 So, welcome to the 33rd lecture on cryogenic engineering under the NPTEL program. We are going to start today a new topic and the earlier topics that have been covered till now are as follows we are introduced the cryogenic engineering part. We talked about properties of cryogenic fluids. We talked about properties of materials at cryogenic temperature. We talked in detail about gas electrification and refrigeration system. Also we talked about gas separation there. We talked about cryopulers. Now taking the matter ahead in the current topic now we are going to cover cryogenic insulation which is a very important part in cryogenic engineering. Under this topic we will cover why insulation? What is the need to have insulation in cryogenic engineering? Then we will talk about different types of cryogenic insulations. We will do a comparative study amongst all these cryogenic insulations that are possible. Then we will see applications of this cryogenic engineering insulations and this topic will be covered in around three lectures and then we will have tutorials and assignments during the course of these lectures. So the outline of this lecture is cryogenic insulations, why insulation? The types of insulations and we will talk about expanded foam and powder insulations and we will have some radiation fundamentals, fundamental associated with radiation mode of heat transfer which most of you know for sure. So introduction as to why should we have cryogenic insulation and before we go to you know the formal lecture you know that we are talking about very low temperature, we are talking about 77 Kelvin 4.2 Kelvin and our ambient temperature is normally around 300 Kelvin which is quite high as compared to this cryogens. So there naturally heat transfer from high temperature to low temperature and therefore we will always have heat rush from outside to inside and therefore our fundamental task is to reduce this amount of heat transfer from very high temperature which is 300 Kelvin which is ambient temperature to the cryogenic temperatures. So this is very straight forward that why should we have insulation? We should have insulation because we want to prevent this heat in leaks from ambient temperature to the cryogenic temperature. We cannot of course make this heat in leak to be equal to 0. So what we should we do, we should try to minimize this heat in leaks and therefore we should have various insulations with their capabilities with their different capabilities so as to minimize the heat in leaks from room temperature to the cryogenic temperature. In fact whatever sample we want to cool for example in physics or we have got a cryostat we have got a sample dipped in liquid helium or we got a cryocooler working at 4.2 Kelvin. The cooling effect of this cryocooler or cryogen is very important and if we do not prevent this heat in leaks then whatever cooling effect is produced by these machines or cryogens will be neutralized. In fact it will be eaten up first by this heat transfer that is going to come from room temperature and therefore it is very essential that we minimize this heat in leak from room temperature to the low temperature. So for example storage of a cryogen let us say ln 2 that is at 77 Kelvin is difficult as there is a continuous boil off. If you see ln 2 anytime and we have seen this earlier you will always see there is some vapors coming out of the cryostat so there is a continuous boil off due to heat in leaks that means whatever you do you cannot prevent this boil off. If you come next day you will find that the level of liquid nitrogen has gone down and that is because of the heat in leaks and therefore the liquid nitrogen level will always go down over the period of time. These vessels cannot be sealed as boil off generates huge volumes of vapor resulting in large pressure rise. If I want to enclose everything and if I say I do not want to see this boil off and we have got a lid on the top what will happen slowly and steadily the pressure inside will start increasing because the volumes of vapor will result in large pressure rise and ultimately this may lead to bursting. So we want to reduce this boil off we cannot of course keep this cryostat or cryo containers completely closed you cannot have a sealed lid over there the boil off will always occur because the heat in leaks will always occur although we can just minimize this heat in leaks. For example at one atmosphere the vapor to liquid volume ratio is of the order of 175 can you imagine this let us say 1 liter of liquid will produce around 175 liters of vapor and that means you can see this is a volume ratio that is going to be generated and if you have got a less volume available over there the pressure will start increasing in the cryostat and this can be fatal sometime this can be dangerous also. And therefore we have to keep this cryostat covered I mean we have to allow this boil off to basically come out of the cryostat and we want to minimize this boil off so that the experiments can last for a longer duration to avoid the pressure rise the need of insulation is vital that means the boil off will be reduced in this case insulations or a combination of insulations minimizes this heat transfer from outside to inside from ambient to the cryogenic temperature. So what we want to do with insulation basically you would like to minimize the amount of heat transfer that takes from outside to inside outside temperature to the inside temperature. So for example we can see in a schematic that we have got a container outside temperature which is around 300 Kelvin and let us say we have liquid nitrogen here which is around at 77 Kelvin and this is open volume where the boil off would get stored. So from 300 K to 77 K we got different ways in which the heat can transfer from outside to inside. So consider a ln2 container as shown in this figure the inner vessel is housed inside an outer vessel and these vessels are separated by some form of insulation so we have got the inner vessel which houses liquid nitrogen we got outer vessel which we should have actually insulation over here we can see that there is inner vessel and then we have got these members which are giving actually strength or which are holding this inner vessel against outside vessel. Also the inner vessel is supported using lateral beams as shown here so basically how will this inner vessel stand here the inner vessel would stand here because of the support given by this lateral beams but do not forget that lateral beams one part is at 77 Kelvin the other part is at 300 Kelvin that means it is going to bring some heat inside alright and what you see in a bluish thing could be some kind of insulation so as to prevent the amount of heat leak that happens from 300 Kelvin to 77 Kelvin. The liquid boils off continuously due to the various modes of heat transfer so as I said whatever you do the boil off will happen continuously and therefore the boil off would happen and you can always see the vapours coming out of this and if this is closed after sometime this will burst otherwise so we cannot keep it close at all we have to have some way out so that the vapour will come outside but what we would like to do we would like to reduce the rate of this vapour generation or reduce the boil off that means in one day or in seven days the level should not go drastically down I would still be able to have some liquid nitrogen left over here so that I can do experiments over a period of time. So different modes of heat transfer most of you know all these things we just have a one slide to you know just brush up your knowledge so we will have conduction so you can see conduction is happening from across this neck it is a very important area because this is something which we cannot avoid so we will have one end of this neck at 300 Kelvin the other neck will be at around 77 Kelvin and you will have always have some conductive path through which heat will get transferred from 300 K to 77 K and therefore this will result in boil off what we should is to minimize this conductive path the heat is conducted through lateral beams lateral beams are also bringing in lot of heat so these support structure whatever we have the inner vessel would also conduct heat from outside to inside alright so we have to minimize the conduction phenomena happening across the neck happening across the lateral beams also we got residual gas conduction many times we will have vacuum between this inner vessel and outer vessel but still depending on the kind of vacuum you have depending on the level of vacuum we have we will always have some residual gas over here and this residual gas will cause residual gas conduction although it will be minimize depending on the vacuum levels we are talking about so conduction will occur as a solid conduction across the neck solid conduction across the beams and we will have a gas conduction or residual gas conduction across the insulation if we have vacuum over here whatever gas we have we will have mostly air and we will try to minimize this air as much as we can but still we will have some residual gas conduction then we got a phenomenon of convection also the air in between the inner and outer vessel will convect heat into the liquid so we will have convection here because of the motion of whatever gas we are talking about air or any gas and it will also have convection if we remove this air by vacuum that means we will have minimum gas quantity over here and we try to minimize this mode of convection the third thing is also radiation so we will always have one surface at 300 Kelvin and other surface at 77 Kelvin and therefore radiation will always occur you know that radiation doesn't require any media basically so the radiation heat will transfer from 300 K outer vessel to 77 K inner vessel so these are the ways in which the heat transfer would always happen conduction convection and radiation and find out always who is responsible for conduction who is responsible for convection and who is causing radiation as we know the surfaces would cause the whole attempt of having insulation or designing this insulation is to minimize this all all these three modes of heat transfer basically alright so sigma conduction sigma q conduction sigma q convection and q radiation we have to minimize this q and therefore we have to design an insulation accordingly but there are various types of insulations and the insulation could be broadly classified as mass insulation reflective insulation and vacuum insulation so you got a mass that means we got some material sitting over there we got some reflective surfaces over there so that whatever q comes will get reflected back or we can have vacuum so we will have some mass insulation reflective insulation or vacuum insulation under mass insulation we will have cellular insulation granular insulation or fibrous insulation so we can have material which has got cells associated with or cellular structure associated with it we can have granular structure associated with and we can have fibrous so kind of mass material that we are going to use depending on the geometry of this material this is further classified and then we got a reflective surface between the outside surface and the inside surface which as you know will reflect all the q that is coming from outside to inside under this reflective insulation we can have metal foils which most of you know and we can have multi-layer insulation about which we will study more so we can have either of these two things metal foils and multi-layer insulation and third thing is vacuum as you know vacuum is a very important development which Dewar had basically you know done that we know that we got two flasks and if we remove the air between them the the modes of heat transfer like conduction and convection can be taken care of but what we can't take care of this is radiation so what we do normally we can have a combination of mass plus reflective insulation so we can do any combination depending upon the kind of insulation we have in mind so we can have a combination of mass plus reflective insulations or we can have vacuum plus reflective insulation or also we can have all these three into account so you can see that we can have any combination possible but then we have to pay for every combination so depending on the kind of costing we are talking about we can have mass only reflective only or vacuum only or we can have a combination of mass plus reflective reflective plus vacuum or all three together and let's see now what what are these different types of insulation which come under this categories so let's say types of insulation we are going to talk about we got a expanded foam so in this case we are going to talk about mass insulation where we can use forms which normally most of you know that we got a foam in the refrigeration also most of the pipes running from you know high temperature to low temperature you can always see that it is covered with foams in air condition also at home you can see that most of the lines are covered with foam and same could be used at cryogenic temperature although that may not be very very effective then we got a gas filled powder and fibrous material which also falls under mass categories it's normally called as powder insulation and this powder insulation could be filled with gas or it could be evacuated powder also then we got a some something called vacuum alone insulation we can call it vacuum insulation all at which most of you know that if we have got a vacuum most of the conduction and convective heat transfer modes can be taken care of then we can have evacuated powder we had a gas filled powder then we have vacuum and then we can have powder with vacuum and this called as evacuated powder which comes under a category of mass plus vacuum and we can have opacified powder which is mass plus vacuum plus some reflective elements and added to the powder so we can have combination of all these three mass plus vacuum plus reflective types of insulations and lastly we can have multilayer insulation which was very well with vacuum only so vacuum plus reflective which will cause you multilayer insulation so these are all the different types of insulation that could be used in cryogenics and depending on their temperatures you are going to talk about depending on the costume you are going to talk about their effectiveness can be justified the use of these particular insulations can be justified so today in this lecture we are going to cover the first two types and eventually in the other two lectures I will cover rest of the insulation so we will talk about now expanded foam insulation and followed by gas filled powder so choice of insulation for a particular application is a compromise between the following factor so what insulation has to be used how do we decide that we want to use only this particular insulation in this case will be governed by various parameter the thermal conductivity of the material itself we want to have minimum thermal conductivity the temperatures we are going to talk about what is the temperature I am talking about 300 to 150 Kelvin, 300 to 120 Kelvin, 300 to 77 or 300 to 4.2 Kelvin so depending on the temperature levels I will have different insulations associated with that for example I can just use foam for helium insulation for helium cryogen I have to have something else now like that depending on the temperature levels I am going to talk about I will decide what insulation I will choose the effectiveness of the insulations this is the result of various parameters and its properties what is the effectiveness of insulation when it is put in place that also can be calculated depending on the net heat transfer from outside to inside the cost of the insulation which is very important alright the age of application for example if you have got a intricate shaped container you can't have any insulation then you can't have geometrically fix we want to have you know flexibility we want to have a lot of age in putting up that insulation on that particular material over there so age of application also is very important then weight and reliability whenever you talk about space application for example you got some cryogenic application in space what is most important therefore is weight weight of that insulation also is very very important and therefore weight and of course reliability so this is a very important term when we go to talk about having insulation for space related applications so a combination of insulation is used to prevent different modes of heat transfer so all these are basically various factors which will enable us to decide depending on these parameters we would decide ultimately that can I use a particular insulation or am I to use a combination of insulation so that my effectiveness of insulation and will be very high and the cost is going to be minimum so all these are parameter which would decide for a particular application how will I choose an insulation for a given application let's define one more parameter which is normally used in insulation studies this is called as apparent thermal conductivity so as seen earlier the different modes of heat transfer are gas and solid conduction convection and radiation consider an element of insulation separated by two temperatures let's say T1 and T2 and which case T1 is more than T2 so here is what we can see that one surface is at T1 the other surface at T2 and Q1 is the conduction Q1 is basically the heat that is being transferred from this surface to other surface all right so let Qt not Q1 this is Qt let Qt be the net heat transferred across the element by all possible modes of heat transfer mentioned above so Qt is the total heat transferred or net heat transferred and this Qt is equal to Q gas plus Q solid plus Q convection plus Q radiation that is Q gas plus Q solid is basically heat transferred due to conduction that is gas conduction and solid conduction then Q basically because of convection and Q because of radiation so all the modes of heat transfer have been covered and this is what we refer to as Qt so if we identify A and L is a cross section area and L is the length of the element respectively so this is cross section area A and length is L the apparent thermal conductivity Ka is defined as Ka is equal to Qt into L divided by A into T1 minus T2 which is using basically a famous Fourier law but this is using a famous Fourier law I am taking however not Fourier law holds good only for conductive heat transfer but I am putting here Qt why I am doing that because basically I would like to compare the effectiveness of heat exchanger effectiveness of heat transfer effectiveness of insulation so if because the heat transfer can takes place because of conduction or convection or radiation I would like to compare different insulation I do not want to compare radiative heat transfer or conductive heat transfer I want to see the total heat transfer and that is why I am using instead of only Q conduction I am using Qt over here and using the Fourier law and therefore I am calling this as not thermal conductivity I am calling this as apparent thermal conductivity which takes into consideration the heat transfer due to conduction convection and radiation all three together and this is what if I want to compare insulation I would compare it with the total heat transfer that happens because of all these three modes of heat transfer so in other words the apparent thermal conductivity is calculated based on all possible modes of heat transfer with this background now let us come to expanded forms expanded form is a low density cellular structure which is formed by evolving gases during manufacturing process so you got a cellular structure this is what we call as the mass insulation which is formed due to cells they have got a low density and it is made out of evolving gases during the manufacture process so you got a small small cells which are filled with gases and all the small cells with gases could be put on running tubes running pipes or a cryogenic container also the gases that generally used evolved during this manufacturing process are CO2 or some free on so it is a solid and gas matrix with void spaces the solid connection together with gas trapped in cellular space form a continuous path the heat is transferred only by conduction or solid conduction the gas conduction is very very minimal in this case so solid conduction the contribution by convection and radiation are negligible so here I would just like to show you the form here so just see form I am showing so here is just the structure which you must have seen this is what we call as form and you can see small small cells over here we have just taken it from a running pipeline but what you can see this will all be filled with some some kind of a gas and there are a lot of cellular structure which houses this gas inside so you got a small cells which are separated and for example I have put this on a pipe the pipe runs through this so the long structure that can be covered up this pipe and sometimes over a period of time the powder comes off that means the cells get distorted with time and the powder comes off so it is not a very long lasting kind of a solution on the back side it would look like this so this is what is exposed to atmosphere while all these structures you know the cell which will see the cryogenic temperature alright so you can see some small powders falling over there when I rub my hand over this so this is not a very reliable kind of a solution but it is a very cheap solution which is available in the market and can be used for refrigeration purposes as well as for cryogenic pipelines so going ahead the examples are polyurethane form polystyrene form rubber silica glass forms there are various kinds of form depending on the kind of material that is used for this and the kind of gas used in the formation of these forms the apparent thermal conductivity k a and density are as follows here the operating temperatures are 77 Kelvin and 300 Kelvin so if I got two surfaces 300 k to 77 Kelvin the apparent thermal conductivity for these different forms would be like this so you can see here I am giving names of different forms polyurethane the density of polyurethane could be around 11 kg per meter cube because the conductivity varies with the kind of density we are talking about so for polyurethane the conductivity apparent thermal conductivity is 33 milliwatts per meter Kelvin so you can see that the conductivity is in milliwatts alright per meter Kelvin and we are talking about a range of 300 to 77 Kelvin so first of all note that everything is in milliwatts over here and as you go from polyurethane to polystyrene or rubber silica glass the conductivity around 33, 33, 26, 36, 55 so these are around two digits and between 30 to 50 milliwatts per meter Kelvin here we can see that polystyrene as the density has increased or the density has increased from 39 to 46 the conductivity apparent thermal conductivity has decreased a little bit from 33 to 26 but you can see the range is normally between 30 to 50 if I can say broadly or maybe 20 to 60 if that would be correct for 30 300 Kelvin to 77 Kelvin temperature range the Ka value apparent thermal conductivity of foam depends on the type of gas used and the temperature of insulation which is which is what we have talked about earlier for a given gas now the performance is improved by varying the void size or the mean cell diameter of the cells and double density so for I have talked about having this mass insulation which depends on the different cells and this cells house different gases so if I go on minimizing the cell diameter the thermal conductivity will vary the apparent thermal conductivity vary or if I change about the bulk density also it will affect the Ka value how does it affect so we can see that here thermal conductivity on the y axis mill cell diameter in micrometer is given on the x axis so if we go on lowering the mean cell size from 400 to 200 or from 600 to 200 the thermal conductivity starts decreasing so we should go for a small size which we can conclude from here the adjacent figure shows that the variation of Ka with the mean cell diameter so what do we see from here with the with the decrease in the mean cell diameter the solid conduction path increases if I make small and small and small cells the path of conduction will start increasing the path of solid conduction because the solid conduction would happen through the cell diameter so the cells and if I make smaller and smaller cell this length will start increasing as a result of which Qt the conduction path will start conduction path increases and therefore Qt due to conduction will definitely decrease and Qt overall will decrease and hence once Qt decreases we say that Ka also decreases the apparent thermal conductivity also decreases however can I go on reducing this cell diameter if I make it cell very very small diameter a too small cell diameter will increase the bulk density all right therefore various cells will come together and this will increase however because now the solid conduction path will increase in this case and therefore the conductivity in that case will be higher and therefore we can't have densely packed cells also so we can't basically we can't from this point of view smaller cells will be preferred but too many smaller cells if they if you go to very low diameter then the solid conduction path will increase and the bulk density increases and this will increase the Ka value so what does it imply it implies that we have to have a optimized diameter where the conduction path where the effect of Q conduction is taken care of properly so hence there is a minimum Ka at an optimum bulk density and cell diameter these two things have to be optimized the cell diameter has to be optimized in such a way that Ka becomes minimum for those values so we have to optimize the cell diameters in this case so what are the different advantages of such expanded foam insulation the major advantages of expanded foam is that it offers an age of fabrication that is very important because you can have in situ application of this insulation the foam is directly blown onto the surface of the vessel to be insulated it forms a self-supporting structure and this is a very important advantage I have got an intricate shaped vessel to be in a foam I possibly cannot use other insulations but I have to use foam in that case also for various space application because the foams are lighter I have to go for foam insulation only the cost of this insulation also is very very low as compared to other types of insulation so from costing point of view also it has various advantages so what are disadvantages exposure of a co2 for example what is the gas being used as I said is co2 and once co2 gets exposed to liquid nitrogen temperature the co2 actually co2 will get condensed it might get solidified and this will increase the thermal conductivity so if I am talking about the temperatures level of ln2 in that case thermal conductivity will increase so at ln2 temperatures the vapor pressure of co2 is less as a result of which most of the co2 is condensed within the insulation and this will cater to the heat transfer and therefore I may not be able to use this insulation for a very low temperature this may be useful for 150 Kelvin, 180 Kelvin, 200 Kelvin or so but may not be very very useful for liquid nitrogen temperature but of course because it's a cost effective solution I can use this for some time and remove it over a period of time and renew the insulation again that's one of the possibilities also over a period of time you can find that air hydrogen you know ambient gases would rush inside they will diffuse in the foam and from external atmosphere increase in the k of the foam so this is also one of the very important disadvantages of foam expanded foams have large thermal contraction and this is very important for cryogenic temperatures the foam will get contracted they will contract and they will pose a major disadvantage over here a rigid foam has a very large thermal contraction between minus 30 degree centigrade to plus 30 degree centigrade and you can see for example the coefficient of coefficient of linear expansions for foam is around 7.2 into 10 to power minus 5 per degree centigrade and if I want to compare it with carbon steel it is just 1.15 into 10 to power minus 5 that means almost as high as 6 to 7 times more the linear contraction so you can see that the contraction will be so drastic in this case the foam will just get you know struck on the material on which it is struck so the foam when closely fitted around liquid nitrogen vessel will crack due to difference in shrinkage the material will crack the foam material may crack if the foam is subjected to some thermal cycling you know coming from l n 2 to room temperature and again going down to l n 2 temperature the foam may crack so the reliability could be questionable in this case so let us see the next insulation now which is gas filled powder and fibrous insulation a gas filled powder or fibrous insulation reduces or eliminates the gas convection due to the small size of voids within the material as the name suggests here it is basically a powder and we got a very small size of powder material basically so small small crystals could be there and there will be very small size and between these crystals what you can see is we will have gas and later on we define that it could be evacuated also so instead of having this powder we can have sometimes fibrous material also and therefore this could be called as gas filled powders and fibrous insulation this is because the distance between the powder particles these are granular particles very small granular crystals granular particles and they are very small within the insulation and the distance is so small than that the gas mean pre path is smaller than that all right. So this is because the distance between the powder particle within the insulation is much smaller than the gas mean pre path that means what you can see is a molecular region if you are talking about all for the gas element. So, as a result of which the gaseous conduction mechanism shifts from continuum to free molecular conduction. That means, distance between the particle is so small that the mean prepath of the gas is larger than that and therefore, we are shifting from continuum region to the free molecular conduction of the gas decreasing the apparent thermal conductivity k a over here. So, we are talking about very small granular particles in which some gas molecules are also there. The commonly used insulation of this type are fibreglass, pearlite or pearlite powder or silica powder and normally, it is referred as pearlite powder in a commercial sense. Santocell, rock wool and vermicellatine. Vermicellatine also is one of the fibrous insulation that could be used for here in this case. So, what before I go further, I would like to show you the pearlite powder. So, you can see here the whitish looking powder or granules. Right now, there is no gas in this thing, but you can just see the powder because the gas must have got out. It was exposed to atmosphere and you can see the powder over here. So, what you can see this powder? Normally, you know this powder is of very very small granules and most of the times, you can find the liquid nitrogen plant will have this fibrous insulation because it is a huge thing which is filled with powder all the time. You can see this white pearlite powder which is very commonly used up to liquid nitrogen temperature. So, we will have drums containing this actually. You know various places, we have got drums containing this particle which are rammed across the 77 k surface or 77 k to 300 k surfaces. Normally, this will not be handled by hand. You have to use some gloves and put it in a place, but what you have to ensure that when you are putting it, it is put uniformly across the available area. So, let us see now what is the apparent thermal conductivity of these materials. So, k A and density are as shown below for the different insulation. The operating temperatures are again kept as 77 Kelvin to 300 Kelvin. So, here you can see now the insulation for pearlite powder, for silica aerosol, for fiberglass, for rock wool and different density. You can see 50 kg per meter cube, 80 kg per meter cube and 160 kg per meter cube. So, different densities are there. So, that the weight also is a constant that can be taken care of properly while what you can see the apparent thermal conductivity is 26, 19, 25 and 35. So, as in earlier case, when we talked about which was expanded form, we were in the region of 20 to 60 kind of a thing and now we have come down below. We have come down let us say from you know 20 to 35 that kind of a region. So, earlier it was mostly from 30 to 60, now it is from 20 to 35 milliwatts per meter Kelvin. The conductivity, the apparent thermal conductivity is around 20 to 35 in this conductivity range. The advantage of such insulation, the advantage of a gas filled powder are low thermal conductivity, low density and low particle distribution to minimize the vibration effect alright. So, this can be rammed properly across the places and it will minimize low particle distribution. That means wherever there are vibration, the particle distribution can be taken care of properly. The insulation can either be evacuated or non-evacuated. The heat transfer by residual gas conduction is further minimized by low vapor pressure of gas. So, if I evacuated, then whatever conduction occurs because of even gas conduction that also can be further minimized. Finally, divided particulate materials make solid conduction path disjointed and discontinuous and this is the reason why the these particles are used. So, all these granular particulate, all these granular particles are finely divided and therefore this creates a solid conduction path disjointed. There is no continuous path for solid conduction alright plus they got a gas also. So, we got some solid conduction which is disjointed plus we have got a gas conduction depending on the kind of gas which we have been using and conductivity of gas is pretty low. Therefore, here while in foam case, we had a continuous path alright. We had a continuous solid conduction path, but in this case, we have got a discontinuous solid conduction path and therefore, the Ka value in this case is less than as compared to what it was for expanded foam. The disadvantages in this case, the fill gas should be non-reactive and compared with powder material, COT is again widely used and this is true for earlier insulation also that it should be a non-reactive and compatible with powder material. The powder tends to this is one of the disadvantages. The powder tends to settle and packed due to vibrations, thermal contraction and expansion. So, this powder over a period of time although we say we got minimum vibration, but you got some vibration and over a period of time this powder will tend down to settle and therefore, exposing particular path for heat in leaks or we can have cake formation at the bottom where the power settles and therefore, this is one of the very important disadvantages that has to be considered for a particular application. So, powder tends to settle and packed due to vibrations, then you have got is thermal contraction and sometimes expansion also because of heating effect also. This creates increased solid conduction and therefore, this has to be considered in the usage of such insulation. The gas till powder and fibrous insulation conductivity can be calculated by Nusselt and Bayer developed the following expression for K A for gas filled powder and this is an expression. So, you got a K A is equal to V R upon K S plus K G upon 1 minus V R plus 4 sigma T cube D divided by V R to the power minus 1 and entire thing to the power minus 1. So, apparent thermal conductivity can depend on various parameter, V R is ratio of solid particulate to total volume, K S and K A are thermal conductivity of solid and gas, T is the mean temperature over here, sigma is the Boltzmann constant, D is the diameter of this particulate, D is the mean diameter of fiber or powder. So, you can see that K A depends on various parameter related to the gas related to packing fraction, V R related to the conductivity of the solid material that is used as fiber or powder, temperature, diameter and of course, the Boltzmann constant. So, this is our expression, we can say at cryogenic temperature the two assumption can be made, T cube term, this is a 2 cube term is going to be very very small as compared to the K G term. So, T cube term is very small as compared to K G term and therefore, we can neglect this term in front of this term. So, and then I can say that this K S term which is a solid conduction is also very large as compared to K G. So, gas conductivity term is always very very less, the gas conduction K G part is very less and therefore, if this is very large V R upon K S becomes a neglected term as compared to this and therefore, I can in that case K S is being very large, I can neglect V R by K S. So, my equation can reduce down to under this assumption as K A is equal to K G upon 1 minus V R. So, basically it is a function of now packing fraction how much what is the ratio of solid you know contain solid part to the total volume which is what I call as packing fraction and the value of K G and therefore, if we say that V R tends to 0 that means, there is no solid particle at all the K A will approach to K G and K G is going to be very very low alright. So, it actually approaches to the gas conductivity in that case basically. So, this is the lowest value that we can have but we can of course, have a gas only gas over there because having only gas will have its own problem because the gas will get you know liquefied or condensed or get frozen also at those low temperatures and therefore, K A approaches K G in this case this is the lowest possible thermal conductivity of this insulation. So, if we have got a V R the K A is going to be higher than the value of K G, but it also tells you that the kind of gas that is going to be used its conductivity also plays a very important role because the lowest conductivity that it can reach is basically equal to the conductivity of that particular gas which is used in gas filled powder. So, gas filled powder and fibrous insulations are generally used in vibrations and shock prone applications. So, wherever we find that there is no vibration and we do not want to have shocks and we do not want to have vibration it will always be preferred to have a gas filled powder and fibrous insulation. However, care must be taken to avoid caking of the powder at the bottom of the insulation. So, we should ensure that the powder does not get you know sitting at the bottom it does not settle at the bottom over a period of time formation of caking should be avoided in this case. Since the gas is an insulation the operating temperature of this insulation should not be less than the boiling part of the gas. So, whatever gas we are going to use we should ensure that the operating temperature is not less than that otherwise the gas will get condensed in that case. Coming from the gas filled powder and fibrous insulation now we will have our next possible ways of having heat transfer which is radiation and before we go further what is important is to understand the radiation fundamentals and let us just brush up our radiation fundamentals so that we can use we can understand why the shields are used to minimize this radiation alright. So, let us see the radiation fundamentals. So, consider two flat surfaces maintained at different temperatures and now we are going away from mass insulation and we are basically going to radiation heat transfer fundamental and then we can use vacuum in that case alright. So, we are going away from mass insulation in which we had examples of expanded form and powder. Now, suppose if you have got two surfaces at temperature T1 and T2 and let us say T2 is larger than T1 T2 is more than T1 then we will have a heat transfer from surface at T2 to T1 and then the continuous heat transfer between the two plates due to radiation because these two temperatures and if the temperature differences is very very large they will have a very effective heat transfer because of radiation. This mode of heat transfer does not require any medium and is given by the following expression for radiation to happen we do not require any medium. So, if you got a vacuum also the conduction and convection in that case could be minimized, but radiation you cannot prevent alright. So, if I remove whatever medium is present between T2 surface and T1 surface I can minimize the heat in leak due to conduction and convection, but I cannot minimize the heat transfer due to radiation alright. So, this mode of heat transfer does not require any medium and is given by the following expression which is Q is equal to Fe into F12 into sigma A1 T2 to the power 4 minus T1 to the power 4 this is a very standard equation. So, Q is basically conduct the heat transfer due to radiation Fe is the emissivity factor depending on the emissivities of the surface at T2 and surface at T1. F12 is what we call as configuration factor or shape factor depending on the geometry of these two surfaces sigma is the Stefan Boltzmann constant A1 is the area of heat transfer which receives the heat from T2 and while T2 to the power 4 and T1 to the power 4 the temperature difference to the fourth order that is what we talked about for a standard radiation heat transfer equation and this most of you know and therefore I will not go in the details of this derivation and understand the basics of this is very straightforward. So, in the above equation it is clear that for a given A1 T1 and T2 and F12 Q is directly proportional to the emissivity of the factor Fe. So, Q is directly if all these parameters are same Q is directly dependent on the parameter Fe which is related to the emissivities of these two surfaces alright. The Fe is reduced now if I want to reduce the value of Fe for a given T2 T1 A1 and F12 that means everything is defined the geometry is defined the two temperatures are defined and therefore A1 also is defined because the geometry has already been defined. So, what I can do I can minimize the value of Q if I could minimize the value of Fe which is the emissivity factor the Fe can be reduced by introducing the radiation shields of high reflectivity and low emissivity which is ES value in the path of radiation heat transfer as shown. So, if I introduce different shields in between T2 and T1 shields T1 T2 and T1 surfaces as shown in this figure this green things show the shields which have got very high reflectivity. So, that whatever radiations come from here can get reflected and low emissivity values. So, the ES associated with this it is minimum in this case. So, if I have such surfaces if I have such radiation shields and if I put them between these surfaces of having temperature T2 and T1 my factor of Fe will get reduced and how it does get reduced most of you know that it is a rule of parallel surfaces 1 upon E is equal to 1 upon E1 plus 1 upon E2 minus 1 by this formula if I put the surfaces of having minimum ES in that case my Fe factor will get reduced further. So, the effective emissivity factor Fn after introducing n shields suppose I put n shields and this n could be equal to 2 or 5 or 10 or 20 and my emissivity factor now for n number of shields will be given as below. So, 1 upon Fn is equal to 1 upon even this is my first surface which faces the temperature having T1 as temperature. So, now I have got a effective emissivity of that particular shield 1 upon even plus 1 upon ES minus 1 this gives me effective emissivity of 2 surfaces which are facing each other having shield emissivity as even and ES and if I show the last term this is my effective emissivity of the last 2 surfaces having T2 temperature and facing the ES for 1 upon E2 plus 1 upon ES minus 1. So, this is my effective emissivity of the last surface having E2 and ES as emissivity the first surface as even and ES shield and then in between now I got n minus 1 shields and if I go on adding all these shields will have ES as emissivity and effective emissivity of all this will be n minus 1 into bracket 2 upon ES minus 1. I will not go into derivation of this thing because very straightforward one can always do all of you can do these things. So, 1 upon Fn is equal to now instead of 1 upon Fe we got 1 upon Fn is equal to this entire expressions and for the sake of understanding let us put some values to this let us get even and E2 as 0.8 and ES having low emissivity the shield emissivity should be as small as possibilities 0.05. Now, I would advise you to calculate the value of Fn in this case and I will just give you directly value and let us call the students are advised to calculate and compare the value of Fn for the following cases let us have a one case whether there are no shields that means n is equal to 0 and the second case when we got n is equal to 10 with the value of emissivity for the shield given as 0.05. So, if I calculate all these things what will get for the case 1 when n is equal to 0 my Fn will be equal to 0.667 and if I put n is equal to 10 my Fn will be as small as 0.00255. So, it is obvious from here that if I put 10 shields of low emissivity and high reflectivity my Fn get drastically reduced my Fe value now will get drastically reduced from 0.667 to 0.00255 this effectively means that my Q because of radiation will get reduced by such a factor all right. So, it is clear that Fn decreases drastically with the introduction of radiation shield and this is one of the ways in which I can reduce the radiation heat transfer. So, if I want to have some fast reduction in fast ways of reducing the radiation heat transfer what I should do I just add the radiation shields which has got low emissivity value and high reflectivity values and I can put those shields between the surface number 1 and surface number 2 and in this way the radiation heat transfer will get drastically reduced. So, these shields are aluminum foils many times you must have seen that for your you know food items also we pack them up in aluminum foils. So, this aluminum foils have got very large reflectivity and low emissivity and therefore, these are normally used as metal shields to reduce the heat transfer. So, summarizing the whole lecture on insulation cryogenic vessel need insulations to minimize all modes of heat transfer this is what we saw the apparent thermal conductivity is calculated based on all possible modes of heat transfer it does not take into consideration only conduction, but it does take into consideration various modes of heat transfer which is conduction convection and radiation. Expanded form is a low density cellular structure allowing only solid conduction with the decrease in the mean cell diameter the k a decreases. However, there is a compromise between the cell diameter and the bulk density for an optimum value of a for expanded foam insulation and this is what we saw how does that come into picture. A gas filled powder or a fibrous insulation reduces gas convection due to the small sizes of voids. So, you got a very small particulate matter but particles sitting over there in which there could be gas and this will effectively reduce the apparent thermal conductivity from 30 to 55 milli watt for expanded foam to around 20 to 35 for gas filled powder case. The heat transfer is reduced by free molecular it is transfer happening because of free molecular conduction in this case. The field gas should be non-reactive and compatible with powder material. Radiation heat transfer does not require any medium it is reduced by introduction by introduction of radiation shields and this is what we saw how addition of this radiation shields would reduce the radiation heat transfer what we require is to have reflective material and low emissivity material. These shields are mostly aluminum foils with a very high reflectivity and low emissivity and in this case now the f n value or the emissivity factor will be reduced from a very high value to a very low value depending on the kind of material you are using its reflectivity and emissivity and the number of shields that are used. Thank you very much.