 Okay, I think we will start now in the last class we have talked about minimum fluidization velocity that is one parameter now we talk about terminal velocities because that also we should know that is parameter number 5 normally terminal velocity of single particles only we talk here so if you take one particle you have some kind of 3D effect I just want to put this yeah this particle is just falling through a fluid right is a terminal velocity of single particle where you take may be very big tube and then fluid is flowing through that and you drop the particle so what are the forces that are acting on this so weight will be acting downwards which is mg and because it is coming down drag will be acting in the opposite direction that is fD fD and you also have another force buoyancy fB so when all these 3 W and these 2 are balanced then you will get the terminal velocity where it will initially when you put you have acceleration and all that then it reaches terminal velocity from then onwards it constantly coming down okay yeah so we can derive this equation if we know all these terms and the balance is fD drag force plus fB buoyancy should give you W mg okay so that is the one yeah and the drag force is nothing but you have of rho ut square multiplied by the drag coefficient and the projected area okay so all 3 so if I have that means drag force is directly proportional to the area okay more the area more the drag force okay that is very simple one and then of course the kinetic energy so if I write that you will have CD of rho ut square rho ut square into the projected area projected area of this is a circular area because it is a spherical particle so I can write this one as pi dp square 4 sorry yeah 4 plus buoyancy is the fluid displaced so that volume is dp cube 6 into rho into rho is becoming low z rho f into g right yeah then this side we have mass into acceleration gravity this again dp cube 6 that is the volume rho p is the particle and then g is the yeah that gravitational constant yeah okay so this is the one so if I rearrange this for ut ut will be ut is yeah 4 third dp rho p rho f into g by cd into rho okay so this is equation number 3 what happened something wrong okay yeah so if I know cd then I can calculate ut for any condition okay so again you have stokes law regime and all that you know what is cd for stokes law regime all that will be there you can derive but I am going to give one shot all the birds died okay so that is why cd given by Levenspiel and some other person called Haider they gave cd for all regimes together okay so idea is I have to calculate ut dp I know rho p I know rho f I know because I am using you know some fluid which I know particle size I know particle density I know so all that I know and g also you know and only cd I do not know so for cd if you get a correlation this correlation by that I will give you later cd equal to 24 by rep where rep is yeah particle Reynolds number at terminal velocity okay that u is ut but rep we are writing to say that it is particle Reynolds number okay yeah this is 1 plus 8.17 1 6 e power minus purely empirical equation so that is why you will have all funny powers phi s yeah this whole thing multiplied by rep to the power of 0.0694 in the power only this one 0.5565 phi s that is one term okay then I have here I think I write here plus this continuation plus I have 73.69 e power minus 5.0748 phi s into rep whole thing divided by rep plus 5.378 e power x point 2122 phi s this is the equation this is equation number 4 okay I do not know how do you remember this you have to remember right right right thank you thank you thank you this entire thing this thing too okay yeah that is right thank you you know that correlation or just like that you guessed 24 by okay so unless it is multiplied by that yeah true this is the one and I do not know how we are going to remember in the examination so I think this is the correlation which we have to use if I give a problem to calculate u t you have to use this correlation okay so this is given by this is given by Haider and Levenspiel the same man C R E man this is power technology that is the journal name and you have volume 58 page number 63 1989 were you born at that time no born on most of you okay good yeah then it happened only in your jamana so I think this is the correlation if you see the literature there will be hundreds of u t correlations but this is very well accepted one because so much effort has gone into it is only to take all the data that is available till now till then published they have put into one correlation okay yeah good so this is the equation and as usual for complete spherical particles you can reduce this equation to simple equation where phi s equal to 1 so this becomes a constant and also this also becomes a constant so this becomes a constant so it is this also becomes a constant it is a little bit simpler okay good so I think how many of you have Levenspiel book with you third edition yeah wake him up yeah only morning I think you know how are you getting sleep it is really surprising early morning you just got a unless of course your early morning is 6 o clock you know 6 pm and this is the night time for you okay I think you came from some other planet already in the US okay so that is why practicing US timings sleep in the classroom and be moving in the night in the hostels that is all US yeah I was asking you something what is that Levenspiel book I mean you know you have the Levenspiel book with you no no why are you are necessarily wasting time for giving or wasting money okay yeah how many you said how many just lift again frankly I am not going to check your room do not really deceive yourself that is most important okay you also have Prabhu he has always something different answer I think my god must be he is from I think Pandora that planet Avatar always very good yeah you book you have how did he get you book so anyone can tell Levenspiel okay most of your books are I think misused because hot copy is easy to read and e copy is easy to store okay you cannot even open unless you want to cut and paste something if I give the assignment cut and paste and you can submit the assignment no that kind of thing yeah so in fact this same equation and also EMF yesterday what we have discussed there is a graph there in the third edition I think all of you should have third edition you belong to third 3G generation 3G section okay so that is why third edition you will have I have first edition second edition 2 because I think I have seen 1G 2G now they will come to 3G right so in the third edition CRE Levenspiel in third edition what you have you know there is a figure 25 chapter 20 figure number 5 this figure in fact gives one dimension as a number that is equivalent to accommodation number versus UMF UT and there are many other things also in that graph okay I think that graph also I have brought here to show because you would have never seen this this graph okay yeah if you know the X axis X axis DP star this DP DP star is he has used some other dimensionless numbers so that will be accommodation number accommodation number all the information you know GDP cubed rho F rho S minus rho F by mu square so rho F and mu are the fluid properties rho P DP are the properties of yeah and G is the property of this planet okay so all the things you know so you have that information you can easily calculate and then read what is UMF or what is UT okay instead of solving but anyway this is not allowed in the examination you have to use this equation to calculate if UT is asked and who knows tomorrow there may be surprise test asking this okay yeah I know how to pain you and you also know how to pain me because I think you come here and sleep that pains me okay and you do not do any work that pains me and also immediately before even class started SAR review class SAR okay and no one tells the SAR Krishna has class sir okay so all these things you know you also pain me in equal direction or reversible reactions okay good anyway so this is the one which very good figure where he has nicely beautifully put that and he has also given in this figure what are the possible ranges of operation what we have done you know normal fluidization fast fluidization pneumatic conveying all that regimes are given wonderful graph okay but I think you know assumption is that you are interested that is why I am telling I think you think that I am a mad man right so generally this fellow talks something I think you know which we come here and happily sleep that is enough for me okay so that is the kind of attitude if you have what you learn what anyone can learn no one can learn anything so this is the problem yesterday we had one and a fourth two hours discussion about J E okay and none other than the D S T chief I think you know next next to minister he is in the scientific thing Dr Ramaswamy he came and spent so much time and I was thinking that why the hell in our country we should have I think I believe you know Mau very strongly you know who is Mau you do not know Shokumar Mau who is Mau chain is something what is the chain is animal or chain is horse or chain is dog or what chain is man chain is student chain is food nood is you know that we know very well yeah Mau once he came to the power he found that many people are not concentrated in academic institutions so then he closed all the academic institutions and then said that you know you have to go and produce wheat that is all send two fields okay so I mean some people say that no no no the entire academic intellectuality gone and all that but I feel that is more practical because if someone is not interested why should we spend time on that okay so I mean yesterday so much discussion about this J E how to improve how to increase the interest in the students where is the interest is once the J E is passed or once any entrance examination is passed you think that life is settled okay any entrance examination it may be T set K set T set F set M set many sets you know everything there is set only okay once that examination is over then life is settled because you do not have to do anything and what do you do in the school all the time there is no school for you anyway it is only coaching centres what you have seen okay so I think that beautiful life of school gone now they want he wants to bring back that school education to some extent that is why I think board they want to have some 40 percent marks okay that school marks in fact we had that excellent time we had really excellent life when we were students no one used to tell that you read or do not read that is all very happy while going also I mean I have to walk nearly 7 kilometres every day to go to school another 7 kilometres to come back so on the way all happy walking happy running happy playing and all that okay and then you come here and then there is no power anyway by the time you come it will be 6 o clock or so eat food and then eat and then sleep most of the time okay but far as I know one year examinations and all that not for every day 10 tests like coaching centre okay or 10 or 24 tests because every hour a test in coaching centre okay every hour a test test test finally I think you do not know what to write at the end okay so everything tick tick tick technology technology has become technology totally beautifully converted technology has been technology now so that is why in Hyderabad I do not know whether I told you some I think I told you last semester also this I think maybe I know all these people may be knowing this or at least they will come to know about this in Hyderabad you know Hyderabad 50% of the Hyderabad in the U S yeah I think every family every hut every building every 5 story buildings all these people I think in any place you take there is one person who has gone to U S from Hyderabad so I think that person stayed there for 5 years or so he came back here to marry okay because I think after finishing B Tech or something he went there after coming back and then he saw four girls and he does not know how to choose right so then father knows his you know strength and weakness or anything so then father what he said is okay first girl A second girl B third girl C fourth girl D then he knows to tick yeah fourth D till then he does not know how to tick how to choose so that is how we have converted all our younger generation to technology to technology that is what I have been telling technology okay so like that I think you know unless that ABCD is there you cannot do anything you go to your mess and if it is you know Idli Dosa and upma and all that is you do not know what to take if that fellow writes A B C D tick and then take that is the kind of life we have here now on this planet particularly in India okay so then what is the interest for you absolutely there is no interest no I mean like a mad fellow I will be talking here if we enthusiastically thinking that oh my god entire thing is fluidization the whole universe again is you know only fluidization so that kind of thing I will say but you come here and then happily sleep okay and then otherwise you go to your own matrix searching for new and searching for other what is our name you have seen no Trinity yeah good he woke up now he is in the matrix so he knows Trinity he is inside the matrix Trinity or an old person like me what is his name Marpheus Marpheus and I think the names also very good names you know switch switch is one person's name you know switch connection so like that is very wonderful movie yeah okay good so this is about terminal velocity the next point is in fact you know terminal velocity also there is a lot of information and when we tell about this particular thing completely we are in a ideal world where is one particle when do you use one particle in chemical engineering you never use except on the board okay even if you go to lab also I think you will have number of particles but in reality you will have again some other thing which is called a transportation velocity and all that I think that will come later when you really take a fluidized bed course okay but I think here it is only an indication for us that what is the maximum velocity that may be possible for fluidization that is why we need this parameter okay the next one is bed height right or you do not know static bed height yeah what is the static bed height we use what is the number 6 static bed height okay see every time I will tell what I have been telling all the time to you is only to make you again temporarily come back to the class that is why that is why I tell that you know you do not have interest and all that so that at least okay may at least this fellow is telling at least 10 minutes to be concentrate so that is the reason otherwise you know you may think that you know this fellow is pessimistic always talks like that no whenever it is trying to go away from the track slightly applying some force to bring it back to the track that is why I do not know any other force except telling this if you have any other information tell me I use that technique okay how to bring you to the class so otherwise I do not know I think that is why every time I will point out the moment I think that you are not concentrating okay so that is the reason probably any comments you will give wonderful comment no comment that itself is wonderful okay so usually HP by D static bed height okay is normally 1 2 2 best fluidization or good fluidization we do not say best good fluidization okay best fluidization means all the particles should be very very spherical and all the particles should be exactly same size all this that we do not get normally so that is why okay this is good fluidization what do you mean by good fluidization if someone asks you what do you mean by good fluidization what do you say Kavya when do you say you have good fluidization yeah what is the meaning of that you are only telling the other opposite quality you are telling so that you know if everyone is lousy I am very good okay that kind of thing okay not that I mean really I mean yeah that means good contact between not mixing yeah mixing also you have without good contact also because you know when you have bubbles and all that so uniform fluidization and also good contact between solids and gas that means each and every particle must have very good contact with the fluid okay either gas or liquid that is what what do you mean by good fluidization okay but when you have HP by D less than 1 you have what is called shallow beds so in the shallow beds generally you will not have good contact because there is no time for contacting because you take only 10 particles height okay if you have 1 mm particles 1 mm is very large for fluidization but easy visualization that is why I am telling 1 mm so 10 mm bed height you put even though diameter is 1 meter those are shallow beds 1 meter diameter also if you have only 10 particle height or 20 particles height then that is very very shallow bed okay under some circumstances shallow beds are preferred if you avoid bubbling because there is no time for gas to bubble bubble to grow okay so that is why shallow beds are used sometime particularly for drying it is also can be used beautifully for drying okay and they call this fluidized bed plug flow dryers you know fluidized bed we know that it is a mixed flow how can you have plug flow not in gases solids are how can you make this mixed flow as plug flow it is shallow but I think how can it be even then they are bubbling they are mixing you increase the length okay and then put the solids here this is just a plate with the perforations may be with a slight angle for flow okay even you do not need a slight angle but better to have if you want better flow otherwise even if you put horizontally also you are feeding here all the time and it may be 2 meters length right straight channel and bottom you have the perforated plate and uniformly distribute throughout the channel the hot air and the wet solids are put in one corner so those particles will slowly dry there and then start moving so till then of course there may not be any flow there once it starts moving then from there continuously it comes out and then you can collect the solids there and the lengthy is designed for how much drying you require may be you know end moisture may be 1 percent 2 percent 5 percent 10 percent depending on your requirement but drawback here is that you cannot use 50 percent 60 percent moisture it is a tertiary treatment for tertiary drying technique that means first you may if it is completely paced what you do you cannot use any column except tray tray tray tray dryers okay then once it dried for some time then you will have some moisture where the particles are not sticking but a little bit flowable so at that point of time you switch over to this and if that is not sufficient then you use some other drying technique there are so many drying techniques okay so then the final one when you want have only 1 percent and all that fluidized beds are excellent particularly plug flow dryers what is the advantage of plug flow dryers because each and every particle again will have exactly same moisture content in fact you use this nylon and all that shirts yeah for polymer drying particularly when they want to make this rayon and all that you know for making this cloth they first make the polymer granules and they have to be they have to be very accurately dried that means each and every particle should have exactly same moisture content it seems if this moisture content is slightly different in some particles okay in some other particles whether low or high then the thread will not come properly it seems okay so that will not come properly so that is the reason why they use this plug flow dryers for polymer drying when you want to use that one for textiles so many advantages okay good so this is the one that is all what we yeah I think another one is of course if HP by D greater than 5 what do you get that means you have not seen at all you just look what I have told to process back one narrow column and then slightly more thing it is slugging that means the entire bed is occupying yeah the bubbles occupying the entire cross-section of the bed slugging but that means if the initial static bed height itself if you have 5 and then of course generally you know when you say this condition slugging means you know narrow construction narrow cross-section then you get this slugging okay I mean what I said was true I think all of you are Gajini only yeah I don't know when you remember maybe I think that Gajini at least below after 15 minutes he remembers something but here I think there is no remembrance at all maybe just examination before before the examination you may remember okay good so that is static bed height and the last one is 7 yeah below you have eaten mass transfer correlations yeah eaten mass transfer correlations all these things we require before we start the reactor models so that is why yeah here you have again correlation so there are there we cannot discuss much unless how do you develop these correlations when you go we can discuss but we don't have that much time but simply we accept these things because they are already available and those who are interested anyway they can definitely go and then read all this information how do you develop these JD equal to JH equal to to save the students I think they have given nice correlation for both one okay this is DPG mu into 1 minus epsilon whole to the power of 0 point minus 0.44 that is 1 this is also equal to 5.7 same number DPG mu by 1 minus epsilon this is to the power of minus 0.78 yeah and the condition is this is less than 5000 and this is DPG by mu into 1 minus epsilon less than 30 yeah so what is that I have equation number 4 I think here we do not have to give this equation number this is 6 this is 7 okay Rani sir do you remember what is that number called DPG by mu is a dimensionless Reynolds question Reynolds no answer why is that the set number what are the units of that what is DP what is G what are the units of mass flow rate KG per second yeah you put KG per second and then try to get dimensionless mass flux okay mass flux okay we call also mass velocity sometimes but it is mass flux so KG meter square per second this is one of another some question which I ask in PHD interviews and all that give two or three different forms of Reynolds number it is not always U rho DP by U rho DP by mu this is also another one what is the other form that is another DP that is Bottle but you know what you have DP DP by mu DU by mu okay so where mu is just know that there are different forms okay yeah good so this is the correlation what we have where of course here you see voidage is the one which has been used right these are empirical correlations very very old correlations but if you see the literature again you will have lots of correlations available for yeah and of course JD definition do you remember KG by mu 2 by 3 very good excellent okay JD equal to K by U or KG by U Schmidt number to the power of 2 by 3 okay good can you also tell me in terms of another dimensionless numbers JD not K by U you also have actually that same thing K K by U or KG by U Schmidt number to the power of 2 by 3 can be also written in terms of Sherwood number Sherwood number Reynolds number and Schmidt number do that exercise you will know that I do not want to write there Sherwood number Reynolds number and Schmidt number again of course that is the original definition JD equal to in terms of dimensionless number all dimensionless numbers okay the problem there is why you cannot have KG by U KG will have some other units you may have some other units but when you make that as a dimensionless number group of dimensionless numbers then you do not have to really worry so that is why originally old people have done that okay good so that is the one good so now all the parameters are over there are many correlations available okay so but still these are the some you know again here you are very nice students know you never ask questions so I have to ask questions and I have to also answer okay when I say this JD equal to JH mass transfer or E-transfer you never told me where this mass transfer going sir from which place to which place so this transfer should be from one to the other know which one is transferring what we have here gas phase or if you have fluid phase and solid phase this is mainly for gas solid fluidization that you have to know done somewhere because for liquid solid applications are so less most of the information is given in the literature only for gas solid fluidization okay yeah so that is why this one if I have particles from particles to if hot particles are there you want to cool them then you send cold air so then some of the heat that is that is there in the particles is taken by the gas gas will go okay so similarly if you want to heat the solids then you have to use drying you know like not drying sorry heating hot air you take right and then send fluidized cold particles they will get heated up so those particles may be used somewhere else in the process okay so these are the things what we have and of course as I told you this fluidizer beds can also be used as combustors coal combustors where they use no power generation power generation they use coal combustors fluidizer bed is used as as the combustor where coal is fluidized and burnt if you go for beyond 650 degrees or 700 degree centigrade it catches fire if you have sufficient oxygen so then it burns and you have to extract that heat to extract that heat you put inside cooling coils with the water so that water will become steam then steam will go through steam turbines steam turbine will be attached to generator and generator will give us AC DC whatever these lights and all that okay so there the heat transfer is from solids to yeah because coal particles are burning and they are at high temperature and you have the cold liquid and water going inside so the heat transfer is from solids to pipes yeah the tubes where you have water so finally it has to cross tubes and then reach water and water will get steam water will become steam okay so those are the things so now we have to go for reactor models that is 8 8 reactor models that means fluidizer bed reactor models okay I think I will tell you the story I think you know quickly so that next class I think you will have because if I draw that figure it may take some time okay so that is why you do not have that time yeah the story here is that in the reactor models what they did was they have taken the conversion available in the literature for first order reactions okay and they have even taken the same first order reaction one particular reaction and then collected data from someone you know publishing from India someone may be from Germany someone from Japan or UK US all the data they have plotted same reaction same catalyst same temperature so when they plotted there in that graph the the points are throughout the graph like our cricket field okay throughout the graph you have the points that means there is no particular trend there is a part there is no particular trend for the behaviour of conversion what they plotted work was conversion versus for first order reaction what is the natural number that comes as x axis for batch reactor normally you use time what is the number for the first order K tau where K is the reaction rate constant and tau is space time okay yeah so K tau versus X when they plotted the entire graph as different you know the all the particles and the same you know for the same reaction same catalyst for the same conditions then they also drawn theoretically what is plug flow line on that theoretically what is mixture flow line on that because we know only first two reactors ideal reactors what we have right so when they theoretically they could draw those lines these are experimental points so they have found that the conversion is even much less than mixture flow reactor now we know that in the extremes one is infinite mixing another one is zero mixing zero mixing for n greater than zero reaction will give me always higher conversion for a given value okay and whereas mixture flow is the worst it will give the least conversion for a given value least conversion for a given value so now I think fluidity is behaving much worse than that much worse than worst reactor so then they thought that what is really happening because you cannot know and expected that you know this much conversion low conversions you will get in a fluidized bed because what is our assumption our assumption is that fluidized bed is equivalent to mixed flow contacting wise so then what is natural tendency for anyone to try whenever you want to model you have done the experimental work what you how you start your data analysis is that whatever you know first the ideal reactors first that you check if you found out if you if you find what is the conversion for various dump color numbers you just try to put that in the form of either mixed flow reactor or plug flow reactor because those are the ideal reactors if they are not properly able to predict this conversion experimental conversion then what you do you will go for what are called one parameter models what are one parameter models axial dispersion model tank series model one more so many times I have brought this last time in the I think here also once I think probably I would have written recycle model recycle also recycle infinity what reactor mixed flow recycle 0 plug flow reactor so all the extremes are covered with axial dispersion and also n number of tanks you know when n equal to infinity you will have plug flow n equal to 1 you have mixed flow dispersion number equal to 0 plug flow dispersion number equal to infinity you have mixed flow that means anywhere in between mixing also you can now try to imagine this is perfect mixing this is zero mixing some intermediate mixing can be imagined with this one parameter model with r recycle with dispersion number and with tanks in series okay they tried that when they tried that also did not work then what is the next logical one compartment models okay it is not just axial dispersion that is coming now let me imagine that I have axial dispersion plus plus channeling dead space all these so even when they put this compartment models assuming more parameters like dead space for solids or dead space for gas channeling for gas all that combinations when these are all called RTD models okay residence time distribution models where we have studied in the I think even you would have definitely studied you have done RTD you know residence time distribution yeah definitely in that Preeti would have told you Preeti only taught you right yeah definitely she would have told this because she is also very much interested in CRE so all compartment models you try to use and those compartment models also did not work that means all these models are not able to predict what is the conversion that is coming out and particularly when you go for 1 inch diameter then you go to 2 inch diameter okay totally different conversions right or otherwise you change the particle size totally different conversions same condition same but instead of using 10 micron particles you may use 100 micron particles then again changes okay so even distributor plate you change the distributor plate perforated plate or instead of perforated plate you may have now porous plate you change that again conversion changes this has become a big mystery what you really do to understand what is going on in the fluidized bed okay so I think that we will discuss in the next class what is really going on in the fluidized bed okay suspense like our cereals in the correct time you know but you never bother anyway whether it suspense or no suspense it is same for you okay but you know what happens in next time I mean in the next class only I will be excited but you will not be you will be sitting there I want some dead space here so that is there okay yeah again you know that is very interesting how they have done it I think really wonderful models they have developed and how much thinking has gone into that you will know when I explain that how they really developed the fluidized bed models okay good you have to run okay thank you