This is part two of Lecture 12. So we've now seen that there are several theories that can help us explain why people behave aggressively. And the bottom line is this. All people, all human beings have the capacity to become aggressive. Aggression is always sort of an option, something that we can demonstrate. Of course there's individual variations in the amount of aggression that people use, but it's something that all people can at times experience and also demonstrate. The crucial factor is, of course, and there we have it again, is the situation that people find themselves in. The situation really determines whether, when and where we express our aggressive tendencies. So let's now zoom into the situation. And we're going to start by talking about culture, because culture plays a major role in aggression. There's a big, huge variations across cultures in the levels of aggression. Some cultures are very aggressive and others are way less aggressive. And if a culture is very aggressive, we mean that it's basically societally appropriate to demonstrate aggression. Aggression is something that is just uncaptured in that culture. One very violent and very aggressive country is the United States. The United States is a very aggressive country. Also if you compare it to similar other countries like Canada, Australia, Western Europe, the United States is a very aggressive country. But also within the United States there's lots of variations in aggression, regional differences. And this basically has to do with a difference in culture of honour. So if there's in the southern parts of the US, there's this honour culture. And an honour culture is basically a sort of a social norm that condones and sometimes even encourages responding to insults with aggression. So it's very societally appropriate that when someone insults you, especially if you're male, then you should respond in an aggressive way.  If you don't show aggression, if you're being provoked. And provocation in itself is also a situational cue to become aggressive. Everybody, if you're being provoked, if someone pushes you or says something mean or you feel treated unfairly, we all become a little bit aggressive. So that's natural. But in a combination of a culture in which the norm states that you should behave aggressively as a response to being provoked, then this is even more so the case. So here you see in this graph, you see the results of a study in which a research participant was walking down a narrow hallway and a confederate bumped into this research participant and started calling them names. So let's imagine you're, for example, in a train or something, you're walking there and somebody bumps into you and also starts to provoke you and say very mean things. Then the researchers were interested in the response of the participants. So if this happens to you. And there were two things that they were interested in. It was the aggressive behavior. So is the participant behaving aggressively? And also what is going on with their testosterone levels? Are testosterone levels going up after being provoked or not? And they had two types of participants. They had Northern Studies students and Southern students. So they were basically born and grew up in either a culture of honor or not in a culture of honor. And you see a huge variation in this culture, the place in the region where they came from on both their behavior as well as their testosterone levels, showing that Southern students that grew up in a culture of honor were way more likely to aggress. You see almost about 80% I would guess from this graph of the students behaved aggressively and also that testosterone levels really increased a lot. So you see that even biochemically we respond differently as a response to the culture where we grew up. So that's one factor that is really important culture. A second factor is something that I think a lot of people don't realize is heat. If it's very warm, we become more aggressive. So warm temperatures and this is shown in many studies are actually related to with a higher likelihood for a violent crime. So here you see that if you hear on the on the X axis, you see the departure from the average local temperature. So if it's really compared to normal temperatures getting really hot outside, there's more violent crimes compared to when it's colder than usual. Also higher temperatures are associated with more physical attraction, more murders, more rapes, more riots. So across the board, the society gets more violent when heat increases. And this is actually a hidden risk factor of climate change. And this is something that researchers are really worried about because of course the temperature is going up for everyone. And we see that this is associated with with more more aggressive aggressive behavior in society.  So we see that people become generally more uncomfortable and they experience more dangers. They become they have less resources and these are all risk factors of aggression. So just as heat, another factor that is associated with aggression is pain. And this is basically sort of similar to heat. If you're very uncomfortable, if you experience physical pain, then we are we are just have the tendency to basically lash out. So if we experience discomfort, then we are more likely to behave aggressively. And this is, for example, shown in a study in which participants were asked to place their hands in water. And in one condition, this water was really, really cold, like painfully cold. And for the other group of participants, the water was at room temperature. So they were asked to have their hands in this bucket of water. You can do so for a couple of seconds. That's perfectly fine.   A person they didn't know. So it was didn't make any sense to do so. There was nothing to gain, but they were just giving the option to aggress. And then the results show that participants that were in pain, having their hand in this ice water, were more likely to use this option and behave aggressively. Then it's important to note that this is not only the case for a physical pain. It's also the case for psychological pain. We know that if people psychologically suffer, especially if they feel lonely, if they feel excluded, they are way more likely to use aggression. And sometimes even very extreme forms of aggression. So here you see a map of the United States with high school shootings across the United States. And this is a map since 2009, where the very famous shooting at Columbine High School took place. And high school shootings is still something that is happening a lot in the U.S. And these are, of course, shootings that are done by students. And at high schools, oftentimes very lethal, killing many other students, also often killing themselves after this act. Extreme forms of violence and aggression. And if you look at all these school shootings, and these are 37 high school shootings since 2009, you definitely do see a pattern. And in general, what you see is that actually all of these murderers are males. So this is in line with what we saw in the first part of the lecture, that males are more likely to commit murders than females. So in this case, it was only males. And all these males had some kind of grievance. Most of the time, they were loners, they had very poor social network. A lot of them were bullied, a lot of them were socially excluded from the group. And sometimes there's even, and this is something that happens a lot, that other children that did survive the attack sometimes didn't even know that this kid was at their school because they felt like they were so invisible. And these were people that were really experiencing extreme forms of psychological pain, which is of course in no way an excuse for their behavior, but it can explain. And it's also sort of something that we should be very aware about, that having undergoing like this social exclusion and bullying can have very serious consequences, not only for the individual, but also for the group that this person lives in. Of course, one factor that all these people also have in common is having access to guns. In the United States, it's really easy to, or really easy, relatively easy to get your hands on a gun, which might also explain why the United States is such an aggressive country because we know that having a gun around makes people more violent and more aggressive. This is called the weapons effect. So also if you, for example, have a flag of a gun in your room, this will affect your behavior. And this has also been studied in having participants do certain tasks and then just having sort of a poster of a gun present that increased their violent tendencies. It's also demonstrated in a study in which college students were first made angry. So they were provoked in a way.  It was not an actual gun, it was a fake gun, but still it was lying around there. Or just another object, a sort of more neutral object. And then they were given, again, they were given the option to hurt another person. And here you see what happened. So here you see, again, they were given the option to deliver shocks to another participant. And if there was a gun in the room, they were way more likely to apply these shocks and also give these shocks for a longer period of time. So this is something that's very important to keep in mind, that just seeing guns already increases violent thoughts and also aggressive behaviors. So the next factor that's also something that's very interesting and studied a lot is media. Because of course in the media there's also guns, a lot of guns, and also a lot of aggressive behaviors. And research actually shows that by the age of 18, American kids have seen 200,000 violent scenes of which 40,000 murders. They were basically, they were seeing murders all the time at television at a very, very young age. And if you look at some other figures in a lot of television programs, the majority of television programs actually contain violence. It's often connected to humor, violence and humor. A lot of times the perpetrators are attractive people, so very nice models. And in the majority of the cases the violent acts or the crimes go unpunished. So this basically gives the viewers indirectly a message that violence and aggression is very normal, it's conducted by attractive people, it's funny and it will go unpunished. So this is basically something that we are learning while we're watching television. So will this also actually lead to more aggressive behavior? And there's quite some research done on that. And one of my favorite studies is a field experiment that is conducted in Belgium. And this was a study done at a mill of teenagers of a Belgian reformatory, which is a youth detention center or correctional facility.  They were already having these more aggressive tendencies. And before the experiment their level of aggression was measured. This is called a pre-measure of aggression. Then the boys were divided into two different groups. Both groups started to watch movies, fun for these kids. They watched five movies in total, one movie every day for five days in a row. And for one group of these boys, these were violent movies, so movies containing violence. And for the other group they were non-violent movies and they were showing these movies. And after that they were again observed and aggression was measured again. So this is called a post-measure of aggression. And the researchers were interested in differences in aggression, pre and post. So was there a difference in showing aggressive behaviors if you've seen violent movies? So let's look at the results here. And I think it's pretty, the picture is pretty clear. So the darker bars, the more orange bars is the pre-measure. So you see there's no difference there for the boys in the violent and non-violent group, which makes sense. It was just a random distribution among the conditions. And then for the boys that watched the violent movies for five days in a row, definitely their amount of aggressive behaviors increased. So you see that they become more violent after watching these violent movies. For the other group actually they become a little less violent. This difference is not whopping, but still for these boys it's interesting. So if you have them watch non-violent movies, which is actually quite rare because a lot of movies do contain violence, they become a little bit more chill and less likely to show aggression. So this is quite clear evidence that watching violent movies affect your behavior. And also longitudinal studies confirm that watching violence on TV predicts higher levels of violent behavior. Even years later, so even for children who watch a lot of violent TV, they grow up into more aggressive adults when they are later on. Of course, here's also a problem with cause and effect because it may also be the case that children that are very interested in aggression are more likely to watch aggressive movies in the first place. So they are more attracted to these violent movies. So that might also have something to do with it, but still there's also quite some experiments like the one I just showed you that really demonstrated a causal link between watching violence on TV and becoming more violent. So this is something that also I as a mother am pretty concerned about when I see my boys watching television. And this effect, this is all about watching television, pretty old-fashioned, right, who watches television these days. This effect is actually even more pronounced when it comes to playing violent video games. And the reason why this is the case is that if you play a violent video game, you're actively involved. You're the one doing the shooting. And this is actually affecting your behavior way more. So as you see here, this is sort of a summary of what happens if you repeatedly play violent video games where you are the one, for example, shooting the bad guys. You see that across the board people become more aggressive. So you see that aggressive attitudes increase, so people think aggression is more appropriate. You see more aggression in your world, so more aggressive perceptions, more aggressive expectations. You expect people to behave aggressively, more aggressive behavioral scripts, so you think that aggression is more common and more likely to occur in everyday behavior. And aggressive desensitization, which means that aggression just doesn't impact you so much anymore. You're used to aggression around you. So across the board there's evidence that this can lead to an increased aggressive personality if you play a lot of violent video games. There's a bot here because it seems that there's also huge individual differences in this effect. So it's especially the case for vulnerable children that are, for example, also exposed to violence in their social environment. So it's not the case that it has the same impact on everyone, but especially if you are already vulnerable, if you are also suffering from lower self-esteem, if you're in an environment that is hostile, that is unsafe, then your aggression can definitely increase due to this playing of violent video games. So we're nearing the end of this lecture, but we cannot stop, of course, before we talk about ways to reduce aggression because in the end, of course, we now know why aggression occurs, which circumstances aggression occurs, but we want to stop it, right? We want to live in a happy society where people don't use aggression so much. So let's see if there's ways to reduce aggression. The first way, the first idea and a very, you know, an idea that's very popular also among parents, like myself, is the idea that if a child, for example, behaves aggressively, what we should then do is punish them. So we should use aggression as a response to aggression. So do you think this helps? I hope you can, I can just hear you say the answer. Of course, it doesn't help. So it's a very natural idea that's, and something that has happened a lot, especially, you know, back in the days where spanking and using physical punishments was even more, was more normal and today that's, of course, no longer the case is actually even not legal anymore to physically punish your children. And there's many reasons for that and I think you can all guess them by now. So if you show aggressive behavior as a response to aggression, you're basically just learning your kids how to deal with aggression. So the next time someone behaves aggressively to the child, they know, hey, I know what to do. If someone punches me, I should also punch back because that's what my mommy told me. So if I get hurt, I should just hurt someone else. So no, if you model aggressive behavior, this will not help. It will only increase aggressive tendencies. So what does help? Now, this is something we actually already talked about in lecture six when we talked about cognitive dissonance. That's threats of mild punishments. So, you know, responding in a way saying, you know, this is inappropriate behavior, you shouldn't do so, please don't do it anymore. So using mild threats or mild punishments that works way better. And also what works very well is ignoring the negative behavior and trying to reinforce positive behavior, which is definitely easier said than done. I can say as a mother of three boys, it's really difficult to ignore bad behavior, but this is something that we should aspire to as parents. Okay, so what else?  If you feel very frustrated, very aggressive, maybe you should, you know, watch a violent K-1 fight on television to get it out of your system or maybe a molester car at the dump somewhere. Will this help? Will this help us get rid of those feelings? It's a very popular idea. It's the idea of catharsis, that just, you know, letting it out of your system, using this aggression, using aggression as a response to aggressive impulses that should solve it. But there's a lot of research that shows it does not work. Actually, using aggression will only increase this aggressive tendencies. Also, watching aggression increases aggression, so if you watch aggression on television, you will also become more aggressive. And even using aggression towards the source of your frustration, so if someone frustrates you and you respond aggressively as a response, this will also not help. It will not help in reducing aggression. It can also lead to the experience of dissonance. So thinking to yourself, yes, I punched him, but he had it come in and, you know, you start desensitizing even more. So giving in to an aggressive impulses doesn't work, even though it's sometimes very appealing. Okay, so now we've seen a lot of things that doesn't work. What does work? Mindfulness. A mindful approach. That definitely works. So you should not, you know, ignore these feelings. You should acknowledge that you have these feelings and sort of embrace them, and then if you sort of let these feelings pass by, then you can let them go. And this is really, really hard, but it definitely, there's a lot of research showing that mindfulness is related to less aggression. So if you experience aggressive tendencies, you should make sure, sometimes it works better to first distract yourself a little bit to get rid of this very intense period of anger and try to deal with this emotion. So what else can help is writing it down, making sure you distance yourself a little bit from the experience. And then you should work on conflict resolution. So oftentimes the source of frustration is another person. And you should talk to this person about your feelings of being hurt. Also try to take responsibility for your side of the conflict and, yeah, try to work it out. And what we also know is that you should actually start from a very young age helping children to deal with their feelings of frustration and anger. And there's actually experiments done in primary school children in which they are taught how to deal with feelings of anger. And this works very well in developing these skills of empathy and these skills of sort of reducing aggression and letting go of feelings of anger. So this is the end of the lecture. I hope you enjoyed.


So, let me have a small quiz before we start. So, what was the system that we talked about yesterday? What was the name of the cycle of which we talked about for air liquefaction? Do you remember? Colline system is one of them, yes. The other one for air liquefaction I talked about one system which had compressor, heat exchanger, expander and an evaporator or liquefier. What is it called as? Linde-Hampson cycle, correct. Now, talking about the cryo genes of the gases, can we recall what are the boiling points of various gases? For example, nitrogen, what are the boiling point? In Kelvin, please say loudly, correct. Oxygen, 90 Kelvin, yeah. Then helium, 4.2 Kelvin and hydrogen, 20 Kelvin. You remember, hydrogen is used as a cryogenic fuel, it is used as fuel to launch cryogenic engine where hydrogen becomes the fuel and oxygen is the oxidizer, all right. Instead of petrol and air what we have normally is spark ignition SI engines, we got hydrogen as a fuel and oxygen as an oxidizer where combustion happens and then the rocket takes off. So, it is very important that it is one of the best fuels, hydrogen is one of the best fuels, it has got something called as the best specific impulse and you find out from Google what is, what do you mean by specific impulse, okay. I will leave it to you for understand. Now, what are different types of heat exchangers and I talked about a compact heat exchanger. What was this heat exchanger? What was the name of this heat exchanger? We talked about fins, plates and all that thing. So, for example, we talked about this, it is written here, plate fin heat exchanger. If you know the car radiators, have you seen the car radiators, it says exactly these things. What are the two fluids in car heat exchangers? Car radiators, air and water, all right. So, water is the major coolant, that is what we do. So, whenever you find that the car is getting heated, you have to add some water to it basically, all right. So, radiators of the car are nothing but this kind of heat exchangers made in a different way, but they are all plate fin heat exchangers, all right. Specifically meant for automobiles, specifically meant for liquid and the heat of combustion to be removed by water. Now, this was all about bigger part of cryogenics and now I will come to smaller part of cryogenics and one of the major usages of cryogenics is to have a cooler in satellite, all right. The satellite which rotates around us has always does need to have a cooler sitting down there, cooling the electronics is a very important thing cooling the electronics and therefore, whenever I say something which is related to space, it has got all the limitations. What are the limitations for space? Small volume, small mass and efficient and no maintenance requirement for at least five years. This actually brings very stringent requirements and big companies actually are working toward this and we will talk about those devices which we have worked for ISRO right now. We are working for them, we have already worked for this. One of the devices is this, this is the cooler, all right and I will just tell you what is that. That device is called as cryocooler or a refrigerator which brings down temperature to 80 Kelvin or lower than 80 Kelvin or 4.2 Kelvin or 1 Kelvin, etcetera. Like a domestic refrigerator you have at home, it is exactly functioning the same way. Now, can you imagine if I were to bring down the temperature 4.2 Kelvin, which refrigerant should I use? Can I use R134 in this? If I were to bring down the temperature, I will of course compress the gas, expand the gas and the cycle will continue, all right. Now, can you think about what kind of fluid I should use, what kind of working medium should I use, what kind of refrigerant should I use in order to come down to very, very low temperature? Can I use R134 which is normally used in our refrigerator? No, then why no? It will get solidified, isn't it? As you come down the temperature, it will get solidified, isn't it? Every gas will become liquid and liquid will become solid. Can I use nitrogen? I cannot use nitrogen also because nitrogen gets solidified at 63 Kelvin. It gets the boiling point at 77 Kelvin and it gets solidified at 63 Kelvin. The only fluid that remain in gaseous state is helium, understand? Up to 4.2 Kelvin, helium will remain in gaseous state at 1 bar atmospheric pressure. And therefore, normally in cryogen is the only inert fluid. At the same time, I want something which is not inflammable, etcetera, all the characteristics that we need to have for a working fluid. So, all these cryocoolers normally will have helium as a working fluid. So, I will compress helium and expand helium in order to go down lower and lower and lower in temperature. Like R134 gas that is in our refrigerator at home, because we are there only at minus 10 degree centigrade, R134 characteristics are ok for that thing. But if I want to come down, this cryocooler normally will have a working fluid which is going to be getting compressed and expanded, alright? And the working fluid always will be, most of the times it will be helium. Sometimes it will be hydrogen also, low pressures, but we are all, there are human beings sitting down there inside the satellite I am talking about. I got all the electronics which is inside the satellite to collect data. Can the human beings, everybody can sit at certain, you have to keep all the normal temperatures and pressure condition. So, all these things actually will be confined to normal temperatures and pressure. So, once you add gas, it remains in the gaseous state because it is a closed cycle, alright? So, this is what a cryocooler will be. Every cryocooler will have a compressor, a heat exchanger which is a very important component again, alright? Then it will have expansion, device and evaporator. Now, let us take an example of your domestic refrigerator. It has a compressor. Have you seen a compressor? There is a compressor, right? Then there is a heat exchanger also. Have you seen the backup of the fridge? There is a condenser what we call as a heat exchanger, alright? Because the heat of compression is taken over by that thing. And then you got our expansion device. What kind of expansion device you have in domestic refrigerator? Do you know? How do you expand the gas from high pressure to low pressure? You get a capillary tube there. You can see in a freezer. If you open the freezer, you can see a capillary tube inside, alright? And that is expansion device over there. You get lower temperature and your evaporator is entire, the freezer is evaporator actually. The air gets cool and air gets circulated in the fridge. And that is why the bottom most part, let us say assuming that the freezer in the top, the bottom most part will be warmer. And the evaporator part which is the freezer is going to be the lowest temperature, alright? By natural convection, then you will have air moving around and therefore everything gets cooled. Here I will have electronics to be cooled. And therefore my object to be cooled, this is what we call in a close, and this is going to be working in a closed cycle manner the way we have domestic refrigerator working. And a cryocooler consists of compressor, heat exchanger and expander as shown in the schematic. The cold generated in the expander is exchanged between, so this is object to be cooled. And this object to be cooled could be anything which is generating a lot of heat, which needs dissipation. If you don't have electronics being cooled there, the job that will be done. First of all, life will have a problem, alright? At the same time, you'll have a signal problem. You'll have a lot of noise there. Whatever data you want to transfer, you'll have a lot of problems there. So this object to be cooled can be cooled at 80 Kelvin, 90 Kelvin depending on how much that temperature need to be there. Now these cryocoolers are classified based on the kind of heat exchanger they use because this class is basically about heat exchanger. This cryocooler classification is based on the kind of heat exchanger that it uses. And therefore it's classified based on the heat exchanger. Now heat exchangers, you have seen several types, but I'm not giving a broad classification of heat exchanger which are called as recuperative heat exchanger and regenerative heat exchanger. Now the very important things. Till now, what you have been studying are all recuperative heat exchanger. And most of the cryocoolers use regenerative heat exchanger. What is the difference between the two? And based on the kind of regenerative heat exchanger, they are further classified on different types of coolers, et cetera. So the refrigerator that we have at home is a recuperative heat exchanger and it has got Joule-Thompson valve or Joule-Thompson mechanism, the expansion in capillary to be called as Joule-Thompson expansion. And while the regenerative heat exchanger I'm going to talk about will be based on sterling cooler, Gifford-Machman coolers or a pulse tube cooler. And they are accordingly called as GM cooler, sterling cooler, pulse tube cooler, et cetera. They're all based on a regenerative heat exchanger. Can you think about what could the differences be between regenerative heat exchanger and recuperative heat exchanger? Can you stretch your mind because of the names, because of the classification, because of the name itself of regenerative and recuperative? As I said, till now what we have studied are all recuperative heat exchangers. And what I'm going to talk about now is going to be regenerative heat exchanger. So what is that distinctly different that you see the heat exchanger that we have studied till now and the regenerative heat exchanger? Any idea? Can you stretch your mind with the names recuperative and regenerative? Come out with whatever you feel. As I said, till now, all the heat exchanger that we have talked about have been recuperative types. What could be the differences be? Same fluid in the recuperative. But we just talked about having water and air, for example. There are two different fluids. Isn't it? We say fluid A and fluid B. It could be water or some hot gas. There are two different fluids. As the name suggests, any idea that what could be the regenerative and what could be recuperative? Nevertheless, let's go ahead. What you said was exactly opposite. So when I said recuperative heat exchanger, it means in the recuperative heat exchanger, the flow direction of two fluid is constant, as shown here. What do you see here? I got a fluid A and fluid. One fluid is a hot fluid, one fluid is a cold fluid. And these two fluids are separated from each other. They never see each other directly. They are, actually, they're always a wall between them. And the heat is transferred through conduction, first convection and through conduction. This in between the wall is there and it separates these two fluids. And therefore, fluid A can be anything. Fluid B can be anything. As long as they are hot and warm and they are designed for those mass flow rates.  They never mix in each other, all right? And they are partitioned physically. The fluid A is different, fluid B is different. And they are simultaneously flowing. That means when the fluid is flowing, fluid B also is flowing at the same time. So their directions are also fixed. As you say, they could be counter-flow or cross-flow or parallel flow, isn't it? So that means one fluid is going this way, other fluid will come other way. Or maybe cross-flow, whatever. But their directions do not change during the operation, during the performance, all right? During the execution. They don't change their directions at all. That means their flow rates remain most of the time constant. The flow rate variations will be minimum in these cases. So in a recuperate heat exchanger, the flow direction of two fluid is constant as shown in figure. The two fluids are separated by a solid boundary across which the warm and cold fluids exchange heat. And the direction of the fluid flow may either be counter-flow, cross-flow or parallel flow as you understand, all right? Now the difference between this recuperative heat exchanger and the regenerative heat exchanger is this. What do you think from this fluid? Can you see this? And can you come out with some conclusions from this? This is what the regenerative heat exchanger will be. You have seen the recuperative heat exchanger schematic. And now I'm showing you the regenerative heat exchanger schematic. Can you now say what is this as compared to what it was, recuperative heat exchanger? From the schematic, what is the first thing that strikes to you here? Correct, very correct. Yes? They may mix, yes. Anybody else? He says in between matrix, he says they may mix. Anybody else? Is there a solid boundary between the fluid A and fluid B? That's a major difference. There is no boundary between fluid A and fluid B. So there is a third party coming into picture now. You've got fluid A, you've got fluid B, and you've got a matrix material. Do you understand matrix material? So now what happens? The fluid A will flow for some time in one direction, and it will give off its heat to the matrix material. The matrix material will store the heat. After the fluid A has gone, the fluid B will come, and it will take the heat from matrix, and this will continue. That means both the fluids do not flow simultaneously. For some time, fluid A flows some other time of the cycle, fluid B flows, and the heat transfer is not direct, heat transfer is indirect. From A to matrix, and from matrix to B, B to matrix and from matrix to A, all right? There is no direct connection between A and B. And secondly, the A and B, the A and B are not physically separated. It is the same matrix which is open to A for some time, which is open to B for some time, and this will be done by valves. That means it will allow A to flow for some time, and it will allow B to flow for some time. But as you said, there can be chances that they can get mixed together some time, because A may not go completely out and B will come in between. So, sometimes there is a possibility that these two fluids can get directly mixed also, all right? Now, this fluid A and fluid B can be the same, or they can be absolutely different. That means fluid A goes, something happens to it, and fluid B comes back. So, these are directional changes. So, in the recuperative heat exchanger, we had both the fluids which were simultaneously flowing. Their directions were fixed. Here, they are not constant flow. They are a flow which go from zero up and comes down. Other fluid comes and goes zero and goes up. That means they are subjected to oscillating flow.  That they are zero for some time, go to the maximum, come down, and the fluid B will come at zero, go up and come down. So, in earlier case, they were all steady flows. Well, in this case, they are oscillating flow. And the oscillating flow heat exchanger is going to be subjected to, or these devices, where in such heat exchangers are there, they are subjected to vibrations. Because the fluid A flows for some time, fluid B will flow for some time, they will be oscillating flow like that all the time. And therefore, vibration is one of the problems, which is not there in steady state flow, which is what we say recuperative heat exchanger. Now, the moment I say oscillating flow, I don't have heat transfer correlations for oscillating flows. And therefore, I have to worry about the design of such heat exchangers also from that point of view. There are no correlations for oscillating flow as such. While most of the time, we have got correlations for steady flow, right? We say Reynolds number greater than this, use this correlation. But here, the flow rates are changing, the mass flow rates are changing. And therefore, now we have to worry about the heat transfer correlations in such cases, all right? So, these are all now regenerative heat exchanger. In the regenerative heat exchanger, a matrix is used as an intermediate heat exchanger medium between the warm and cold fluids. The flow is periodic as I just talked about in nature, alternating between the warm and the cold fluids across the matrix. It is important to note that it is an example of indirect heat transfer, all right? There is no direct heat transfer between fluid A and fluid B, and they are not moving simultaneously. Now, this was the example what we talked about yesterday, recuperative heat exchanger. This was what we talked about Linde-Hampson. And then we talked about other cycle called Brighton cycle, that is what most of you know. And we also got Claude cycle, if you know about this. They're all recuperative heat exchangers. Collins cycle will come after that, six heat exchangers. But the regenerative heat exchanger now will work like this. A regenerative heat exchanger will have a compressor which actually moving oscillating. There's only one compressor and you can see one output only here. So, the gas goes through this and this is the heat exchanger, a regenerative heat exchanger which is filled with matrix material. Now, can you imagine a matrix material through which the gas flows? And therefore, the matrix has to be porous medium, all right? Because there is a heat transfer between the gas, the working fluid and the matrix. And we have to ensure that this heat transfer is perfect. What is the requirement from the matrix point of view in order that heat transfer is fantastic here? What do you think that the requirements from matrix material will be? Can you think? What kind of matrix material should be there? We should take heat from this fluid A, store it and give it off, give it off. What do you think? Can I put anything here? Yeah, can you think what are the properties characteristic requirement of this matrix material will be? First of all, it should be porous. You understand that? It has to be porous. If it is not porous, what will happen? The fluid will not be able to go through it. All right, so it has to go through. Now, suppose it is just 10% porous. That means only some fluid will go through it. That means the mass flow rate or the pressure drop will be there. If it is very much porous, if it is 90% porous, all right, what will happen? That means the mass of the matrix material will be less. So it has to be optimally designed. Important characteristic it will be that it has to hold heat. It has to have very large heat capacity. You understand this requirement, the very important requirement of the matrix material that it has to have very, very large heat capacity. And as the temperature gets lower down, the heat capacity of the material starts coming down. And therefore you have to choose such matrix materials which has got very high heat capacity even if the temperature comes down. Do you understand this requirement of a matrix material because it is going to store heat? Its heat capacity at lower and lower temperature should be higher and higher. But every material heat capacity will start coming down. And therefore we should see that it has got finite heat capacity at load. I'm talking about 4, 5 Kelvin also. And therefore the heat capacity at 4, 5 Kelvin also has to be substantial in order to store the heat. They are called as storage heat exchangers also many times. Storage type of heat exchangers. And therefore this is a heat exchanger and this is a moving component piston and this is called a displacer. And because of the motion of this piston and displacer, you will get cooling effect at this point. And whatever electrons you want to cool that will be cooled at this point. We are not talking about how Sterling cycle works. Sterling cycle works. Sterling cooler works on Sterling cycle which all of you know. Sterling cycle has got a COP equal to Carnot cycle. And that is achieved by the movement of this piston and the displacer and the phase difference between the motion of the piston and displacer. What is important however is the heat exchanger design or the regenerative heat exchanger design here. This is a Sterling cryocooler. There's a compressor sitting here which is a linear compressor working on linear motor. What is linear motor? You've got a magnetic field, you've got a current, you've got a force. Understand the left hand rule. And the moment you've got a current which is oscillating flow, your piston also will go up and down. So this is the piston which is moving up and down here and it's a linear motor here. Can everybody see how? All right. So you've got a piston which is sitting here and a displacer which is over here. And I generate cooling effect at this point. And whatever electrons you want to cool will be kept here at this point. It's called as cold finger. And I will get around one watt of cooling effect at 80 Kelvin at this point continuously. You know, even if it works for years together at this cold finger, you will get a one watt at 80 Kelvin cooling effect. And the power input to this will be around 50 watts power input and you'll get one watt of cooling effect at this point. So what is the COP of this machine? I'll get one watt of cooling effect at 80 Kelvin for 50 watts of power input. So one by 50, that kind of a thing. At 80 Kelvin. COP is always required to be defined at temperature. All right? So this is, there is a inside, you've got a displacer. So this is a piston which is moving up, this is a displacer which is moving up and you get a cooling effect at this. This is developed in our laboratory here. This has been handed over to ISRO. We couldn't meet the target of mass reduction, but performance we could get. But we could not, this is heavy, it's around two or three kilo right now. And they wanted 1.5 kg, which they are working on that for. So technology was developed and they can do further things. Coming back to this cryocooler, this is sterling cryocooler based. All right? There's something other other cryocooler like a Gifford map on cryocooler and something called as pulse tip cryocooler also. And in practice they look like this. They are big cryocoolers, they are small cryocoolers, miniaturized cryocoolers. This cryocooler sits on every MRI machine. If you go to any MRI machine in the hospital, this is the cryocooler which sits on it and keep the magnet superconducting. All right? This costs around 30 lakhs rupees and produces around one watt of cooling effect at 4.2 Kelvin. So you can imagine what numbers I'm talking about for which eight kilowatts per input has to be given. So this is called as GM cooler and this is called as pulse tube cooler. And this is the regenerator here. This structure houses regenerator. That is what we are talking about. This regenerator is filled up with porous material and the porous material with that, we use this stainless steel mesh. Mesh, you know, everybody knows the mesh, right? And these are the meshes which I can show you which we have made in our laboratory. Can you see these meshes? Maybe you can pass it behind just to have a look at this. It's like a cloth. It's like a cloth of having 400, all right? So have a look at that and this is what regenerator is. This regenerator is housed with these meshes and as you come down the temperature, the material will change. Why the material will change? Because as you come down the temperature, the heat capacity of the material goes down and therefore you have to choose material in such a way that the heat capacity of this material is finite at lower and lower temperatures. This is a two-stage cooler. So you've got a first stage here and a second stage here. This will bring down to 4.2 Kelvin and this is what is used and this is what is done by various company called Sumitomo and Leibold and all these people. They are big players in the market who charge heavily. There are three or four big players who sell these companies. Now this is what we call as pulse chip cooler. In the pulse chip cooler, we don't have any displacer at all and therefore you've got a compressor and you've got a regenerative heat exchanger here and you get cooling effect at this point. So you can see here. I can put it like this here. You can see that. So there's a compressor sitting down here which is this. This is filled with regenerator. The meshes are filled inside this and I get cooling effect at this point at the center and these are pulse tube. So you can see lowest temperature at this point which is at this point, all right? So these are different types of mechanism but the major important thing is this regenerator which is the heat exchanger that we use in all these things. So depending on the temperature that we talk about, you have to use the correct material. Now these are all normally 80 Kelvin for space applications but as I said, as you come down the temperature, application changes. A lot of people use it for gas liquefaction, superconducting material. In order to get superconducting devices we reach lower and lower temperatures. So now we have got superconducting motor, superconducting generator, superconducting transformer, superconducting energy storage devices. They all need lower and lower and lower temperatures. I think you all know superconductivity, right? As you come down the temperature, the resistance of the wire will come down and you can send more and more current through it. So this regenerator needs to be analyzed and they are subjected to pulsating flow rates and therefore the matter of research here is that how to analyze these things? So you all do CFD analysis, you all do heat transfer analysis to design a regenerator. So these are heat exchanger which need to be analyzed numerically because as you travel the length of regenerator, the temperature, the density changes, you know everything changes. The fluid changes, the fluid properties do change. So these are all subjected to various conditions and therefore pressure drop, heat transfer coefficient of cryogenic condition, steady flow analysis may be used, property changes of gas and materials and these are all topic of research and still today if you go to University of Wisconsin, if you go to MIT, if you go to Stanford, all these matters are up under research. There are a lot of research groups who are working on this. The whole idea is to, can we still make it miniaturized? Can we still make it smaller and smaller and make it more and more efficient? The effectiveness of heat exchangers for the regenerator one also has to be more than 95%. So we want to have minimum pressure drop and we want to have maximum cooling effect. That is all the objective for every heat exchanger normally will be. So these are different ways that you analyze and normally the numerical techniques will be used for these things. As you go, yeah. So we can use recuperative heat exchanger, but then I will have to use isenthalpic wall or isentropic turbine for example. Here just because of the motion of the piston and the displacer, I get cooling effect. The gas get expanded. So what I want is the oscillating flow and because of the motion of these two parameters, displacer and piston. If I go for recuperative heat exchanger, then I have to have expansion device which is basically the Joule-Thompson wall. I mean I'll come to recuperative heat exchanger also for Joule-Thompson, but it has got a lot of problems. Why is it better? This can be miniaturized. Joule-Thompson can also be miniaturized and I'm coming to that, but then there is a very important requirement there and I'll come to that in now. So as you come down the temperature, the heat capacity of the regenerator material starts coming down and this is what you can see. So you can see all these materials, this is copper stainless steel. You can see that the CP heat capacity is coming down below 20 Kelvin. But now there are magnetic materials which are normally coming from China. You know rare earth materials which are normally coming from China. These materials show a second order transition. Do you understand second order transition? Phase change. The first order phase transformation happens between water where the latent heat is involved from liquid to gas. Here the phase change is not there. It's called a second order change where the entropy goes higher and you can see that this material suddenly shows peak here. The material go from ferromagnetic to antiferromagnetic transition. These are a very big topic of research in material science and suddenly at lower temperature, these materials show very high CP value and now we want to use these materials in the regenerator because their heat capacity below 10 Kelvin suddenly goes through a transition, all right? So I cannot use now stainless steel mesh but I use rare earth materials, erbium-3 nickel, erbium-nickel cobalt, holonium copper. These material cost a lot. For 100 gram, you have to pay $10,000, all right? And a lot of research, therefore, is happening on this material science. A lot of material science is very important in heat exchangers, all right? And because China somehow manages to have 80% of the rare earth come from China and we got only 67% remaining from Japan, the cost of these materials have heavily increased during the last 10 years, all right? So these are the things that you know, you can just, because of this transition at low temperature, we want to exploit that characteristic and use it as regenerator material. And therefore what I do is normally make hybrid regenerator, yeah. Can you see these materials? These are not small spherical balls now which we use in the second stage of the material. So up to 20 Kelvin, I can use these meshes which I have circulated. At 20 Kelvin, the CP of this material almost touches zero. Then I use these materials, small spherical balls and they are made by a company called Toshiba which I'm sure all of you may know. And these are now used in the heat exchanger device. They store the heat because their heat capacity at below 20 Kelvin goes through this transition phase and then they can store the heat. Then only I can use this. So it's very important that you understand the pressure drop across this now, the heat transfer to this also. The porosity is a very important problems. All these things have to be analyzed and have to be understood by this. So what we do normally, we go for a hybrid regenerator. You can see hybrid regenerator. So up to some point you can use one material, material A, material B and material C depending on their heat capacity variations at lower and lower temperatures. And these materials as I said are very, very costly. Therefore they should be optimally designed, optimally used. I have worked on all these things. So you can see that they are all called hybrid regenerators. All right, so now with this background, I will now take a small case study on which we have worked in India with Indian missile program. And the question that you asked was, why don't you use recuperative heat exchangers? Yes, we do use recuperative heat exchanger. But in the recuperative heat exchanger can be miniaturized, but then I have to use very high pressure. I expand the gas from 150 bar to one bar because I want cooling effect within fraction of a minute. And I can't use it continuously now. I just want cooling effect when the missile takes off. Do you understand this? So I use recuperative heat exchanger cryocooler, which is called Joule Thompson cryocooler, which can be miniaturized. And this is what we have designed. I'll talk about small case study and then we'll come back to some question answers. So any question till now, till the time I have talked about cryocoolers with regenerative heat exchanger. Any questions on this? Anything, whatever you feel has. And if you want to see more, you can come to our lab. We've got 10s on 15s of cryocoolers made and given to various people in atomic energy and space and everybody. Any questions on this? Could you understand the specific heat capacity requirement at lower and lower temperatures? All right, and that is where we use magnetic materials to go down to four Kelvin, three Kelvin, two Kelvin, et cetera. So we stack them together, one by one. So everything will be filled one by one through this so that this completely will get filled. Almost we require 1000 meshes like that. Every mesh is characterized by mesh number. These are all 400 mesh numbers. That means in one inch, you've got 400 wires. And the porosity of such meshes are around 65 to 70%. That is what we require to calculate the pressure drop across it or the frictional pressure drop across it. All right, any more questions? Okay, with this background now, I will give a small case study which we have designed a cooler and given the data to government of India. And this was the project. So performance analysis of miniature Jules Thomson cryocooler for infrared detector for cooling in missiles. So where do you require this? When the missile takes up, and you can see all this in Google again. So miniature Jules Thomson cryocooler, when the missile goes, it has to strike a particular object. And this object needs to be corrected through the infrared because in nighttime also you'll work on this. Such devices are also used by the border security forces because you work in the night vision camera. You work at very low temperature. You work at when the normal light is not there, visible light is not there. And you want to see, you know, thermal imaging. All right, for which you require infrared detector. And this infrared detector works only at very low temperature, 80 Kelvin because at that time, the noise gets minimized. At that temperature, noise gets minimized. And therefore signal to noise ratio is very high. I want very high signal and very less noise. So SNR, signal to noise ratio is going to be very, very high in those cases. So here's the, I've taken a figure from here. And at this point somewhere, the object to be located will be sitting down. It's called a seeker. It is called a seeker position. And this seeker will be somewhere here. You can see here, seeker assembly. This seeker assembly has got infrared detector sitting down there. It detects the object to be hit. And therefore it needs to be cooled to 80 Kelvin. Immediately when the something gets launched within a fraction of a minute, its temperature should reach down to 80 Kelvin. Now in no coolers, you can reach 80 Kelvin from room temperature in a fraction of a minute. If I were to do that, I were to do that thing, I use now Jules Thomson recuperative cryocooler. But then my inlet pressure is around 200 bar nitrogen gas. So the cooler sits with a bottle. It has got 200 bar nitrogen gas sitting down there. And suddenly you expand from 200 bar to one bar. Thereby generating cooling effect reaching down to 80 Kelvin within seconds. And during the flight time, this detector is maintained at 80 Kelvin. Very important device. And we are still importing from a lot of other facilities right now. So this Jules Thomson is a simple one. You can see the container, small bottle sitting down here, right? With 200 bar or 400 bar nitrogen gas, just goes through heat exchanger. And gas gets expanded and cooled the secret assembly or infrared detector and goes back to atmosphere. Nitrogen gas is let go to the atmosphere. It's not a pollutant anymore. So this small cryocooler and this is a miniature cryocooler. This should be as small as possible. This should be as small as possible. What is important? The success of all these cryocoolers depends on the heat exchanger design. How compact, how small, how efficient, how much heat transfer area that you have in a given volume that you have decides the success of such cryocoolers. So this infrared detector is required on missile to guide to the target. These detectors need to be cooled to 80 Kelvin in order to get a clear SNR here. The cooling mechanism should be compact, fast and reliable. And it doesn't want any moving parts. So there is no moving part here. We are just getting a high pressure gas. There is no compressor now. High pressure gas, expand the gas and get low temperature, all right? But that low temperature I should get within less than a minute time. Very important design requirements. This cooler will look like this. And I'll show you from very close that you have got a, this height is of the order of, let's say, three inches. 100 millimeter or something like that. All right, how do you make it? You've got a mandrel here sitting down around which you find fin tube, all right? This is a fin tube. And through this fin tube, the hot gas or the warm gas will go inside the tube. It will come down across the length and at the end you've got a Joule Thomson expansion, small orifice. Expand the gas and the expanded gas will go through this fins, go over this fins. So gas can come up to 200 bar. Can you imagine this gap? The gas at low temperature will go around this and go to the atmosphere. While it is going up, it is pretty cooling the incoming gas again. So heat exchanger happening between the gas in the tube which is at 200 bar. Expand from 200 bar to 1 bar, 1.5 bar. And then it goes out, cooling the incoming gas over the fins. Now what is making it very compact is the number of fins per millimeter sitting down there because it is very high number. And this is the structure of a Joule Thomson recuperative heat exchanger. Aren't these recuperative heat exchanger? The two gases are separate. They are not mixing each other. This is not taking matrix here, all right? One gas is at high pressure coming through the tube. Other gas is at low pressure going over the fins, all right? And how does it look? It looks like this. Can you see fin tube wound around here? And I get low temperature at this point. The gas will come over here, go through the tube, get expanded, actually get liquefied here. So I get latent heat cooling at this point. At 80 Kelvin, I'll get liquid nitrogen here. It cools whatever to be cooled. And this gas goes over this fins from outside and goes to atmosphere. If I magnify, can you see the fins here? If I magnify, you can see. And now I will show you actual piece. It is as small as this. This cryocooler produces 80 Kelvin in 16 seconds. And you can see that how efficient is heat exchanger. Everything depends on the heat exchanger design, all right? So not only the manufacturing is very important, but at the same time, the design is very important, all right? So the design task came to us to make. And this was a consulting project for almost a year. But then design has to be done because the gas, you can see the properties of gas will change from 200 bar to one bar.  So here all the numerical analysis has to be done. So in fact, all the academic knowledge that you are getting in this course is very important. You actually solve the mass, condition of mass, momentum, energy equations, take the property corrections, and then couple it with heat transfer knowledge and the correlation that you have here. We have done exactly the same thing, but very important that whatever you are learning, exactly same thing we did. It's not the thumb of rule or so whatever. Solve momentum equation, mass balance, energy equations, for every fluid, high pressure gas. So you can see that fin tube material will come into picture. Across the fin tube material, the heat transfer is happening. So I have to worry about the properties of the, conductivity of the heat transfer material also. Conductive of the gas, conductivity of the material also, because this side is 300 Kelvin, that is room temperature, this side is 80 Kelvin. So you have axial conduction also, across what is what we call as solid conduction. All these things have to be, milliwatts of cooling effect are very important, because I'm going to get only 700 milliwatts of cooling effect at 80 Kelvin. I have to worry about every small losses in all these things. Not forget that radiation loss also will come into picture. For this design, I can use effectively fluids of argon and nitrogen, both because ultimately the working fluid has to be inert gas always. It can be any explosive gas or inflammable gas or poisonous gas or reactive gas. Nothing, normally all the refrigerant should be of this sort basically. What is important is this heat exchange, their length, heat exchange dimensions and all these things, very, very important. Can we understand this? And absolutely at the end, can you optimize the design? And then comes the manufacturing. So before that you have to understand all the thermal aspects, the mechanical aspects and then design. So this heat exchanger has gone through a typical control volume approach, which is what you will understand later. And the governing equation, continuity, momentum, for hot fluid, cold fluid, the wall, the mandrel and the shield. So everybody who is involved in the heat exchanger has to be analyzed. And they have to analyze in a control volume operation. Not, you don't take broad K into DT by DX, no. Actually I made a lot of meshes there and take property correction for every control volume, small, small control volume. What are the inputs? The inputs say that this has to be in this area only. These are got boundary conditions. So I have to worry about that thing. Property data, heat transfer correlation, friction factor. This is what the property data will come from. This is what governing equation will come from. This is input. And the output, therefore, will come to all this. What is the temperature distribution across the line? What is the cooling effect that I'll get? Will it be okay with these things? All right? So cooling capacity, temperature distribution across the length of heat exchangers and all these things are important aspects in order to design a heat exchanger. So whenever you go in industry later on, the heat exchanger is such an important thing that you can't change it every time. And therefore your efficient design, the optimized design has to be understood with all this basic thing. Nowadays a lot of packages have come. A lot of NC's and Fluent and all these things have come. But if you want to design something extra, all right? For such a heat exchanger, they will not be part of normal designs. And therefore you have to understand that first and then only can design. So actually now, say, I will go through a very big academic exercise which we have done and solve all the, they're all equations now here. And across a given control volume, we solve all these equations simultaneously. We need a lot of computer time, of course, but yes, they can be solved. And this is what you all can do for your BTEC projects or anybody who's interested in all these things can always be doing those things. You can publish, we have published several papers on this and you can read that in the applied thermal and cryogenics and all those papers. Ultimately, I get validation from some data that is available in the literature and I see that my results match, that is what normally we do benchmarking. If my code is correct or not. I'll see what are the results published in the literature and I'll see my code gives the same results so I can say that my mathematics is correct and then I apply to new design now. So there I wanted to study about various parameter. What happens if my pressure changes? What happens if 150, 200, 250, 300, what will happen?  The pressure drop is the most important thing in this case because 200 bar input, by the time it comes to Joule-Thompson expansion and other end, 50 bar is lost at the delta P across. So I have to take into account how much pressure drop that happens in heat exchanging. 50 bar is the pressure drop, almost of this order. So by the time it comes for expansion, there's 150 bar only. So I have to therefore worry about what should my starting pressure be in order to come to the correct optimized design. All right, so as a function of mass flow rate, fin density, fin length and then I'll see what is available in the market. Do I get such a fin density? Can I manufacture it? So we understand first the basic knowledge and see what is standard availability in the market so that then I can actually see nearby and make my design. So you can see from this figure that I have plotted effectiveness of heat exchanger versus the mass flow rate and versus the pressure drop. So you can see that as the mass flow rate, this is for Aragon and Aragon the inlet pressure is 140 bar and the return pressure is 1.3 bar. So you can see the gas is coming at 140 and going at 1.3 bar from below. As the mass flow rate increases, the pressure drop increases. So you can see the pressure drop here is 60 bar at 0.25 gram per second and as the mass flow rate increases because of the increase in pressure drop, the effectiveness starts coming down. It has come down from 98% to 96% or whatever. This effectiveness will design can I get cooling effecting 16 second, 20 second, 25 second, et cetera. But as you can see that if I increase the mass flow rate then the pressure drop is V square, isn't it? Pressure drop is velocity square, delta P proportional to velocity square. And therefore as you go ahead, this is like increasing heavily. So I have to understand these parameters and then decide what should my flow rates be? What should my starting pressure be? Pressure drop of 60 bar, 70 bar. So I can possibly come somewhere here. I have done this study for various fluids and then I understood the effect of fin density. You can see as the fin density increases it is getting better and better. But can I manufacture this? Can I manufacture such densely spaced fins? Then the fin height. So all these things have to be understood. And here you see that effect of fin density on cold fluid pressure drop, all these analysis has to be done. And then based on this, based on understanding that we had, we could design our own cooler. Which wanted to have 1.2 to 1.5 watt at cooling, cooling effect at 80 Kelvin working fluid nitrogen, diameter 10 millimeter. Can you imagine outside diameter to be 10 millimeter not exceeding 10 millimeter. And the length should be only 30 to 35 millimeter. Such a compact heat exchanger. Which will sit on the missile to cool. So there are different diameter. Inner to 0.3 millimeter is the tube diameter. Can you see manufacturing at 0.3 millimeter tube on which the fins are wound? Very difficult to manufacture such things. All right, so outside diameter up to is 0.4. So 0.3 to 0.4 is the fin height. And this is what makes it very, very difficult. Fin density is around four fins per millimeter. Can you imagine in one millimeter we got four fins. That kind of manufacturing requirement we have. And then I have done the temperature plots across the length of heat exchanger. This is high pressure and this is low pressure. At this point the gas expand from high pressure to low pressure and you get rich 80 Kelvin temperature. This is the exit of heat exchanger. Which is subjected to isenthalpic expansion then and you get lower temperature. And this is the return temperature. And this is what we want to calculate. We want to see that thing. And this is what you say as the heat exchanger length increases the cold fluid pressure drop will change. And the hot fluid pressure drop will change. So it starts with 205 bar around. By that I mean it comes 170 bar. So around 35 bar is the pressure drop in this case. And this is what we wanted to optimize. And if I want to optimize further, this is my optimization chart. Where you can see at 0.2 gram per second I get maximum cooling effect. And the pressure drop starts increasing further. So this is a pressure drop. And this is what I say optimize when the pressure is 207 bar. And now I can do whole optimization, which you can see the next slide. So this is what you can see. With the different pressures that you have, 180, 200, 207, 250, 450, you can see the optimization chart of design of different mass flow rate. And this is what was the knowledge required for this. What should my pressure drop be? What should my mass flow rate be? And what should my starting pressure be? In order to get so much of cooling effect at 80 Kelvin. So this is the maximum cooling effect that we get when you got 180 bar as the pressure. As you go on increasing the pressure at 280 bar, you can get up to five watt of cooling effect, but for which corresponding mass flow rate has to be 0.35 gram per seconds. And now this has been handed over and the manufacturing is in progress. So this is a very important exercise, long exercise. It needs a lot of computer time. But ultimately we have verified these figures. We have done some experiments also in the defense lab that we had. And the knowledge has been transferred. These are all recuperative heat exchanger, miniatures, Jules Thomsen cryopolar, as we call it. So a numerical model and all these things. And this is all given to Ministry of Defense. And you can see the letter that we got ultimately from Government of India that the work is very much appreciated and the work is being considered as Jules Thomsen and the work is in progress right now. This gives us confidence, this gives them confidence that nitrogen argon could be used and all that thing. I'll stop here and questions now, any questions on this. So a lot of knowledge has been given to you in one hour. We talked about various regenerative cryocoolers and we talked about the Jules Thomsen which is the recuperative cryocoolers. Could you understand the difference between the regenerative cryocooler and the recuperative cryocooler? Could you understand the difference? Could you understand the requirement of specific capacity at lower temperature requirement for regenerative cryocoolers? What is the material I use for, let's say 20 Kelvin? The stainless steel measures that you have been seeing. Can you give me all the measures back, please? And at lower and lower temperature, what are the material that we used? Magnetic materials, rare earth materials, right? Irbin 3 nickel, cobalt, a lot of materials are coming basically. Any more questions anybody has or any curiosity you have, you can always come down to our lab and all these things you can see yourself there. Working models are there. Everybody is working at 20 Kelvin, 10 Kelvin and all that thing. And also we are working on cryogenic engine now to help all the heat transfer and heat exchanger requirement. Any questions you can send email or of course, Professor Gaitundi, you can always ask. Okay, thank you very much.