 so in the last few classes we have talked about shinking core model shinking core model is one of the models which we have discussed earlier and the other model is homogenous model okay so here the imagination is that we have a single particle but it is highly porous particle right so that means gas can easily diffuse through the particle and then the reaction is going on throughout the particle there is no core which you can really identify there in the previous shrinking core model there is a clear boundary between the reaction zone and unreacted zone that is why we call that one as shrinking core model because the core which is not reacted is slowly shrinking and finally disappears but whereas in this model because it is a highly porous particle gas can easily diffuse through the pores and at any time if I look into the particle this particle is completely occupied by reactant here with the same concentration if outside concentration is C A not for example the same concentration is also there throughout the particle and if you ignore the film resistance that is definitely true right film also is not contributing so we have lot of pores so then all the molecules of A can go inside and occupy the pores and then they simply stay there right because they stay there and there are reaction conditions so continuously the reaction is going on so how do we picturize this in our mind first before writing the equations right so we have a particle porous particle something like this then we have reactant B here reactant B and after sometime we have the same size particle we are talking about constant size but now this concentration will reduce then after sometime same particle the concentration is almost concentration of B only product you will have so with time this is time t equal to 0 sometime t large t good so as usual and we are neglecting film so that we know if it is film control we already know how to develop the equation the same equation can also be used here whether shrinking core model or homogeneous model right if only film is controlling so then the same model can be used right but if it is there is no diffusion here diffusion control here diffusion through ash layer because I have large number of pores or large size pores so that the gas can easily enter into the particle and then the reaction is going on throughout the particle good so if I want to plot the profiles here profiles of what profiles of solid okay how the concentration of B is changing so here at time t equal to 0 you may have here C B not at time t equal to 0 this is throughout same no so that is why horizontal profile throughout okay this is complete particle we are drawing now it is okay yeah so then if it is truly homogeneous model this is C B not that means everywhere supposed to be C B not throughout so after sometime t what do you expect yeah I may not 0 here at this point yeah you will have something below here this is C B profile and after sometime it will still go to less and C B will be 0 so that is how the profile decreases right because number of moles here are more then if I take here number of moles which are spread throughout is less and here number of moles again throughout spread is almost 0 for B because B would have already reacted and the reaction is same reaction what you have been thinking what is that A gas plus B B solid going to products okay good so now what is what kind of profile you get for A A is the gas so if I draw those profiles here yeah so A how do you imagine A A profile you know all the cases because I have sufficient amount of gas diffusing and then staying there it is reacting continuously and continuously again it is entering because you know that when immediately concentration is less there and you know this gas goes there so continuously it is always it is as if you have immersed this particle in a concentration of C A not you have lots of A there so that is why you will have C A not same here if I take that one as C A not again here C A not again here C A not with time so now with this we should be able to imagine what is the rate of reaction for us okay good how do you do that in this case you think you know we know that now the rate should be proportional to concentration of A and concentration of B okay so earlier case we took you know the concentration of B is so large that is why it is not it is zero order reaction so it is not directly coming we are taking only with respect to with respect to A first order and all that but even here because the rate is proportional to concentration of A and concentration of B concentration of A is always constant whereas B is changing right so we can write that as okay you are right rate of consumption of rate of consumption of B is proportional to concentration of of A bathing the particle multiplied by amount of B unconverted you know already converted one will not participate in the reaction no unconverted good okay so if I write we can write also this one in terms of C B or we can also write in terms of X B X B is the conversion which you already familiar so if I write this one as the change D X B by D T is this proportionality constant I will write something K R reaction rate and C A not which is constant throughout and 1 minus X A sorry 1 minus X B so if I take this as equation 1 this will be equation 2 can I integrate this equation this is very simple no because it is concentration of A and concentration of B left okay so 1 minus X B and if you the simplest integration and then the integral expression for this is 1 minus X B equal to exponential of minus K R C A not into T which one same thing here also left side also I have C B not so it gets cancel yeah same thing this X B also will be there right so the definition only I have differentiated this side so you can write the same thing and then you will get cancel okay good so this is the simplest equation in you see now this equation simplest equation to calculate time and also it is related with X B it is simply like your homogeneous reaction in homogeneous reaction assuming that this is you know pseudo this is almost constant throughout C A not you know that becomes a pseudo first order here with respect to A and it is not always true that I should have 1 minus X B I can have in fact X B to the power of 1 minus X B to the power of N okay so what you do with all this is that once you conduct the experiment and if you know initially it is a porous particle and truly homogeneous model may be valid there that you know the physical condition of the particle which you know because you are conducting the experiment right so once you know that then we have to find out whether it is really first order or second order or whatever order and you should see that the concentration of A throughout the particle is same for long time because without any change in that so if you have those conditions then this is the equation I have to try but still I do not know whether it is first order or second order so then I have to imagine this nth order and then try to plot my X B versus T and then see whether I get a straight line for first order if not square then second order this is called integral method okay otherwise you know you can take the data like this and then put as X to the power of N again you have to plot on log log sheet and then try to find out that is a differential method okay try to find out what is the order and then correspondingly fit it right and here the imagination is only integer orders may be one first order second order it may not be so that is why if you are able to get the data for dx by dt versus X B better thing is differential thing you can use differential technique and then try to find out what will be the order of that particular reaction so once you are able to fix here here it may be 1.5 correspondingly we have to integrate that and then find out the relationship between X B and then the time what is the ultimate aim in the design I should be able to tell that how many hours if this particular particle or particles must be there in the reactor sorry for complete conversion okay and for most of these solid particles we wait till complete conversion occurs okay so that is what is the ultimate idea and this is one of the simplest models in gas solid non catalytic reactions simplest because we have taken here first order good so now as per our discussions all the time earlier that we need information for the reactor design this plot again I am just diagram this is input output we have here kinetics here we have contacting here we have physical chemical here we have M F okay this is the diagram we have been talking so now we with all these discussion now for non catalytic reactions we are supposed to be experts in this now that means given any reaction you know how to find out the kinetics kinetics means how the reaction is taking place with the time and what are the quantities or what are the parameters that you have to evaluate if it is sinking core model with three controlling film controlling ash diffusion controlling and also reaction controlling you have three coefficients there you should know K G and you should know D effective diffusivity and still you should know K S and all three when you are able to evaluate from the experimental data then you should have the relationship between X B and then time for a single particle right so that is what is the kinetics will tell us now we have to put that information here and because you are already experts of this contacting you know that when you have to take mixture flow when you have to take plug flow now these two have to be combined to finally get the input is given by demand market survey right so how many tons of particles you want to process or how many tons of gas you want to process if you are interested only in the gas phase even in non catalytic reactions but most of the time non catalytic reactions we are interested only in solids like because you know combustion gasification leaching and extraction of ores leaching is extraction of ores only okay so in all these react most of them are metallurgical reactions okay in process metallurgy they will be touching like this but not thoroughly like us they do not discuss for example in blast furnace right so when you have that non catalytic reaction you should be finally able to design the furnace so that you will have 100% conversion of iron ore to that comes from this information kinetics and because you are taking blast furnace then you should be able to visualize in blast furnace whether I have plug flow or mixture flow so that is why now the question is the design of we will go to the design I think this is where I stop with respect to kinetic models right we have done the sinking core model with three controlling and individual controlling also so we have also done that is for constant size particle for changing size particle we have done again one model right and this is the homogeneous reaction model and this particle is not changing okay if this also changing but porous particle what kind of model you use just try to extend what you have learnt till now is it possible to do or it is not possible for you to do now because we have not done all the models we have type A type B type C type D type E type F okay six models of we have six type of categories out of this we have done type A type B and also type D type B and type A together we have done it and this is type D earlier gasification and all that what we have done so three plus this homogeneous the other things are gas gas gas reaction straight away giving you the solid product that we have not done and some other variations we have not done good yeah so if I have for example changing size this is not constant this becomes a little bit smaller this becomes a little bit smaller okay is it difficult to handle or what what actually do you have that information just think I hope question is not confusing you know the first thing generally students say is that sir question is not clear okay once more okay yeah here we have taken this as a constant size particle size here is not sinking core because there is no core no you cannot use sinking core model because it is highly porous model there is no core where is the core throughout the particle reaction is going on there is no clear boundary between unreacted and reacted zone when you have that boundary only then you will have sinking core model okay remember you know when you are taking this gulab jam what do you call gulab jam only rasgulla yeah if it is not properly cooked you will see inside unreacted core some hard material right yeah so then you have to now chew it slightly more difficult otherwise it will simply melt in your mouth if it is properly cooked that is sinking core model okay even rice also if those people are very angry with you and they did not properly cook then outside will be soft inside will be slightly hard then that is also sinking core model rice cooking also okay so unless there is a clear boundary between cooked and uncooked you cannot have sinking core model this is a porous particle but what I am asking is this is changing with time the size is changing with time do you have any difficulty in handling that what is saying no I am just asking you to extend your thinking I say don't just sit there as statues there is no film let us not take that film I am only talking about particle becoming smaller and smaller do you have that information there is no ash layer no everything is becoming see again ash layer comes if you have the yeah the reacted core separately and then product separately here product is distributed throughout when the reaction is going on product also is distributed through yeah it is actually very difficult because now particle is shrinking you know you do not know how many moles have been you know at the time yeah sorry the size is shrinking but generally you can just imagine the question itself may be stupid because what is the reason for shrinking why should you do it we are talking about one particle I say that is why yeah if I have two different size of particles there distribution of particles each one I can deal with separately that is not a problem that is a design problem what he is asking is I have taken one centimeter particle five mm particle both are both are you know homogeneous models okay so then it is not a problem because I will design which takes the longest time and then wait same size particle in a porous particle is it similar or analogous to a particle of constant size porous particle where in its pores are filled completely but in shrinking core the diffusion regime where you have pores he is unreacted core he is you know he is a inert core shrinking core model you cannot bring at all here because shrinking core is porous particle shrinking size yeah shrinking size there is no ash around the particle okay yeah but here we are not saying that I think you know this particle is only decreasing by size but as I told you question itself would have been stupid because what is the reason for shrinking you have to also ask surface area per unit mass of the particle or the catalyst in this case if we assume that the size is shrinking uniformly we can calculate the volume and therefore the surface area of the pores which are getting destroyed area of the porous particle in that case we can actually like he was saying that we can compare it to the deactivated catalyst model can we do that or is it is that too difficult as well deactivated catalyst yeah where the you know deactivated catalyst is almost same in fact the similar model usual for deactivated because the deactivation all our catalyst particles are porous particles okay so that must be homogeneous so the deactivation goes here in the reverse way here we are converting the reactant into product but there the entire particle is very active in the beginning but when the during the reaction there is a reason for you know getting it deactivated like for example I have been telling you the example of FCC FCC catalyst is highly porous particle but one of the side products of FCC fluid is fluid catalytic cracking is very fine a carbon coke so that coke will go go and then uniformly try to sit here and there throughout yeah so then the surface area which is actually participating in the reaction is slowly decreasing that also got exponentially if I assume first order kinetic there in fact the same equation can also be used okay so that is why when the particle is shrinking I think first of all these particles what is the reason for shrinking yeah but here throughout the particle it is happening right this is homogeneous model now it is the surface as well as throughout but that is not the reason for particle to reduce in size I am talking about overall particle there is no core overall particle it is possible only when you have the total molar volume increasing or decreasing I think already I told you this one for calcium carbonate okay then you have calcium carbonate particle becoming calcium oxide and calcium oxide is reacting with sulphur dioxide in the presence of oxygen then you will have calcium sulphate so calcium sulphate molar you know molecular weight molar density is higher than cao under those conditions there particle expands right and if you have a similar reaction where the molar density decreases then particle shrinks otherwise we do not have any reason for increasing or decreasing why I am telling all this is even though we simply tell all this student is very happy to copy all this and then keep it wait for the examination but so much discussion can be made so much thinking can go right so that is why I try to discuss all this but it was found already most of the time in the in the models also that whenever you have molar change during reaction or decrease or increase that is not affecting that much the overall model predictions even if I take this right and then I will assume that is a constant particle someone else will say that no no it is a little bit changing so he also takes the model and he also develops a model now with slightly changing particle or expanding particle right so under those two conditions it was found that the difference is very very less and carberry already proved that right so if you are really able to imagine all this after the class is over when you are preparing for the examination then you will have lots of ideas okay but if you are treating this only as examination point of view there is no excitement at all you see how much time we have now spent on this just to ask you know whether the particle is shrinking or expanding what is happening Shankar you are asking something if my reaction rate constant is very high I mean my gas reason need not have to go totally inside the particle then the reaction will again happen on the surface itself and because of which the surface I mean the size of particle will get reduced if the reaction is very high if the K s is very high so in that case my reaction will happen on the surface itself the gas may not have time to go inside the particle that becomes equivalent to shrinking core model if the reaction is very fast but here when you derive this automatic assumption is that it is rate controlling what is rate controlling reaction is rate controlling no reaction I have large pores where the diffusion is very free just going inside okay so automatically when you say homogeneous reaction model that is only the reaction control but actually that is also true when you have very very fast reaction even though I have porous particle that behaves as if it is a shrinking core model so there are beautiful things and these two are the basic models and in reality in reality you will not have completely homogeneous model okay and that is why actually what happens is you have to draw the profile inside okay profile inside and now that model is very very complicated which I am not doing here because it takes lot of time the derivation okay why it takes lot of time because first of all I have to establish the profile inside profile of what CA and CB both CA profile because there is diffusion of resistance for CB and that is CA so that is why CB cannot uniformly react throughout right so at any point here inside what is the corresponding CA and then CB and then equation is again same this is not no more constant so every time I have to find out what is the average conversion throughout the particle what is the average concentration of A throughout the particle then I have to integrate okay so if people have already done it people have already done it but we are not doing because I have to do so many things actually we had earlier in IIT Madras a separate course called heterogeneous non catalytic reaction engineering there we used to discuss all those models but here I have to do justice to many things so that is why just giving some information and then beyond that you are thinking okay so that is the reason and straight forward if I take that model where I have homogenous model but still it is not purely homogenous model porous particle then I think you know at least it will take one or two weeks for me to develop all those by the way it is not that easy it is very complicated model okay and but lot of imagination is required I think in 70s there was one when Chinese professor in US I think West Virginia he was the starting point for all these models I think of course sinking core model was already done by Yagi Kuni long time back but lot of mathematical details of this homogenous model was given by that when okay unfortunately after I completed my PhD I wanted to apply to him as a PDF but at that time there is no emails and there is no fast communications so I wrote the letter and I later came back after may be two months later so saying that when has died recently I think he was young also may be around 50 on 50 but he has done lot of work in you know gasification you take coal combustion you take some of you may be doing gasification combustion projects everywhere you see his mark because it seems West Virginia is very famous for coal lot of coal mines are there so that is why that university was concentrating mainly on that USA West Virginia so that is why you know USA has that tradition of doing very good research work depending on the need here also we have lot of coal we have naveli but we do not have any project you know we had some project but not for conversion and all that because that interaction between industry and academics if you see that old papers 1967 I do not know whether journal called industrial engineering and chemistry how many of you know that only you know you also know industrial engineering and chemistry I think it was there till 80s or so then they changed it to industrial engineering fundamentals industrial engineering research and development industrial engineering product development three same issue same journal then after 7 or 8 years again they went back to now the current name is industrial engineering industrial engineering research I think it is there now industrial and engineering research industrial engineering research now it is available we are also getting INDCR or something we have research they added but all sections again together in that journal when it was industrial engineering chemistry this when published those paper the original paper is still with me because someone gave me that paper so this is what about these models and lots of work is going on even now in these models because this reaction is a very funny reaction non catalytic reactions are really very beautiful reactions I do not say funny reactions very complicated reactions and calcium oxide to calcium sulphate is one of the very famous reactions just for the sake of environmental pollution okay calcium sulphate is available plenty on this planet what is calcium sulphate gypsum gypsum mines are there okay so that is available we do not have to produce that so this reaction is not famous for that particular one but it is famous because when SO2 coming from the chimneys from power plants for example so you can remove that SO2 capture it with the solid and then make it as CASO4 and the CASO4 can be used by someone or I think you have to regenerate and again use that calcium oxide and by regenerating what you get is you are not solving the problem you are again producing SO2 okay but the difference between that SO2 and this SO2 this is more concentrated what you are again regenerating so that SO2 can be sent to which industry sulphuric acid industry so that is the reason why it is very famous thing and many power plants and all that have been doing it and the reaction is not that simple I have told you once that calcium sulphate plus not calcium sulphate decomposition is easy calcium sulphate decomposition but calcium oxide reacting with SO2 in the presence of O2 is not that easy reaction again I am repeating because molar volume is increasing there the pores will block if more the faster the reaction then pore closure is faster so that means sorry if I have this is the particle if the reaction is very fast only this outer layer will be completed that will become CASO4 because it is large inside I mean the molar volume is large all the pores are blocked so SO2 cannot diffuse inside SO2 or O2 cannot diffuse inside so all this one is unreacted calcium oxide so that means you are now producing lot of solid junk environmental problems are wonderful problems okay so then how do you avoid that you have to what you have done is your air pollution problem you have made it as a converted into solid pollution problem right so that is why people you know in Germany I saw that in Lurghi they used to break this particle and then after breaking simplest way of breaking is to putting water spray water in that during the reaction calcium oxide reacting with what is highly exothermic reaction calcium hydroxide highly exothermic bubbling actually I have seen with my own hands in our villages when we are doing you know white washing once in a year you do for that pungal and all that at that time so we used to bring the raw calcium oxide okay calcium oxide and then pore water and you make as a simple as small bowl like this and then put that pore water bubbling it will be bubbling so that is why that reaction and the modelling also is very difficult the reason is that your idea is to predict when the pore is closed because behind that it is useless so that is why lot of work wonderful work is there on this I think one Bhatia from India only but all our people will work only in the U S not here so this Bhatia I think he was in U S and then he worked there wonderful models they have produced and process control people do you know there is a professor called Perlmutter in control and all that this Bhatia worked with that Perlmutter Perlmutter and Bhatia they have got these papers and at that time the specialization means Perlmutter is also specialized in process control and all that but still they used to work in common chemical engineering problems like this diffusion reaction problems distillation absorption all these problems so everyone is expert there but here now I think we are expert means we do not know anything else only that part I know absolutely no connection there so that is why when I think in the same building this Benj CEO someone has come from Germany this auditorium just below us I said this auditorium he was giving that lecture and then he was telling even in Benj company also this expertise has come it seems there is no connection that people say that no no no I am only expert in left back left wheel I do not know anything about all other three wheels that is all back side left wheel only he is expertise you do anything with other parts he knows only about that he was also telling that may be jokingly or I do not know that but that is what he was telling it is so serious about our expertise now so I think there are wonderful books also by pearl motor and all that in our library and process control and all that okay anyway good so our next job is using all these kinetic models how do we now design the reactor okay so what kind of reactors we can have like for example the reactor means we have reactor design in the form of either plug flow or mixture flow that is all whatever reactor you bring we can convert that into either plug flow or mixture flow ideal reactors non-ideality will come later that we have to see when non-ideality is taken into account ya so here we will write design of non-catalytic gas solid reactors the factors affecting design may be factors controlling design one we have reaction kinetics size distribution of particles and number three flow patterns of phases these three do you have information on all these three for the design that means do you know anything about all these parameters reaction kinetics do you know any information now at this point of time to you I am asking what is that you do not know stupid question ya so you know definitely you have learnt but I think I do not know everyone learnt or not that is why I am saying that okay reaction kinetics we have some information like what you can use either sinking core model or homogenous model or very complicated models also which we have not done okay good that information I say knowing information in any course at the end you should know some information it is not that you are I am asking you to remember the equations but at least you should know the moment you someone asks you okay can you design a non-catalytic reactor then like a real it has to go yes first kinetics then what are the models and then contacting what kind of contacting possible right how the particles move how the gas move so all this they should real move in the mind as if it is a real continuous real so once you know that information then getting the details okay kinetics which model is the best either sinking core or homogenous okay or in between so you know that information and details you can get from literature I am not asking you to remember all that but anyway definitely in this course you have to remember till exams are over you know those equations I am not allowing you to copy or I am not allowing you to bring the notes and all that so you have to remember that okay so that is why kinetics you know you have some information and flow patterns we have discussed already but still for continuity now I will discuss some more things okay you know already we have discussed and size distribution of the particles we have not discussed till now because we have only talked about single particles okay so now what we do is if I have this one is 1 centimeter particle or 500 5 mm particles and 1 mm particle all 3 together okay design is not that difficult when we have that yeah average you have to take okay so what is the conversion in the 1 centimeter particle conversion in 5 mm particle and conversion in 1 mm particle so you have to just average it out weighted average in fact 20 percent may be your 1 centimeter particles may be another 40 percent may be your 5 mm particles and 40 okay another 40 may be 1 mm particles so that is why that also is not difficult for you you can easily handle it okay good so if you are talking about contacting pattern now for non catalytic reactions generally what kind of reactors used do you have any names in your mind see non catalytic reactions can you say first of all what are non catalytic reactions iron ore for example okay that is one of the easy things to remember so which reactor is used blast furnace that is only one nothing else okay what is the difference between blast furnace and rotary kiln when they when they get the product at the end blast furnace you do not remember at all these ice cool question I say ice cool you should have studied blast furnace no so what is the product you get I mean liquid metal or so you know the why it is called pig iron I mean I was why it is called pig iron the relation between pig and high oxygen content carbon content okay even carbon content what is the relation how do you relate pig with carbon tell me someone was telling me I do not know whether it is 2 or not but when metallurgies told me when I asked this what is this pig iron not now I think may be 15 18 years back or so he was telling me that you know when liquid metal is moving after liquid metal comes out it moves in the channels so when it is moving that you know it is highly viscous so it forms this kind of boundary and then moves this is the channel you will have like this and then it is moving when it is moving it looks as if it seems very fat pig how it walks you are looking from the top this is you know beautiful very smooth surface for the pig very nicely I have seen pigs also so may be you would have not seen so beautifully walking and then you know that moves as if it is like this so that is why we call it as pig iron is it so very nice you know I do not know the story or may be 2 also okay so but you get the liquid directly there then you can directly put it in the form of rods or in the form of plates all kinds of things you can do it but whereas here in rotricine it is solid okay you know what is the name of that product called not clinker clinker is put you can also use that kind of thing and wash your body not soap sponge you heard of sponge iron no why it is called sponge iron it is not soft like sponge so what you get is sponge iron in rotricine not only in rotricine fluidizer beds can be used fluidizer beds also can be used so that is why we have the equipment for example may be it is a blast furnace here we have the gas and here we have solid this solid contains iron ore plus you know that slag what they put calcium calcium carbonator and also they put coal coke coke they put so all it is a solid-solid reaction there right I mean that coal will become that coke will become CO that CO will be reacting with that okay yeah and yeah this is how it looks then you may also have this is rotricine may be gas you can send like this solid like this solid gas okay this will be rotating this is too slant in fact you will not have this much slanting yeah nice okay this is the one other react also we can use this fluidizer beds this is gas these are the solids you also have what is called bubbles here and solid continuously solid continuously gas goes out okay and that solid is nothing but your iron ore okay but only in the blast furnace you will have solids iron ore plus coke and for making that slag I think you add calcium carbonator thing or calcium oxide you add there with that okay but here you do not have to add all those things it is simply Fe3 O4 plus CO2 or H2 this gas can be either H2 hydrogen or CO carbon monoxide I think we have written that you know you are looking at me as if you do not know that reaction at all Fe3 O4 plus CO or H2 okay giving as the product yeah so these things and this will tell me what kind of interacting patterns I have like for example quickly going through in blast furnace what can there are two phases now okay till the iron is iron becomes molten here only at the bottom here till here almost you will have only solids moving okay so and gas may be going this they blast the gas that is why I think this is called sides also bottom slides and all that okay yeah of course not through liquid iron but slightly above they put it and then it will go so how the solids are moving how the gas is moving solids and gas how means whether it is going as if it is plug flow or as if it is mixed flow and you know the height of blast furnaces normally very tall 5 storage 6 storage buildings blast furnace heights very big very large yeah how the solids move are they in plug flow or how gas moves is it in plug flow or mixed flow imagination I say that is what it is which one is mixed flow there are two gas or solid solid in mixed flow why even if you say plug flow I will ask why so that is why I think why is a very you have to give the answer sathya just imagination I have a large building and where I am slowly pouring that you know solids and then finally I get liquid somewhere down here but of course reaction may be going on till that point yeah how the solids are moving you can do all these experiment I say you can go your home and then take pulses like you know green grams or something and put in a funnel and open the funnel slowly how that moves plug flow very simple imagination unfortunately that imagination also we are not able to create in your mind I do not know it is our fault or you have totally insulated brain okay nothing can go in nothing can come out at least black holes are better black holes radiation comes out but here nothing can go perfect insulator is our mind if you if you do not want to listen nothing can go correct no really if someone something if you want to avoid 100 percent efficiency only this there is no other system which can be so efficient there okay so that is why it is simple imagination only it is not at all difficult I think you know I do not know why you are not able to tell okay gas gas plug flow so that is why when I have mixed flow I will tell you why you cannot use mixed flow the reason is definition of mixing itself okay a particle which is here any instant of time can also come here okay and that particle can also go here go here go here go here go here any time is it possible in a blast furnace to have that kind of flow never and by the by you know what is the size of the particles they use in a blast furnace gas 1 kilometer to any size yeah that is very good gas 4 inches 4 inches and that is why they have the pelletization plants okay so they cannot use simply very fine because during mining they get also lot of powdered ore or small particle ore and because it is a blast so much gas is going inside I mean blasted inside what will happen if you have fine dust or you know small particles all of them will come out they will be thrown out terminal velocities okay yeah that is where I think when I was handling this BTEC lab I was asking the question tell me one use of terminal velocity in industry for 5 years no one told of course I only told them later yeah because beautifully we derive equation stokes regime what should be the one other problem regime what should be the one terminal velocity and all that but I think definitely we do not know where to use okay but you have not only here in atmosphere terminal velocities how the dust falls on you okay it goes into the air and then when there is no sufficient wind to carry it out then slowly they attain the terminal velocity and fall on you that is how your cars your people like me this surface all that will be dust yeah so then you have to wipe it out so I think you know our cars you just leave or your motorbike or your cycle you clearly I mean clean it one day and then wait how many days you will get 1 micron thickness 2 micron thickness 4 micron thickness okay yeah so these are the examples but otherwise how do you relate what you teach I say you are not asking anyway but at least I have to tell you know and you are interested whether I give this question also in exam or not that is what only your interest okay good so what about this one gas is plug flow this one yeah gas is plug flow that is oh yeah gas is plug flow so I wanted to answer is mixed flow and wrote mixed flow there neural network also sometimes won't work I say okay many process control people use neural network but with wrong learning sometime okay good so that is the one and what about this one solids are continuously fed here this moves slowly don't think that it goes like your other one what is that washing machine is very high but the other one where you sit and then go merry go around merry go around merry go around also if you go to centrifug velocity you will go horizontal so if you make any mistake you will land somewhere okay so it is very easy have you enjoyed that good all of us would have done that recently not when you are kid no that is why I think as a kid only you enjoy many things I say after writing that entrance examination whether it is JEE or whether it is Andhra entrance what is that m set k set r set s set all you know every state has one set after that we become I think very serious without learning anything because I think particularly engineering I think medicine education is thousand times better than engineering education a person who has studied medicine comes out he will know how to treat at least but we don't know how to even lift a pump how to carry a pipeline how to tighten a bolt if you go to doctor if you go to doctor first he will ask everything what are you feeling according to that he will take medicine he is not going to check on whatever you have oh my god too simplification I say so I will tell a headache but then if he gives something you know diary or tablet to me so then you should understand no you should relate he says that whatever you say and then he listens and then writes the thing to write that medicine you should know what is the disease that is standard you know basic medicine always yeah because you know this is much more difficult veterinary doctors are much more difficult because they cannot ask dog where do you feel so what you have taken today morning dog owner but you know how it feels how dog owner tells feeding he can tell what you fed to that fellow you know he knows but how it is feeling it is a problem so that is why I think somehow we are not able to you know do after our degree is over we are not competent to do anything I am not degrading anyone but that is the kind of engineering education what we have that is why one proposal is that finishing school you take the degree but afterwards one year you work somewhere very seriously in a workshop learn all this and then only your degree will be given some countries do that that promotional exam at the end anyway I think I will quickly tell here this one solid is in plug flow gas is in mixed flow sorry in plug flow both are in plug flow here also okay here gas is mixed flow but gas solid is in mixed flow gas we do not know how it flows but simplest assumption is it can be in plug flow so then definitely you know why it is mixed flow because in fluidized bed all these particles are held up or floating in gas and then these bubbles are there where they go up and then break when they are breaking solids can jump up and then again fall so when they are falling they will go anywhere and that is how you will have almost perfect mixing RTD also you can do that and then find out it is almost equivalent to plug flow okay so that means a particle in the fluidized bed can move anywhere anytime that is the definition of perfect mixing and that is true in a fluidized bed you see now if I am concentrating on solids assuming that gas is not important for us then I should use here plug flow for solids conversion or solids you know for solids and here also plug flow for the mixed flow so in the next class we will derive equations for assuming solids in plug flow what are the kind of equations we get for the design design means finding out what is the volume of the reactor okay that is what we will do in the next class okay thank you