qualitative representation will be the same only fact that the H value heat transfer coefficient would be a little bit higher the slope of the curve would be a little bit different because of the effect of the convection force convection that is all otherwise the nature is the same, but this rosin of pool boiling is valid only for pool boiling. So, critical heat flux I told you what critical heat flux is rosin of correlation is restricted to nucleate boiling does not reveal the excess temperature at which heat flux reaches maximum or critical heat flux is obtained at which nucleate boiling breaks down and insulating vapor film is formed it does not tell you anything about that for heat flux control surface the temperature rise when critical heat flux is exceeded can be very very large sometime even 1000 Kelvin we saw that. So, critical heat flux is characterized by this expression where again see these are all experimental correlations they are not coming from any other way they are coming from experimental. So, textbooks give this form if you know the surface etcetera you are going to have a geometry dependent parameter C R characteristic dimension is given L star is also given. So, you can calculate critical heat flux for a particular application this is the so called lead and frost temperature lead and frost temperature as again this phi is heat flux and this lowest point in the heat flux is given by this. So, again from a U G treatment point of view I do not think you will have to go into details of all these things I think introduction to boiling what are the aspects what are the characteristics and then coming and showing rosin of correlation that is enough these we are just included. So, that you know there is completeness. So, that we traverse the whole boiling curve if we stop at nucleate boiling and say this is the boiling curve it does not make sense. So, if you have to plot the boiling curve for a particular fluid then what are the things that you would need is what is shown rewetting of hot surfaces your dosa making is rewetting essentially basically you are trying to make the surface more wettable by spraying water on it. Liquid does not wet a hot surface because liquid is separated from the plate by a thin film. So, this friction for sideways motion of the drop is very small heat transfer across the vapor film is. So, that is why you will see this drop dancing all around this drop will dance all around vapor film moves outward fresh vapor is generated by evaporation on the underside this will this is the surface at which evaporation will happen because it is very very hot here. If the plate is allowed to cool down it will reach a temperature at which this vapor film no longer exists that is why after sometime you put the sprinkle water it will remain as liquid in contact it will not dance that is why this surface temperature that is sudden wetting of the plate occurs is called lead and frost we saw that already. Film boiling we said vapor film in contact with the heated surface external flow it can happen it can happen even in internal flow and there is depending on the geometry vertical plate horizontal plate vertical cylinder horizontal cylinder the broad mechanism is the same when the temperature of the heated surface goes very very high this film boiling will occur it is again dependent on the delta T which is there and the properties of the fluid. Bromley Berence and all these correlations exist for various geometries and analytical solution was developed by Bromley for laminar vertical plate film boiling it was developed probably in 1952 or 1954 I do not remember this still used. So, taking an example for water you are you are try to generate the boiling curve this I am not going to present here thing that you need to know which you need to emphasize is that experiment to generate the boiling curve actually can be taught can be kept as an undergraduate heat transfer experiment we are not doing it for various reasons simply because most of us do not even each boiling in our pool boiling experiment is there then this fundamentals that you give them is more than enough I think. So, that is why this whole fundamentals are put together in a capsule. So, I do not know how much time colleges spend on this topic, but if you are having an experiment on pool boiling we urge you to at least give this capsule of 1 hour information. So, that they know what they are doing what they are getting what is nucleate boiling what is CHF at least if they know what they are talking about I think the experiment will be of use to the student otherwise it will just become an academic exercise. So, this just represents the completion of boiling curve I am not going to go into detail sudden slope changes you will see which indicates the transfer change in the regime with that I think I will stop will take questions for about 10 15 minutes E road, E road institute of road and transport E road. In case of in case of in case of heat pipes if nano composites are used as fluid working fluids instead of conventional refrigerants what are the it is observed that there is an enhancement in heat transfer characteristics. In such cases what are the limitations of using nano composites in heat pipes and what happens to the liquid vapour interface because it is a composite mixture of two fluids what happens to liquid vapour interface in such cases there would be two liquid vapour interfaces can you kindly clarify this point Professor honestly I do not know the answer for this question why because it is a two phase flow nanoparticles which is a research topic by itself where tens of phd students are working. So, please put this in the model I can only suggest some papers it is a first of all it is multi phase flow it is nano particles are there and liquids are there and over and above that the life has been made complicated by making it boiling also. So, that is two phase there is liquid vapour solid all three you have put. So, it may life is very difficult it is not so easy to answer the way we have closed form solutions for single phase. Next question professor you said you have two questions what is the next question. Yes, yes professor, next question is compact heat exchanger we have a 700 meter square of heating surface per meter cube that is defined as compact heat exchanger while designing the compact heat exchanger what are the limitations and constraints what about the j factors and i factors that is delta p and friction factor characteristic for the design of compact heat exchanger that is my question. See what is the in the design of the compact heat exchanger what are the constraints in the design of the compact heat exchanger what are j's and f's and what are the problems involved in this. Although this is also application oriented question let me take it. See first of all plate fin heat exchanger are generally used for low pressures. So, not for very high pressures for example, even if you are thinking about high temperature reactor of today although plate fin heat exchanger is a good idea in terms of decreasing the surface area. So, it will take it is not possible to build high temperature reactor because the operating pressures are very high. So, first limitation of plate fin heat exchanger is that it can operate at very low pressure may be at 1 to 2 bar or maximum at max 10 bar why because the plate fin heat exchanger is made of plates and it is there are they are all essentially they are all separated by small laminar channel. Flow is in a compact heat exchanger essentially laminar. Essentially laminar why because each sub channel in this plate fin heat exchanger is going to be very small very small may be like 1 mm by 1 mm or 2 mm by 2 mm or 3 mm by 3 mm or 2 mm by 3 mm of that order. That means essentially the flow is laminar what is that we are playing there is by increasing the surface area. So, main problem is the fabrication which restrains us to go for higher pressures that is number one, but definitely they are compact no doubt about that. Wherever one wants a compact heat exchanger in fact for an aircraft for an aircraft as a regenerator in an aircraft compressor combustion chamber and the what is that turbine regenerator is used. So, that whatever heat is going out from the turbine a grid is utilized back again that regenerator again is used as a plate fin heat exchanger why because it is compact why I took aircraft because for an aircraft I need compact compactness is required because I do not have space. So, I need compact. So, that is why compact heat exchanger is you can be used in an aircraft. Now, what about J S and F S? J S and F S again professor again you have opened Pandora's box you have tens of configuration hundreds of configurations where in which you have serrations no serrations you have offset strip fin lots of configurations you can there are hundreds of configurations even today 2012 papers in press all sorts of papers are there per plate fin heat exchanger. Now, however these are all papers for single phase heat exchanger. Now, come to two phase flow heat exchanger no paper no paper use complete J and F for two phase flow heat exchanger because doing experiments is very difficult number one, number two honey well, alpha well they have data but they do not share data why because that is their proprietary information. So, there is lot of scope for plate fin heat exchangers especially for two phase. So, with this I will close this question and we will move on to next question. Hello, one more question professor can you please compare can you please compare the performance of shell and tube heat exchanger and the compact heat exchanger for the same heat load as it got to the delta p and friction factor. See question is how do I compare how do I compare compact plate fin heat exchanger compact plate fin heat exchanger and shell and tube heat exchanger for any given application pressure drop heat transfers and all that one rough idea I can give you is that for actually people have designed for high temperature reactor where the loads are of the order of 500 to 600 megawatt 500 to 600 megawatt the shell and tube heat exchanger whatever shell and tube heat exchanger we have designed let it be area a compact heat exchanger compact plate fin heat exchanger will have roughly an area of roughly roughly it is a ballpark number roughly 20 times lower 20 times lower than that of shell and tube heat exchanger compared to this. Now shell and tube heat exchanger does not come cheaply compared to in shell and tube heat exchanger pressure drops are not very high, but in plate fin heat exchanger pressure drops are very high why because my channel sizes are very small and it is laminar and pressure drop is function of inversely proportional to d to the power of 5. Now another compact plate fin heat exchanger still compact in today's world this is shell and tube this is shell and tube and this is what I am saying is plate fin plate fin heat exchanger there is another called printed circuit heat exchanger p c h e printed circuit heat exchanger in the printed circuit heat exchanger this is almost 100 times the 100 times less area, but in shell and tube heat exchanger we are using tubes instead of using simple tubes if I use a twisted tube instead of using a simple tube if I use a twisted tube the area will be roughly a by 2 area will be a by 2 whenever I decrease the area it goes without saying the pressure drop is going to go up in same thing whenever I decrease the area by 100 times pressure drop is going to be very very high because now I have gone from mini channel to micro channel in plate fin heat exchanger I said 1 mm 2 mm that can be considered as mini channel, but in p c h e it is going to be micro channel why we are going for p c h e a micro channel because it can withstand high pressure, but plate fin heat exchangers cannot withstand high cannot withstand high pressure that is the reason p c h e is very much in practice and lot of research is going on in p c h e at the same time plate fin heat exchanger lot of research is going on manufacturing side not from thermal side how to fabricate plate fin heat exchanger such that it can withstand high pressure because generally plate fin heat exchanger is done by simple welding or soldering which cannot withstand high pressure we have to do away with joints and get that solid then only it can withstand high pressure the point is the point is heat exchanger industry is not going ahead or the progress of the heat exchanger industry is not just related to thermal thermal issues it is related to manufacturing issues that is the crux of the matter ok. Thank you very much for all that thank you ok we will sign off.